# Thread: Profit and Probability

1. ## Profit and Probability

Given a game with a probability of 1/x and a payout of y:1 where y=x/2 and a number of players n, where n>x and n%x=0. Build a distribution of profits and indicate the confidence limits for CI=.95 and CI=.90. Assume each player bets the same amount.

So far I understand the the payout is 50%.

And also the the number of players is a multiple of the probability...

This must be just to simplify?
And also should allow us to model the thing on n=x right?.

Consider n=x then:

Each player has a 1/x chance of winning, but profits depend on payouts, and there are chances that more than one person *could* win, in which case your profits would be nil or negative. 2 people winning would mean nil, anything more than that would be negative, and anything less than 1 would be 100% profit.

And, now I'm lost... Not even sure where to start...

2. This is the way I understand it...

We'll work out an example: Let x=4 and n=4, and each person bets 1.
ie game probability = 1/4, payout is 2:1, and 4 players.

Each player has 2 possible profits: -1 (probability=3/4), or +2 (probability=1/4).
So the distribution of profits for all 4 players is
+8 (probability=1/256), +5 (probability=12/256), +2 (probability=54/256), -1 (probability=108/256), or -4 (probability=81/256)

I assume that's what they mean by "build a distribution". And when they say "indicate the confidence limits", I guess they mean the CL for all profits.

3. I think they want the SD, and the profits are for the game owner, not the players...

4. Let be the profit for the game owner.
Let be the number of players win.

Then

Then you can build the model from this..

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