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《Cottage Garden》(栽花乐)

3人玩1次、2人玩1次。



游戏大纲



《Cottage Garden》是 Uwe Rosenberg (《农家乐》(Agricola)、《港都情浓》(Le Havre))的小品类作品,和《Patchwork》、《A Feast for Odin》一样,有像 Tetris 式的拼图机制。





每一个玩家有两个 5x5 格的小图板。这些是花圃。玩家要做的事是把这些花圃填满,每一次填满能得分。花圃上有一些花盆和透明盖子。把花圃填满时,要尽量让它们露出来,因为它们是用来得分的。用来填花圃的,就当然是花丛和各种花园饰品。它们的形状大小不一。

左边 L-形的是玩家的计分图板,上面共有六个计分棋子。 橙色的是花盆得分时用的,蓝色的则是花盖得分时用的。计分表上可看见花盆通常是每一个一分,而花盖则是每一个两分。不过如果到了14、15分,可以一步跳到20分。每一次有花圃填满,就做得分。玩家只能选其中一个橙色棋子和一个蓝色棋子来得分。得分做完了,就换上一个新的空花圃。





猫儿是用来帮助玩家填满花圃的。它们基本上是 1x1 的板块,是任何时间都可以用的。不过它们本身没有分数值。





这是主图板。游戏设置时会随机填满花丛。玩家从这里拿花丛来填各自的花圃。左上角的骰子是计时器,同时也限制玩家可以从主图板拿的花丛。每一轮玩家拿花丛时必须从骰子位置的那一行或那一列拿。花丛越拿越少,选择也会越来越少。当一行里只剩下一个花丛,玩家在拿花丛之前必须先把那一行补满。玩家也可以选择提早补满,不过得付一只猫。玩家拿了花丛后,在自己轮次结束前必须让骰子走一步。这样轮到下一个玩家的时候,就要从下一行选花丛了。骰子每绕图板一圈,就得把骰子上的数字加一。当到达六的时候,就进入最后阶段。这时候花丛太少的花圃得立刻放弃,而其他的花圃则必须要完成,游戏才结束。最后阶段里每一轮玩家都得扣分,所以是要尽快完成花圃的,要不然花圃赚来的分数可能会比被罚的分数少,会吃亏。





右边那图板左上角的花丛板块,有画了一个花盆。这花盆也是能用来得分的。





我在看规则书的时候,觉得这阳伞是很多余的。当玩家要把图板上的一个花丛暂时借来在自己的花圃上比划,这阳伞就要放在那花丛原有的位置,方便玩家还花丛的时候知道要放回什么位置。我的第一个反应是:多此一举。谁知道自己玩了后,发现借花丛的时候确实是很容易忘记是从哪里拿的。原来是我自以为是。





还没用到的花丛要在图板以外清楚地排成一条线,让玩家知道下一个补上的花丛会是哪一个。这手推车用来标明下一个要上场的花丛。





这是填满的花圃,上面有两个圆形的花盆板块。玩家的轮次内可以选择不拿主图板的花丛,而拿这一些花盆板块。花盆有分数值,咋一看似乎是比拿花丛强。不过花丛通常是比较大片的,让玩家比较快填满花圃。所以拿花盆通常是为了填那些很难填的单一空格。照片里这花圃会让其中一个橙色棋子走六步,一个蓝色棋子走两步。





主图板是双面的,因为游戏会按照玩家人数有所调整。





计分图板转弯处的红线是有意思的。每当有棋子越过红线,玩家就能拿一只猫。玩家在选择走哪一个棋子的时候要考虑这一点。这是质与量的衡量。每一次做得分专一地走同一个棋子,让它能达到14和20分之间的那一跳,是很划算的。而且最早达到20分的玩家有奖励分。这是质。但是量方面也有两种推动力。第一个就是送猫。如果让同色棋子平均地走,每一个都跨过红线,就自然能多一些猫。另外,每当同色的第三个棋子离开起点,能立刻拿一个花盆。猫和花盆都有助于填满花圃,继而得分。



亲身体验





孩子们陪我玩。



解说《Cottage Garden》规则给两个孩子听的时候,似乎有点复杂,因为要一一解释几种状况发生时要怎么处理。不过实际玩起来是很简单的,大多数的时候,每一轮就不过是从主图板拿一个花丛放到自己的其中一个花圃里。这是个可以轻松玩的游戏。



主图板上的花丛要怎样选,是有一些小技巧的。玩家是可以看到有哪一些花丛适用,也可以计算到自己有没有机会拿到。当然还要留意有没有别的对手会想要自己要的花丛。如果没有别人要,就可以先拖一下,等下一次有机会才拿。另外也要考虑到还未上场的花丛。有的时候付一只猫让自己要的花丛提早上场是值得的。



游戏节奏是另一层考量。玩家要为最后阶段作准备。一旦进入最后阶段,是每一轮要扣分的。所以自己面前的两个花圃,那时候最好是接近完成,要不然就尽量空置着,以便可以立即放弃。



我这样形容,好像游戏是很有策略感觉的游戏,但其实这是轻量级游戏、悠闲游戏。不需要想太多。也许是美术设计和题材给我这样的悠哉感觉。我被它们催眠了。





这是两人游戏进行中。





晨睿建议花盆放在手推车里。这是不错的点子!



感觉/想法



《Cottage Garden》适合当家庭游戏,也适合和休闲玩家玩。里面有一点策略,但整体感觉是轻松的,没有很大的冲突性。它是有空间性的游戏,大家都在设法好好把花圃填满。这空间性是它最大的乐趣和特点。《Patchwork》里玩家是几乎不可能把自己的图板填满的,但《Cottage Garden》里是必须填满,而且有各种元素帮助玩家将它填满。《Cottage Garden》看起来应该是比《Patchwork》复杂的游戏,因为配件比较多、规则比较多。不过有些部分我反而觉得《Patchwork》是比较有深度的,因为《Patchwork》一面玩一面要考量经济平衡。玩家选布片时要衡量它的生产能力,要为未来打算,不是单纯的要尽量填满图板。


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UK CC:
********
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CA CC:
********
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AUS CC:
********
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EUROPE CC:
********
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Germany = $30 ___ (fullz info = $50)
Italy = $30 ___ (fullz info = $50)
Sweden = $30 ___ (fullz info = $50)
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*** All our cc are checked before sending.
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Format Card (Random)
====================

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4117733939985949|03/2016|790|Mike|Philippe|3815 AVENUE I 3RD FL|BROOKLYN|NY|11210|USA|347-394-7074|supermike718@gmail.com |

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6011008260905564|03|2020|673|Stacy|Liu|2820 SW 33rd Ct.|Miami|33133|UNITED STATES|9167042216|staacy.liu@gmail.com

373965748412007|07|2016|7922|sandy beechinor|N 36715 sherman|DEER PARK|99006|WA|USA|5092767387|scoitaartworks@aol.com

**** DEMO CC UK:
4921816704367231|04|2017|653|SOHAIL|AHMED|137 Springfield Road|Moseley|BIRMINGHAM|B13 9ND|UNITED KINGDOM|441217778326|sohail4001@yahoo.co.uk

**** DEMO CC CA:
5457499001853366|05|2018|302|Cassandra Tourangeau|1417 Flower Station Road|Lanark|Ontario|K0G1K0|Canada|6138126338|

**** DEMO CC AUS:
5430489100598014|10|2014|815|Sharyn Brew|6 Inglewood Close Croydon|Croydon|Victoria|3136|Australia|0417805265

**** DEMO CC MALAYSIA:
5472310269029105|04/2021|899 Ee Hong Lau No 2314|Chieng Son Garden,|Riam Road MIRI|state 98000|Malaysia

***** DEMO CC SPAIN:
4966267615954012|02/18|683|SALVADOR GALISTEO MUNOZ / SALVADOR GALISTEO MUNOZ|BULEVAR ALTO TAJO 4 4 B|GUADALAJARA|N/A|19005|Spain|

***** DEMO CC FRANCE
4561079000681111|04|20|400|Benjamin|chayette|9 rue benjamin godard |75116|paris |0235240732|FRANCE|

***** DEMO CC ITALY
4565420079693239|11/2017|159|SILVIA CARLETTO|VIA SIGNORI, 2|S. CRISTINA DI QUINTO|TV|31055|0422471003|elpampurio@libero.it

***** DEMO CC DENMARK
4571717006927149|0117|057||Søren Damsgaard|Andersen|Tjørnevej 13|Salten|Them|Midtjylland|Denmark|8653|sda@mail.d k

***** DEMO CC BRAZIL
5256640301990043|02|2018|415|Ivan Carlos|Buzzi|Rua Campo Alegre,454|Ilha da Figueira|Jaragua do Sul|SC|89258-100|ivanca@yahoo.com.br

***** DEMO CC NORWAY
4110021010519390|06|19|719|MORTEN NILSEN|Morten|Nilsen|Steinmoguto 23||Nesbyen|3540|NORWAY|morach@chipmycar.no

***** DEMO CC NETHERLAND
5209530059564397|06|2016|437|P.J.M. Vervoort-van Doorn|Eerschotsestraat 40 Sint-Oedenrode|State|5491|AC|Netherlands

***** DEMO CC CHINA
4063651030374256|10|2018|254|MAGGIE|HUANG||802 BANK ST.|Ottawa|K1S3V8|+1 6135670382|CHINA|

***** DEMO CC ARGENTINA
4546400019311815|02|19|461|Facundo Badillo|Facundo|Badillo|Blanco Encalada 5678|Buenos Aires||1440|Argentina

***** DEMO CC JAPAN
4541147834772011|12/2016|400|TAKASHI KOSUGE Takashi  Kosuge|1-1 Oho||Tsukuba|3050801|Japan

***** DEMO CC PHILIPPINES:
5194630205920498|03|2026|776|LORNA|MIRANDA|APOLLOLAAN 7|AMSTERDAM|1077 AA|+31 684476978|PHILIPPINES|

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4999132341881247|11/2016|052|Michael Hobbs|1116 Leeston Rd,Irwell Village,RD3|Leeston,Arizona,7632 |New Zealand

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4319454004186406|04|2020|420|michelle|plunkett|132 forest hills|Rathcoole| 0851268766|IRELAND|shellybellyjelly@hotmail.com|

***** DEMO CC SAUDI ARABIA
4339870060055886|02|2019|755|Seba|A|421 W Broadway, long beach|Los angeles|90802|+1 9492954885|SAUDI ARABIA

***** DEMO CC INDIA:
5546370226887914|02|2017|918|Bhamini|Pattabhiraman||Old 43/2, New 52/2, 11th Avenue,|Chennai|600083|+91 9500032305|INDIA

***** DEMO CC MEXICO:
4179670383241608|03|2018|679|Aida Monica|Valdez||Paseo de los Estudiantes 2035 Col. Cumbres 2o Sector|Monterrey, Nuevo Leon|Nuevo Leon|64640|+52 8110804973|Mexico|

***** DEMO CC BELGIUM:
4454719292556113|10/2017| 880 |Christine Rillaerts | leuvensebaan 51| Ottenburg Antwerpen| 3040 | BELGIUM |

***** DEMO KOREA:
5462521402227917|09|2018|170|KOREA, REPUBLIC OF|SEON YEONG|BAK|397 E 54TH ST KT9465|Elmwood Park|NJ|07407|201-568-3865|SINKLREAR@GMAIL.COM|211.205.6.157|

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Sample Dumps Track 1/2 with & without Batteries
==================================
Track1: B5466388405414686^Mohammed/FARRIED^2004201190100000000000875000000
Track2: 5466388405414686=20042011901087500000
Country Code : US
State : VA
Type : MASTERCARD
Debit/Credit: credit
Subtype : WORLD CARD
==================================
Track1: B4782009999506014^KOSNIEWSKI/PAMELA M^16111010000000208000000
Track2: 4782009999506014=16111010000020800000
(101) - VISA CLASSIC - JPMorgan Chase Bank NA
Track1: B4784559000586171^andrew/mayerbach^150310100000334330000370000
Track2: 4784559000586171=15031010003343300003700
ATM Pin: 2252
====================================
*USA:101
MasterCard Standart, Visa Classic ? $45
Visa Gold|Platinum|Corporate|Signature|Business ? $50
American Express ? $50 ( WITHOUT SID )
Discover ? $50

*CANADA:101 201
MasterCard Standart, Visa Classic ? $55
Visa Gold|Platinum|Corporate|Signature|Business ? $60

*EU:101 201
MasterCard Standart, Visa Classic ? $85
Visa Gold|Platinum|Corporate|Signature|Business ? $90

*ASIA/AUSTRALIA/Exotic:101,201,121 and others
MasterCard Standart, Visa Classic ? $75
Visa Gold|Platinum|Corporate|Signature|Business ? $80

Worldwide | CreditCard | DebitCard | Dumps Pin | Track 1 | Track 2 | Validity (95%)
==================================

Price: MSR 206 605
*****************************
MSR 206 + 2x CRM41 = $930
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MSR 206 / MSR 300 = $550
MSR 206 / MSR 3000 = $730
MSR 505 / TA - 48 = $640
MSR 505 / MSR 300* = $500
MSR 505 / MSR 2000 = $550

Price: ATM Plastic Card
******************************
Plastic Card 2500 = 150 (Dollar,Pound,Euro)
Plastic Card 5000 = 250 (Dollar,Pound,Euro)
Plastic Card 7500 = 350 (Dollar,Pound,Euro)
Plastic Card 10000= 450 (Dollar,Pound,Euro)

Price: YESCARDS
PRIX POUR YESCARDS
******************************
Gold Visa - 150€  ----> plafond 10000€
Gold Mastercard - 200€  ----> plafond 20000€

Platinium Visa - 150€ ----> plafond 10000€
Platinium Mastercard - 200€ ----> plafond 20000€

Platinium Visa - 200€ ----> 20000€
Platinium Mastercard - 250€ ---> 25000€

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Note :
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=======================================================
ICQ: 1671716 | e-mail: big24hours@gmail.com | ATM™Worldwide
Dumps/Fullz/Bank/YESCARDS/Plastic TRACK1&2 Visa,MasterCard,Amex,Disco
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====== DUMPS WITH PIN,TRACK 1 & 2 ==========

-Dumps + Pin,Tracks 1&2 US = $70 per 1
-Dumps + Pin,Tracks 1&2 UK = $80 per 1
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-Dumps + Pin,Tracks 1&2 AU = $80 per 1
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Sample Dumps and Track 1 & 2 with pin:
**************************************
Dumps + Pin (USA)
Track1: B4784559000586171^Andrew/Mayerbach^1503101000033433000037000
Track2: 4784559000586171=15031010003343300003700
ATM Pin: 5241
------
Dumps + Pin (Canada)
Track1: B4530920124710013^Bibliotheque^17032206128000000547000000
Track2: 4530920124710013=17032206128000547000
ATM Pin: 3377
------
Dumps + Pin (Australias)
Track1: B4072209014479002^Priya/Selva-Nayagam^1808201000000112000000
Track2: 4072209014479002=18082010000000112000
ATM Pin: 5081
------
Dumps + Pin (China)
Track1: B4067701731557109^Wei-Chun/Chang^19011014045400000988000000
Track2: 4067701731557109=19011014045400988000
ATM Pin: 2405
------
Dumps + Pin (France)
Track1: B4974903419054100^guihard/pascal^18021104400000000091000000
Track2: 4974903419054100=18021104400000091000
ATM Pin: 0004
------
Dumps + Pin (Turkey)
Track1: B4155650149958727^FATIH/GUCER^17101103410400000211000000
Track2: 4155650149958727=17101103410400211000
ATM Pin: 9889
------
Dumps + Pin (Japan)
Track1: B4541148282107007^Mamiko/Kobayashi^25072100000000000221000000
Track2: 4541148282107007=2507210000000221000
ATM Pin: 5447
------
Dumps + Pin (Republic of South Africa)
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User/Subscriber Economics: An Alternative View of Uber's Value

In the week since I posted my Uber valuation, I have received many suggestions on what I should have done differently in the valuation, with many of you arguing that I was being a over optimistic in my forecasts of total market, market share and margin improvements and some of you positing that I was too pessimistic. I don't claim to have any certitude about these numbers but the spreadsheet that I used to value Uber is an open one, and you are welcome to convert your suggestions into valuation inputs and make the valuation your own. In just the last few days, though, I have been watching an argument unfold among people that I respect. about whether the reason for my low valuation for Uber is that I am using a DCF model, with the critics making the case that valuing a company based upon its expected cash flows is an old economy framework that will not yield a reasonable estimate of value for new economy companies, driven less by infrastructure investments and returns on those investments, and more by user and subscriber economics.  I have long argued that DCF models are much more flexible than most people give them credit for, and that they can be modified to reflect other frameworks. So, rather than deflect the criticism, I will try to build a user based model to value Uber and contrast with my conventional valuation.

Aggregated versus Disaggregated Valuation
If you are doing an intrinsic valuation, the principle that the value of a business is the present value of the expected cash flows from that business, with the discount rate adjusted for risk, cannot be contested. That is true for any business, manufacturing or service, small or large, old economy or new economy. Since that is what a discounted cash flow valuation is designed to do, I have to believe that what critics find objectionable in my Uber DCF model is not with the model itself but in how I estimated the cash flows for Uber, and adjusted for risk. I followed the aggregated model for discounted cash flow valuation where I estimated the cash flows to Uber as a company, starting with its revenues and working through the consolidated expenses and total reinvestment each year and discounted these cash flows at a cost of capital that I estimated for the entire company. Along the way, I had to make assumptions about a total market that Uber would go after, the market share that I expect the company to get in that market and the operating margins in steady state. 

Disaggregated Valuation
Value is additive and you can value any company on a disaggregated basis, breaking it down into different divisions/businesses, geographical areas or by units:
  • Business Units: In a sum of the parts valuation (SOTP), you can break a multi-business company into its individual business units and value each unit separately.  I have a paper where I describe the process of doing a SOTP valuation, using United Technologies, a conglomerate, as my example. If that SOTP valuation is much higher than the value that the market attaches to the company, you may very well find an activist investor targeting the company for a break up. 
  • Geographical Groupings: When valuing a multinational, you can break the company's operations down geographically and value each geographical grouping (Asia, Latin America, North America, Europe) separately, not only using different assumptions about growth and risk in region but even different currencies for each region. 
  • Unit-based Valuation: More generally, when valuing any company, you can try to value it on a unit-basis, building up to its value by valuing each unit separately and then aggregating across units. Thus, a pharmaceutical company can be valued by taking each of the drugs that are in its portfolio, including those in the pipeline, and valuing that drug based upon its cash flows and risk and then adding up the values across the entire portfolio. A retail business can be valued by valuing individual stores and adding up the store values and a subscription-based company can be valuing by valuing a subscription and multiplying by the number of subscriptions, current and forecasted.
I may be misreading the critics of my Uber valuation but it seems to me that some of them, at least are making the argument it is better to value Uber, by valuing an individual Uber user first, and then scaling the value up to reflect not just the number of users that Uber has today (existing users) but also new users it expects to add in the future. 

Aggregated versus Disaggregated Valuations: Weighing the Trade offs
Valuation on a disaggregated basis allows you to be much more flexible in your assumptions, allowing them to vary across each grouping but there are four reasons why you seldom see them practiced (or at least practiced well) in company valuation.
  1. Law of large numbers: As companies get larger and more diverse, there is an argument to be made that you are better off estimating on an aggregated basis rather than a disaggregated one. The reason is statistical. To the extent that your estimation errors on a unit basis are uncorrelated or lightly correlated, your estimates on an aggregated level will be more precise than the unit-based estimates. For example, you will have a much better chance of estimating the aggregate revenues for Pfizer correctly than you do of estimating the revenues of each of its dozens of drugs.
  2. Information Vacuums: Information on a disaggregated basis is difficult to get for individual businesses, geographies, products or users, if you are an investor looking at a company from the outside. If you are doing your valuation from inside the company (as an owner or venture capitalist), you may be able to get this information, but as you will see with my Uber user valuation, even insiders will face limits.
  3. Missing Value Pieces: When valuing a company on a disaggregated business, it is easy to overlook some items that are consequential for value. In sum of the parts valuation, for instance, analysts are so caught up in estimating the values of individual businesses that they sometimes forget to value "corporate costs", which can be a multi-billion drag on value.  
  4. Corporate Structure: There are some items that are easier to deal with at the aggregate level, because that is where they affect the business. Thus, you can model when taxes come due and the effect of losses easier when you are valuing an aggregated business than when you are valuing it on a disaggregated level. Similarly, if you are concerned about legal penalties or corporate governance, these are better addressed at the aggregated level.
It is true that aggregation comes with costs, starting with the blurring of differences across disaggregated units (business, geographies, products, users) as well as the missing of competitive advantages that apply only to some units of the business and not to others. It is also true that using an aggregated valuation can result in a process that is disconnected from how the owners and managers at user-based companies think about their companies and thus cannot help them in managing these companies or valuing them better.

User Based Valuation
Now that we have laid out the pluses and minuses of aggregated versus disaggregated valuation, let us think about how you would construct a disaggregated valuation of a company that derives its value from users or subscribers. In general, the value of such a company can be written as the sum of three components:
Value of user-based company = Value of existing users + Value added by new users - Value drag from corporate expenses

1. Valuing Existing Users
The key step in a user-based valuation is estimating the value of a user and that value is a function of many variables: the cash flows that you are currently generating from a typical user, the length of time you expect that user to use your product or service, your expectations of how much growth you can expect in cash flows from a user over time and the uncertainty that you feel about all of these judgments:

Consider the implications that emerge from this simple framework:
  1. The value of a user increases with user stickiness and loyalty (captured in the expected lifetime of a user and the annual renewal rate).
  2. The value of a user is directly proportional to the profitability of that user (captured as the difference between the revenues from that user and the cost of servicing that user). 
  3. The value of a user is directly proportional to the growth that you can generate in profits over time, by either getting the user to use more of your product or service or coming up with other products or services that you can sell that user. 
  4. The value of a user decreases as you become more uncertain about future cash flows from that user, with that uncertainty being a function of the revenue model that you use and the discretionary nature of the product or service. A subscription-based model, where users agree to pay a fixed amount every period, will generally be less risky and more valuable than a transaction-based model or an advertising-based model, that delivers the same cash flows. A product or service that delivers a necessity (transportation) is less risky than one that meets a more discretionary need (travel). 
    If you can value a user, you can then estimate the value of an existing user base, by multiplying the value/user by the number of existing users. If you have multiple types of users, with perhaps different revenue models for each, as is the case with LinkedIn's premium and regular members, you can value each user group separately. 

    Value Added by New Users
    The second segment of value is the value added by new users that you expect to see added in the future. To estimate this value, you can start with the value per user from the last section but you have to net out the cost of acquiring a new user, which can take the form of advertising, introductory discounts and/or infrastructure investments to enter new markets. That net value added by a new user  (value per user minus cost of acquiring a user) then has to be multiplied by the number of new users that you expect to add each period and brought back to the present, adjusting for both the risk in the cash flows and the time value of money.

    Again, I will agree that this is simplistic but consider the common sense implications:
    1. The value added by a new user increases with the value of a user, estimated in the last section. A strategy of going for fewer and more intense users may create more value than one with more and less engaged users, a warning that pursuing user growth at any cost can be dangerous for value.
    2. The value added by a new user decreases as the cost of adding users increases. That cost will be a function of the competitiveness of the business (increasing as competition increases) but also of networking effects. If you have strong networking effects, the cost of adding new users will decrease as you accumulate new users, thus creating a value accelerator for your business.
    3. The value added by a new user decreases as you become more uncertain about user growth. That uncertainty will be a function of competition and whether the technology that you have built your product or service on is sustainable.
    Corporate Expenses and Value
    To get from user value to the value of the business, you have to bring in the rest of the company into your analysis. To the extent that you have expenses that are unrelated to servicing existing users or adding new ones, i.e., corporate expenses, for lack of a better term, you have to compute the value of these expenses over time and reduce your value as a company by this amount:

    While at first sight, this item may look like wasteful that should be eliminated, it represents both a danger and an opportunity for young companies. It is a danger to the extent that bloated corporate expenses can drag a company's value down, but it can be an opportunity insofar as it is at the basis of economies of scale. If corporate expenses represent necessary expenses to keep a business going, and they grow at a rate much lower than the growth rate in users and revenues, you will see margins improve quickly as a company scales up.

    Valuing Uber: A User based Model
    Can Uber be valued using a user-based model? Yes, but it will require assumptions about users that are, at best, tentative and at worst, based upon little information. While I will attempt with the limited information that I have on Uber to do a user-based valuation, I will leave it to someone who has access to more information than I do (a VC invested in Uber or an Uber manager) to tweak the numbers to get better estimates of value.

    Deconstructing the Financials
    The numbers that we have on Uber's operations are minimalist, reflecting both its standing as a private company and its general secretiveness. In 2016, according to the financials that Uber provided to a Bloomberg reported, Uber reported $20 billion in gross billings, $6.5 billion in net revenues (counting all revenues from UberPool) and a loss of $2.8 billion (not counting the $1 billion loss on the China operations). According to other reports, Uber had about 40 million users at the end of 2016, up from 24 million users at the end of 2015. Finally, other (dated) reports suggest Uber's contribution margins (revenues minus variable costs) in its most profitable cities ranges from 3-11% of gross billings and its contribution margin in San Francisco, its longest standing and most mature market, is 10.1%. Bringing in these noisy and diverse estimates together, here are my estimates of user statistics:

    These numbers are stitched together from diverse sources and vary in reliability, but based upon my judgments, I break down Uber's operating expenses in 2016 into three categories: to service existing users (48.17%), to get new users (41.08%) and corporate expenses (10.75%); the last estimate is a shot in the dark, since there is no information available on the value. The annual profit from an existing user, based on 2016 numbers, is about $50.50 (Net Revenues - Expense/user) and the  cost of adding a new user is about $238/75, and both will be key inputs in my valuation.

    Valuing Existing Users
    To value Uber's existing users, I use the framework developed in the last section, in conjunction with the estimates that I obtained from the limited financial information provided by Uber. I valued existing users, assuming four additional parameters: a lifetime of 15 years for users, an annual renewal likelihood of 95%, a compounded growth rate of 12% in annual revenues from users expanding their user of Uber services and a growth rate of 9.9% a year in annual user servicing expenses (on the assumption that 80% of the servicing cost is variable). Assuming a cost of capital of 10% (in the 75th percentile of US firms), the resulting value per user and the overall value of existing users is shown below:
    Download spreadsheet
    The value per existing user is about $410 and the overall value of Uber's 40 million existing users is $16,412 million. Not surprisingly, this value is sensitive to user stickiness (as measured by user lifetime) and user growth potential (as measured by the growth rate in annual revenues):

    In a market where investors swoon at user numbers, this table makes an obvious point. Not all users are created equal, with more intense, sticky users being worth a great deal more than transient, switching users.

    Value Added by New Users
    To estimate the value added by new users, I start with the value per user (estimated in the last section to be $410), which I grow at the inflation rate to get expected value per user over time, and use the cost of acquiring a new user from 2016 (about $240/user). Assuming a growth rate of 25% a year for the next five years, 10% between years six and ten and overall economic growth after year ten, I estimate the value added by new users over time. (With those growth rates, I more than quadruple the number of users over the next ten years to 164 million.) In coming up with value, I assume that new user growth is more uncertain than the value created by existing users, and use a 12% cost of capital (at the 90th percentile of US firms) to get today's value.
    Download spreadsheet
    The value added by new users, based upon my estimates, is $20,191 million. That value is sensitive to the net value created by each new user (value of a new user minus the cost of adding a new user) and the growth rate in the number of users:
    This table illustrates the point made earlier about how some companies will be better off trading off higher value added per user for lower user growth, since there are clearly lower growth/ higher value added scenarios that dominate higher growth/lower value added scenarios in terms of value creation.  

    Corporate Expenses and overall Value
    The final loose end is the corporate expense component, a number that I estimated (arbitrarily) to be $1 billion in 2016. Allowing for the tax savings that these expenses will generate and assuming a 4% compounded growth rate, well below the 15.16% compounded growth rate in total users, I estimate a value for these corporate expenses (using the 10% cost of capital that I used for existing users):
    Download spreadsheet
    The value drag created by corporate expenses is about $10,369 million. Bringing together all three components, we get a value for Uber's operations of $26.2 billion
    Value of Uber's Operating Assets:
    = Value of Existing Users+  Value added by New Users - Value drag from corporate expenses
    = $16.4 billion + $20.2 billion + $10.4 billion = $26.2 billion
    Adding the cash balance ($5 billion) and the holding in Didi Chuxing (estimate value of $6 billion) results in an overall value of equity of $37.2 billion for the company (and its equity, since it has no debt):
    Value of Uber Equity = Value of Operating Assets + Cash - Debt = $26.2 + $5.0 + $6.0 = $37.2 billion
    This is close to the value that I obtained for Uber on an aggregated basis, but that is a reflection of my understanding of the company's economics.

    Pricing versus Valuing Users
    As you can see, valuing users requires assumptions about users that can be difficult to make. So, how do venture capitalists and other early stage investors come up with per user or per subscriber numbers? The answer is that they do not. Drawing on an earlier post that I had on how venture capitalists play the pricing game, venture capitalists price users, rather than value them. What does that involve? Very simply put, the price per user at Uber, given its most recent pricing of $69 billion and the estimated 40 million users is $1,725/user ($69,000/40).  To make a judgment on whether that number is a high or a low number, you would compare that price to what you the market is pricing a user at Lyft or Didi Chuxing and if naive, argue that the lower the price per user, the cheaper the company. Using the most recent estimates of pricing and users for the five big ride sharing companies, here is what we get:

    CompanyMost Recent Pricing (in $ millions)# Users (in millions)Price/User
    Uber$69,00040.00$1,725.00
    Lyft$7,5005.00$1,500.00
    Didi Chuxing$50,000250.00$200.00
    Ola$3,00010.00$300.00
    GrabTaxi$4,2003.80$1,105.26
    If you follow the user valuation in the last section, you can see why this pricing comparison can be dangerous. The aggregate pricing that you get for individual companies reflects not only existing users but also new users, and dividing by the existing users will give you much higher numbers for companies that expect to grow their user base more. Even if every company is correctly priced, you should expect to see users at companies with less cash flows per user, lower user growth, less intense and loyal users and more uncertainty about future cash flows to be priced much lower than at companies with intense and sticky users, with more growth potential.

    The Bottom Line
    If your argument against using discounted cash flow valuation (at least in the aggregated form that it is usually done) is that you have to make a lot of assumptions, I hope that this process of valuing users brings home the reality that you cannot escape having to make those assumptions. In fact,  the assumptions that you need to make to value a company on a disaggregated basis (based on users or subscribers) are often more involved and complex than the ones that you have to make in an aggregated valuation. That said, I do agree that looking at value on a disaggregated basis can not only give you insights about value drivers but also about questions that you would want to ask (and get answered) if you are thinking about investing in or building a young company whose value is coming from its user or subscriber base. 

    YouTube Video

    Attachments
    1. Uber User-based Valuation
    2. Uber aggregated DCF
    Previous Posts on Uber

    SUR ORDRE DE SES MAITRES BANKSTERS ET LEUR CREATION DE TEL AVIV, LE CHABAD LOUBAVITCH KUSHNER/TRUMP PROVOQUE UNE GUERRE TALMUDIQUE DE 42 JOURS DEPUIS LE MOYEN ORIENT, ET UN GENOCIDE ANTI-MUSULMANS EN EUROPE, ET AUX ETATS-UNIS



    LE SHOFAR TALMUDISTE, CHABAD LOUBAVITCH KUSHNER/TRUMP EST SUR LE POINT DE DÉTRUIRE LE PETRO-DOLLAR ET L'ÉCONOMIE MONDIALE, DE PROCÉDER A LA DESTRUCTION D'EDOM DURANT LA 33IEME SHEMITAH DU DAJJAL, CELLE DU 11ÈME JUBILE SATANO-TALMUDIQUE; UNE GUERRE DE 42 JOURS DÉCLENCHÉE DEPUIS PARIS PAR TEL AVIV/WASHINGTON: L'ENTITÉ SIONISTE A JUSQU'À FIN SEPTEMBRE 5777/2017 POUR COMPLÉTER SA TRANSITION, SON

    The Judge’s son



    I was starting my senior year at a new high school when I rounded a corner and crashed into a guy I had not seen before. He was with a group of about four or five guys, they were talking loudly and laughing, until I ran into him that is.

    “What the fuck?” He said.

    “Sorry, I didn’t see you.” I replied as I tried to straighten the stack of books that I was carrying.

    “What am I fucking invisible? Can’t see or are you just plain stupid?” he said as he pushed my books out of my arms and onto the floor.

    The other boys laughed and egged him on to hassle me even more, they seemed like the school jocks but not really knowing them, I was not sure, could be they are in a school click of bullies, thugs and assholes.

    “Look, I said I was sorry for bumping into you, there is no need to be a dick about it.” The words were hardly out of my mouth before I regretted saying them and knew it would add to my trouble.

    The thug that I ran into grabbed me by the front of my tee shirt lifting me to my toes while he ranted with his spit flying into and near my face, I looked to the left and to the right to figure which way would be the best exit route and lifted my knee sharply into his crotch as hard as I could.
    Thug boy’s face went pale as he released his grip on my shirt and melted to the floor groaning as he went, his friends were momentarily at a loss on what to do, that was my moment for a fast exit and I grabbed up my books and walked away quickly to my next class.

    By the end of the day the “incident” was the talk of the school, it seems like I picked the wrong guy to mess with according to the masses that warned me that I would not live to see the next day.
    I was trying to get to my locker and drop my books off before making a rapid and quiet exit to the parking lot where my car was parked. I nearly made it to the car before I heard his voice.

    “Hey fuck face, you are dead meat son.”

    I turned to see the thug, his friends and a group forming that has anticipated the beating that he planned for me.

    “Look, I think we got off on the wrong foot earlier, I don’t want to make enemies the first week of senior year, what do you say we forget what happened today?” I asked.

    He laughed as I finished talking, the crowd was getting larger and larger, and it was like a wave of kids pushing up to see the fight.

    “I am going to beat the crap out of you and that will be the way it goes.”’

    I was going to give him all I could, I was not going to just take a beating. I took my jacket off and was ready go when he punched me in the stomach taking the wind out of me. I stood upright and went after him, I punched at his face and missed causing everyone to laugh.

    I moved out of his range while I got my bearings, I dodged his fist and gave him a knee to his nuts for the second time of the day, down he went, I walked over and leaned toward his face that was against the asphalt.

    “Are we done here?” I said softly.

    “Fuck you.”

    “Get up or shut up.” I said more loudly.

    He lay in a curled position holding his crotch.

    I turned and got into my car and drove away knowing that this problem was not over by far.
    I looked in my mirror at a stop light, there was a car behind me that I was sure was following me, probably that asswipe. I drove for a couple of blocks more before stopping in front of a burger place, the car pulled in next to me, I was ready for a fight in case this was a friend of the guy from school, I walked over to his car door just as he got out.

    “You looking for trouble too?” I asked.

    “No, chill out, I just wanted to talk to you, I don’t want any problems. My name is David.”

    “My name is Joe.” I said, still apprehensive.

    “Yeah, I know, you are in my chemistry class, I have been checking you out.” David said with a cute smile.

    “What do you mean, checking me out?”

    “You know, you are the new kid in the class, everyone checks you out, have to see if you can figure out your story, smarty, geek, jock, gay, figure out who you are is all.”

    “Well I am me, that’s all anyone needs to know, I don’t need to be pegged into a specific group.”

    “Let’s go inside and have a burger, I’ll buy, after all you are the guy that dropped Kyle Ryan to his knees twice in one day.”

    “Kyle Ryan huh? Well he needs to keep to himself and leave me out of his drama.”

    We got inside and into a booth, and ordered Cokes while looking at the menu.

    “One thing you can count on is that Kyle will not leave you alone, so he will either need to make a friend of you or beat you down, probably the latter one.”

    We ordered burgers and fries and went on to talk about school and our families, it turned out that David’s dad is a Judge in town, and this being a small town, that means allot. I only had my dad, mom passed away in a car crash a few years ago and dad seemed lost without her and had little mom skills to pass on to me, I was pretty much left to fend for myself on a daily basis.

    David moved his foot and it brushed against mine, I instinctively moved mine away, and within a moment his was brushing against mine again, this time I did not more it. Our food arrived and we ate while talking about whatever came up, David reached over and helped himself to one of my sweet potato fries popping it into his mouth.

    “I always forget about sweet potato fries and order regular fries, I really like them.”

    “Help yourself, I have plenty and if I run out, I will help you eat yours.”

    “You can eat mine.” David said with a crooked grin.

    I smiled and declined the comment but was sure that he was speaking sexually but did not want to cross signals and have things turn into a mess.
    I reached for a fry and David reached for the same fry off of my plate, he twisted it and we each got half, if that was not a signal, I was crazy.

    “So, do you have a girlfriend David?”

    “Nope, you?”

    “I just moved here a couple of weeks ago.”

    He moved his foot up my ankle, I did not budge, I wanted to see where this goes. David kept eating my fries and dropping little flirts here and there that got more and more suggestive.

    “Do you have a boyfriend David?”

    “Nope, not yet.”

    Well, that seemed to answer that question, the toe of his shoe was near at my inner thigh and I was starting to get hard.

    “Wanna go make out?” David asked.

    “I just met you and besides, I may not live beyond tomorrow if Kyle has his way with me.”

    “I will take care of Kyle, after I take care of you.”

    “You are pretty sure of yourself.”

    “Kyle won’t mess with me, he is worried about the Judge, and dad will be all over him if I tell him that Kyle is a bully and was bothering me."

    We finished eating, and walked outside, and stood against his car, David is good looking enough, boyish looks and dark hair with a medium build.

    “Get in.” David said as he opened his door to get in.

    I walked around and got into the passenger side, the door was hardly closed before David was leaning over and had a hand under my tee shirt groping on my chest. I faced David and his lips were on mine, man this boy was horny and moving fast.
    David’s kisses were intense and felt like he was really taking charge, his left hand was tweaking my nipples and headed for my belt buckle, trying to get it open with one hand.

    “Slow down some, we are in the restaurant parking lot, people are walking by.”

    “Fuck them, okay, we can go for a short drive for more privacy.”

    “Let’s can go to my house, my dad works nights and never checks on me, he knows I will call him if I need anything.”

    “Cool, jump in your car and I will follow you there.”

    We got inside the house and walked into the kitchen to grab a couple of bottles of water I turned around and David was all over me, I set the water on the counter and in about two moves David had my fly open and my jeans pulled to my ankles. I leaned back against the kitchen counter while David kissed me while his hands roamed my plump ass and started rubbing a finger into my ass crack.

    “You sure your dad is gone to work?”

    “Yeah, good thing, my jeans might as well be off.”

    “Okay.” David said as he leaned and pulled my jeans from my feet and tossed them aside.

    His mouth was on my cock in a flash, he took it fully down his throat making my knees buckle some. I have messed around with only a couple of guys before where neither of us knew what we were doing, it was evident that David clearly knew what he was doing.

    “Let’s go to my room, I don’t want to risk anything, although my dad never comes home at till about three in the morning but let’s get behind a closed door before we go any farther.”

    In moments we were naked laying on my bed, David was all over me and pushed my knees up to my chest pinning them against me as he tried to push his dry cock into my ass.

    “Wait, there is some lotion on my dresser.”

    David sprang up and had it back in a millisecond, he squirted some on his cock head and more onto his fingers, rubbing them around my ass hole. I had never had a cock in my ass before and really was not sure how it would feel and just hoped for the best.
    David pushed his cock into me in a couple of good pushes, the pain seared through me like a hot poker tearing me apart while burning me alive, I cried out and had tears in my eyes.

    “Wait, stop, something must be wrong, it hurts too much.”

    “Its fine, it always hurts a little till you get used to it, and the pain will pass.”

    “Oh hell, I don’t this this is gonna work, I think my ass is splitting open.” I said.

    “Just bear down some, like you gonna take a, well you know.”

    I pushed back like I had to push out a log, it opened me up some and things got a little better than before. David’s hips were moving a hundred miles an hour, and my ass was ablaze, it was like he was possessed by some sex demon and was set to pleasure himself thinking of only getting his cock into my ass and fucking me harder and harder.
    I looked into his face, he sort of gave me a smile, but never slowed a bit.

    “Feeling better Joe?” He asked.

    “Some, but it still burns like hell, I’ve never been fucked before.”

    “Well, baby, you can’t say that anymore, and that ass is tight.”

    My cock had shriveled up and all but crawled up inside me, I looked past the pain and at David, fucking me in the ass, he was my first and all of a sudden I didn’t want him to stop, it hurt still, but I wanted him inside me and wanted to be his boyfriend. My hands roamed his shoulders feeling his muscles strain as he pumped my virgin ass.

    “It’s better now, still burns but better than before.”

    “Good, I told ya.”

    David fucked me faster and faster until he started panting and groaning, his body jerked out of rhythm a few times and he was spent, he had flooded my ass with his cum. He lay on top of me for a while before his cock slid out of my worn and hurting ass and onto the bed next to me.
    I straightened my legs out and felt between my legs fully expecting to have blood on my hand but there was none.

    “Do you want me to fuck you now?” I asked.

    “Naw, Joe, I don’t take, I give, I’m a giver.” He said with a smile.

    David leaned over and took my limp cock in his mouth and sucked it to life, in no time I had a full erection that David was doing a good job of sucking it into his throat completely. His finger went into my ass but there was no pain, just the burning from before, it was way smaller than his cock and I liked him fingering me while sucking my cock.

    I was getting close to cumming and warned him so it did not go into his mouth if he didn’t want it to but he kept swallowing my shaft until his lips hit my dark pubes, I exploded into his mouth as my hips thrust it deeper into his throat he worked to keep each drop of my jizz in his mouth.

    “Holy crap that felt great.” I said panting and out of breath.

    David looked up from between my legs and smiled at me, he was an animal, no one has ever swallowed my cum before and no one has taken my cock into their throat. Well, even though I had only messed around with one guy before two or three times, it was mostly rubbing and licking some, he was as un experienced as I was.

    David encircled my balls with his finger and thumb squeezing my ball sac and pulling on it like he was taking possession of it, as if they were his balls now.
    He got up from the bed, standing near me, I reached over and touched his cock as it bounced while he pulled his shirt over his head, I felt the sticky syrup still leaking from the tip of his prick and took my finger into my mouth tasting his cum for the first time, it was salty and good, and I wanted more.

    “Do you have to go so fast?” I asked while touching his loose hanging balls.

    “Yeah, I’ve got things to do before school tomorrow.”

    “Will I see you again?”

    “Well, yeah silly, I’ll be at school tomorrow.”

    “I meant like this.” I said tugging on his cock lightly.

    “Yeah, sure.”

    He put on his jeans without his underwear and tucked his prick into his fly, put his shoes on and left.

    I slept good but woke up feeling like I had a chainsaw in my ass, it was really sore, but it made me smile thinking of why it was so sore, David fucking my ass like a wild man.
    I got up and showered, came back to my room to dress and saw David’s briefs laying on the floor next to my bed, I picked them up and took them to my face and sniffed them deeply, I was not sure why but I put them on and finished getting dressed.

    It was not until the third period before I saw David, I could not remember if he was in more than the one class of mine and third period, there he was in gym class, I saw him across the room with his locker door open as he undressed, he looked over and gave me a wink and I smiled back at him.

    David walked past me and told me that Kyle Ryan would not be bothering me anymore and I dint have anything to worry about. We played basketball before coming back in the locker room to shower, I stripped and headed in and turned on the water, standing under the spray, my ass was still quite sore but I wanted to see David next to me, the water running down his body as he showered off the sweat from the game.

    David walked into the showers with one of his friends talking and laughing, he didn’t take the vacant shower next to mine but was down at the end with the other guy. I felt betrayed, it was silly but I wanted him near me, I was jealous and wanted him just for me. I looked over as I walked out of the showers, he had soaped up and was washing his cock and balls, the soap suds made them slick looking and he seemed to give them extra attention but was looking right into the eyes of the other kid.

    Later that day in chemistry class, I sat in the back row, David came in and sat at the desk next to me, he looked over and smiled.

    “How ya feeling?”

    “A little sore.” I whispered.

    I was still a little miffed about him not showering next to me earlier but I guessed that I was being a silly girl, thinking that his world would change and revolve around me instantly.
    The teacher was talking about who knows what, I was hoping that I would not be called on to answer anything because all I was thinking of was David, I was picturing him fucking me, like what it looked like from above, his ass cheeks tight as his hips moved while he plowed my ass.

    I looked over at David, he had a handful of his jeans at the crotch rubbing and pulling at it while he looked into my eyes. I motioned for him to stop before someone saw what he was doing. He got a devilish grin and put his second hand under the desk and unzipped his fly, then the button at the top of his jeans, my heart raced as he pulled his cock out of his jeans and wiggled it at me, my face went red but I wanted to dive to the floor to suck it.

    David put his cock away and whispered for me to go to the restroom, I stood up worried that someone would be able to see my boner through my pants.

    “Uhm, I have to go to the bathroom.” I announced as I passed the teacher heading for the door.

    I heard movement behind me and David mimicked my exact words and he trailed me toward the door.

    “Some new club meeting?” the teacher said.

    “Nope, just need to drop a duce.” David said.

    I could hear the kids laughing as I passed the doorframe and felt relieved to be in the hallway.

    “They will know what we are going in the bathroom for with both of us leaving at the same time.” I said.

    “No, they will think we are going for a smoke.”

    We hit the boy’s bathroom, and David pulled me close, his hands roamed my jeans in front and then rear.

    “I need that ass again Joe, it was all I could do not to bend you over my desk back in chemistry class, I don’t care who saw.”

    I reached for David’s jeans fly and unbuttoned it, my hand went inside and down to his cock, it was warm and soft and it felt good in my hand.
    David opened my pants and pulled them down some, he looked at the briefs I had on.

    “Are those mine?” he asked.

    “Not anymore.” I said smiling back at him.

    “That is why I left them, wondering if you would wear them or..”

    “Or what?”

    “Sniff them or jack off on them.”

    “I’m not a pervert, who sniffs another guy’s underwear?” I asked.

    “You.” David said as he pulled me close, kissing me on the lips.

    Just then some kid walked in, our pants were open and he saw us kissing, he just froze.

    “Come here.” David said in a firm voice.

    The kid walked over but looked like he wanted to be anywhere but here.

    “What do you see?”

    The kid looked stunned and did not know how to answer. David grabbed his arm, and asked him again.

    “I didn’t see anything, and I will leave.”

    “You came in here to pee, so go pee.”

    David took my cock in his hand and kissed me again, I could see the kid standing at the urinal peeing or looking like he was, he kept looking back at us, and David seemed not to care.
    He turned to zip up and washed his hands, looking at our cocks as he passed to leave the bathroom.

    “Not a word.” David said as he was walking out.

    “Damn, he saw us kissing, and pants were open, hell, he saw our cocks out.”

    “He won’t talk.”

    David sucked my cock until I shot my load into his mouth, then it was my turn, I got to my knees and took his balls in my hand, his cock was very stiff, I put the tip into my mouth and was going to go slow, but David had other plans, he pushed it in all the way making me choke and gag some pulling it back only for a moment. He put his hands on the back of my head and pushed it back in, tears came to my eyes, as I fought the urge to gag as much as I could.

    He tilted my head back and rode my lips until his cum started spurting into my mouth, I pulled back some and took two blasts onto my face, cum was running down my lips and cheek onto my neck, I dove back on taking the rest into my mouth.

    We heard a noise in the hallway and shoved out cocks back in and zipped up quickly, one of the guys from our class came in and walked over to the urinal and started peeing, he seemed not to notice that we were standing in the middle of the bathroom floor not appearing to be doing anything, I guess he thought we were smoking.

    We left and about the time we walked back into class, I felt the cum drip farther down my neck, I had forgotten to wipe it off with a paper towel so I moved my hand to block it from view and moved quickly to my seat. David was getting ready to sit down and ran his finger across the stickiness on my neck and took it to his mouth sucking it off of his fingertip.

    I looked around to see but it seems that no one was paying any attention to us whatsoever. The bell finally rang about twenty minutes later and I was happy to get out into the hallway, David trailed behind me acting as if nothing had happened minutes before.
    I asked David to come over after school and we could spend more time together, he seemed to have no problems agreeing to it before I had the words out of my mouth. After school we headed to my house and like before David was hot to have sex as soon as the door was closed.

    We stripped and jumped onto the bed, I was on my back and David was face down but his feet were past my head. David sucked my cock while I sucked his, he put a finger into my ass and began finger fucking my ass extremely fast while he blew me, my ass was still a bit sore from the day before and this was making it burn hot again.

    I pushed a finger into David’s ass but he squirmed around letting me know that he didn’t want it inside him. I played with his balls some and was quite happy sucking his teen cock. I was getting close to shooting, and did not announce it, I just let it go, and he sucked on my cock until it hurt from tenderness long after I finished shooting.

    David moved around some and was now straddling my chest and jacking his cock with it aiming for my face, he was beautiful and it was great looking at him sitting atop me jacking his cock, and then the cum flew from it, splashing all over me, he took the head of his still spurting cock and rubbed cum all over my face.

    He moved up and put his ass up to my face at first dangling his balls against my lips, I liked this allot, feeling them hang free as I flicked at them with my tongue, he moved up a little farther and started putting his ass right onto my face and directly on my mouth.

    At first I pushed at him and could not figure out what he was doing, I had no idea that anyone would do this. He used more pressure until his asshole was pressing on my lips, I opened my mouth and licked at it a little and another moment I was chewing at his ass, and pulling his hips down tighter onto my mouth, I licked at his ass all the way up to his balls and back, it was like a sweet forbidden place, that I could not get enough of.
    We rested on the bed for a while, my hands roamed his body caressing it anywhere and everywhere.

    I called out for a pizza to be delivered so no one had to leave, we ate the pizza while naked in my room and David was so comfortable to be with it all seemed like we had been with each other for a long time.

    After we ate, David got up from the bed and took his belt off of his pants, I just watched intently, he took the belt and lashed my wrists together to the headboard rail, I was liking where this was going and went for the ride. David took the lotion from my dresser and squirted some onto my cock and began rubbing it, my boner was so stiff it almost hurt, it was slick with lotion and his grip on it was strong.
    David would jack me off till I was about to shoot my load and he would stop, I was panting and moving around, he did this several times until he had me begging to cum.

    “Oh, fuck, that feels so good, but I want to cum, I need to shoot.”

    But David continued doing as he had done, jacking my cock to the throbbing point and stopping, he would trace his fingers along my chest and down my treasure trail to my cock and start again.

    ”Mmm, please baby, let me cum, I really want it.” I begged softly.

    He only smiled and did the same as he had been doing, this went on for about twenty minutes, it took less and less time before he had to stop and let my frenzy settle before starting again. Finally he lifted my legs and ass into the air to the point that my cock was just above my mouth.

    “Suck it.” He said.

    “I can’t reach, I can’t suck my own cock.”

    “Then you won’t cum.”

    I reached my tongue out as far as I could and could just tough the tip of my cock, David pushed down on my legs and ass a little at a time and finally with moving around some I was able to get the whole head of my cock into my own mouth.

    “There, suck it, I want you to cum right in your own mouth.”

    He helped with keeping some downward pressure and put his face right by mine, he was watching intently as my cock bobbed in and out past my lips.

    “Yeah, that’s fucking hot, suck it Joe, I want to see the jizz shoot into your mouth.” He whispered near my ear.

    He jammed a finger into my ass which in this position made me even harder and he gave a bit more pressure until I had more of my cock going into my mouth. His finger reamed my ass getting me hotter and hotter, it did not take long before I was moaning with my own throbbing cock shooting salty cum into my mouth.

    “Don’t swallow it all, just hold some for me.”

    He pulled my legs down and stuck his tongue into my mouth, he was tasting my cum while kissing me, we both swallowed my load and he fell to the bed next to me. David removed the belt letting my hands free and tossed his belt onto the floor.

    “Oh my God, that was so hot, I had no idea I could get my cock into my mouth, it did take some help but it was in pretty far.” I exclaimed.

    “I have been thinking of that since we were in the restroom earlier today, in fact I have been thinking of lots of other things too.”

    “Like what?” I asked.

    “You’ll see, but not today.”

    My dad had two days off so we could not get together at my house, once we went to the woods to an old tree house and jacked off together as we watched our cum shoot out and all the way down to the ground about twenty feet below.

    The next time we got together, David put a blindfold over my eyes and said he would be right back. Moments later I could feel him on the bed next to me, I liked this sexy game, I reached out and touched his leg and ran my hand up to his cock, this cock was not David’s, it was not circumcised, I started to get up and pull the blindfold from my face but David pulled my hands back to my side.

    “It’s all okay, it is one of the guys from our gym class, him and I have had sex before and I told him about what we have been up to, he wanted to join us but didn’t want you to know who he is right just yet.”

    “But I only wanted to have sex with you, I don’t know who this guy is even.”

    “It will be fine, I won’t let anything happen to you and we can stop whenever you want, just relax.”

    I could feel my legs being spread apart but did not know who was doing it, there was a lot of movement and I could feel balls bouncing against my lips, I opened my mouth and licked at them and in a moment a cock went into my mouth, and it had foreskin, it was the other guy.

    His cock went down my throat while I could feel lips against the underside of my shaft, kissing it and licking my balls, it must be David, he moved up and joined the other guy, now there were two cocks at my lips, I sucked on one, then the other and then both at the same time, it was quite difficult to get both into my mouth at the same time but they did not give up.

    I sucked hungrily at the pair of cocks, one of them pinched at my nipples making them hard and sensitive, my cock was straining and stiff but I did not touch it. They jacked off until one then the other spewed a flood of cum into my mouth and all over my face.

    I could feel lotion being rubbed onto my cock and expected that I would be jacked off over a period of time again like before, stopping before I could shoot. This time I felt something different and knew it had to be the other guy, he was lowering his ass down onto my cock, I could feel it slipping into him, and it was so wonderful I almost shot my load then and there.

    I held back and he started riding my cock, up and down, my cock was harder than it had ever been before, it felt like it was huge and bigger too. I took my hands to his arms that were near my shoulders, he felt strong with lots of muscle, I wanted to see him, the guy who I was fucking but I didn’t take off the blindfold, it actually made it hotter.

    In another few seconds, I started shooting my juice into this sexy feeling guy, I could hear him panting as I finished cumming in his ass, he slipped off of my cock and I could hear him getting dressed, he must have sat on the bed to put his shoes on before he slipped out of the room. David took off my blindfold and stood next to the bed smiling.

    “Pretty hot huh?”

    “Who was that?”

    “I can’t tell, he made me promise but said that he might let you know after he saw how it went today.”

    The next day in gym class, I got into the showers as soon as I could and watched every guy as he showered, looking for that uncut cock, that was in my mouth and I could picture the shoulders from when my hands touched them. There were only a few un-cut guys in our class, and only two seemed to have the build that I had felt, I wanted to know who I had fucked, and he was the first guy I had ever fucked at that.
    I gave both guys a once over and looked right at them, neither one gave any indication it was him and I did not want to stare too much or they would wonder about me being gay, I wanted to know but then it was kind of hot not knowing who it was.

    At lunch I picked up a tray and moved down the food line getting a burger, fries and a small salad, I sat off to the side away from the noise, I just wanted to think about things, a lot has happened since starting at this school. I was deep in thought when I heard a voice and looked up to see a well-built blond guy holding his lunch tray.

    “Mind if I join you?” He asked.

    “No, I don’t mind, there is plenty of room, help yourself.”

    “You are like me, right?”

    I looked up and was a little confused, did he mean gay?

    “What’s that?” I asked.

    “The burger, it is the safe thing to eat, that chicken something with gravy looked a bit creepy.” He said as he flicked the tomato off of his burger and put the bun back on.

    “Oh, yeah, it really did, I’m not sure who would choose to eat that.”

    Maybe this is the guy I fucked, his shoulders looked like they could be the ones I felt on the mystery boy, his hair was flopped off to one side and a bit bushy but in a cute way, I wanted to reach over and brush it back from his eyes.

    “I got to school late today, it is odd coming just in time for lunch.”

    “What classes did you miss?” I asked.

    “English, math and gym, probably did not miss much though.” He answered.

    I almost choked on my fry, hell, this guy might be him, hell, and he is not bad looking. I just started watching his lips move and was hypnotized by them, they were full and a little darker than mine. I was thinking of what he would look like naked and riding my boner.

    “Wow!” I said out loud.

    “What?” He asked.

    I had not meant to say it, it just came out when I was thinking of him sitting on my cock bouncing up and down.

    “Oh, nothing, I was just…” I let my voice trail off.

    “My name is Nat.”

    “I’m Joe”

    “Yeah, I have seen you around, maybe in the hallways.”

    “So, Nat, you got a girlfriend or boyfriend, what does Nat do when not at school?”

    “No, no girlfriend, I just hang out with my friends and stuff.” He said in between bites of his burger.
    I noticed that he avoided the boyfriend part, I studied him while he ate, this must be the guy, and maybe he sat with me to tell me.

    “So, what do you do after school?”

    “I just fuck around with my friends mostly.” I said, just throwing the fuck word for reaction.

    “Sounds fun, we should hang out.”

    “Sure, want to come over today?” I asked.

    “Why not, what’s your address?”

    I wrote my address down and asked him if he knew where that was and he said he did, of course he does, he has been in my room, but maybe he was not ready to tell me yet.
    I did not see David after school so I just headed home, not really expecting Nat to show up but within a few minutes, my doorbell rang.

    “Hey Joe.”

    “Hey Nat, come on in, let’s go to my room and hang out.”

    “Sure,”

    I shut the door behind us and we sat on the edge of the bed, Nat started talking about his computer and some new game he was playing, I was done playing cat and mouse and leaned over and kissed him. He looked a little embarrassed but I went for his fly without giving him time to back out.

    “Well, umm.” Was all the noise he made.

    “Stand up and let’s get you out of those pants, it is time for some fun.” I said.

    I un zipped him and opened his fly and in one smooth motion I pulled his pants and underwear to the ground, his cock flopped out and I almost fell over, he was circumcised, this was not the guy that I fucked yesterday, I just made a huge mistake, Oh, hell.” What have I done?

    This guy must think I am a big slut and what if he is not even gay, he could out me to the whole school.

    “I didn’t expect to have my pants down within moments of being in your room.”

    “I can explain, well I can’t.” I stammered.

    Nat kissed me on the lips while I was trying to explain and I figured that the best thing was just to shut up. I kissed him back, his tongue was in my mouth and the kiss became more and more frantic and hot.
    Nat unbuttoned his shirt and tossed it aside as he kicked out of his shoes and pants that were at his ankles, his hands were all over me, pulling my tee shirt over my head. His chest had a good build and he had nipples that begged to be sucked and twisted, my mouth went to them.

    I took off my pants and now we were both naked, I gently nudged him back onto the bed, he lay there on his back looking all sexy and hot, I climbed on top of him, laying there kissing him while our cocks went to full blown stiffies as they crushed against each other between us.

    Nat’s hands went to my ass cheeks pulling up and pushed a finger deep into my hole before rolling me off of him, he sat up on his knees next to my face, his meat was about two inches away from my lips, I could feel the heat coming from it just before I parted my lips and tasted his cock for the first time.

    “Damn, Joe, you don’t waste any time do you? I was not sure you were gay, more like just hoping that you were.”

    I sucked Nat’s cock while he gently thrusted it in and out of my mouth, unlike David who seemed to always be very aggressive and a little rough. I took my time with Nat also, my hands caressed his broad shoulders and I kissed his full lips while we made slow and passionate love together.

    I asked Nat to fuck me and he gave no hesitation, using the same lotion which was not a very good lube, he pushed his meat into my ass, slowly at first and then speeding up as he went and I got used to his size filling my hole, we stopped for a moment and I moved around doggy style and leaned into his thrusts, I could feel each inch as it moved.

    Nat’s hands roamed around feeling my chest and down to my stiff cock, I did not stay soft like I did with David who was a bit larger than Nat but it was more about the care that Nat gave me that made me feel good. Nat twisted my nipples as he leaned against me with his hips. He climaxed and fell on top of my back, breathing hard while his hands roamed my underside.

    “Now it is your turn to fuck me Joe, and tomorrow we buy some better lube.”

    I laughed and slipped between his legs and lifted his hips before sliding my hard prick into his love hole, I looked right into his face while I fucked him, he seemed sweet and kind and I really liked being with him.
    I fucked his ass lifting his legs higher as I got closer to shooter, I wanted in him deeper and deeper, it felt so good being inside him, I blasted my juice into him and kept fucking him until I had spent my load inside Nat.

    We lay side by side for a while before we went to the shower and moved under the water again, I soaped him and he soaped me, after rinsing off we ran naked back to my room and under the sheets of my bed.
    We talked and laughed over the stories we told each other, I nuzzled up on his arm and we fell asleep, a restful satisfying sleep. The next morning I realized that Nat was still here and we had slept through the night and my dad was home, I would have to sneak Nat out of the house somehow. Just then there was a knock at the door, Joseph, breakfast, and bring your friend down, you boys have to have a good meal before school.

    My face went hot, he must have looked in on my when he came home from work and seen us sleep in each other’s arms, I was not out to my dad but I guess I am now. Dad did not make a big thing of it and was pretty casual while we ate breakfast. Later he did say that I should be who I am and that he was fine with me being gay, I was a little embarrassed but it was good to have things out.

    I ran into David the next day and played things cool with him hoping that he would lose interest in me and I also hoped that Nat and I could build a good relationship.
    I never found out who the guy was that was un cut and wondered why he never came forward to me, maybe it was just sex to him or he could see that there was something growing between Nat and I.