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Which game makes more money on a daily basis?

game A, which has 175,000 DAU, a 32% second-day retention rate, a $0.05 ARPDAU, and a 30-day lifetime

or

game B, which has 150,000 DAU, a 22% second-day retention rate, a $0.08 ARPDAU, and a 15-day lifetime

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    What is it that you do not understand? Please tell us what you have tried, as it looks like a question straight from some textbook at the moment.2012-07-24
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    What's a "DAU" and "ARPDAU"?2012-07-24
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    I do not believe this has anything to do with the field of "mathematical logic", and instead it is about the value of social games2012-07-24
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    @J.D.: DAU is "daily active users" for a game (like Farmville) and ARPDAU is "average revenue per daily active user". But I am not sure what units they are using for ARPDAU, nor why the 2-day rate matters, because DAU is already measured over a period of time (in other words, it's not clear from the question whether the calculation is such that we can assume DAU is constant).2012-07-24

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Lets label Dau $= D$, retention rate$=R$ and arpau $=P$ and Lifetime$=L$. Im guessing your DAU is for day 1. for any day n, The amount of money you make each day is$ D*R^{(n-1)}*P$. so the sum of the cash you make with a game is $$ \sum\limits_{n=1}^L D*R^{(n-1})*P$$ using wolfram alpha. Using this formula for game A you get: $$ \sum\limits_{n=1}^{30} 175000*.32^{(n-1)}*.05\approx 12867.6$$ Using it for game B you get $$\sum\limits_{n=1}^{15} 150000*.22^{(n-1)}*.08\approx 15384$$ (I did these computations using wolfram alpha. I would appreciate it if someone double checkes using mathematica.) Also, this is based on what I understood from the question.

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    Do not have Mathematica. It costs money. But a grocery store calculator can handle it. For first sum, terms from $n=31$ on are negligible. So for all practical purposes (error $\lt 10^{-10}$ dollars!) answer is $(175000)(0.05)/(0.68)$.2012-07-24
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    @AndréNicolas what o understood from the wuestion is the following: at day one, 175,000 people play the game. at day two. only 32% of the poeple who played at day one will play at day 2. at day 3 only 32% of th epeople that played at day 2 play. I think that this is what he meant because he added a "life expenctancy to the game" also he accepted the answer. He didn`t make it clear but i think this is what he meant.2012-07-24
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    I agree that is the likely interpretation. All I was saying in the comment is that the numbers you got can be computed with no help from fancy program.2012-07-24
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Assuming that DAU stands for "daily active users" and ARPDAU stands for "daily revenue per daily active user", then $$\text{daily revenue}=\textit{DAU}\cdot \textit{ARPDAU}$$ So the revenue of A is $8750 \$/\textrm{day}$, and the revenue of B is $12000 \$/\textrm{day}$. The other parameters are irrelevant.