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# Need help figuring out the "House Take" over time.

Fri 8 Mar, 2013 02:16 am
I am trying to figure out a formula(s) that will help me figure out how much casinos make on ongoing transactions where they take a "vig" or "take" (for a lack of a better word)....but I've always been terrible at modeling things so I just can't figure it out. It's been a good 20 years since I learned this stuff in school. Wanna Help?

Here is how the games work. Lets say there are 2 players, Player A and Player B. Each has a starting balance of \$100.00. They enter a game with an entry fee of \$10. (they both have a \$90 balance at this point). The contest runs and Player A wins....lucky him. Player A gets \$18 in winnings. The "House" takes \$2 for its trouble (this represents 10% of the total entry fees and is the "take"). This leaves Player A with \$108 (\$100 - \$10 + \$18) and Player B with \$90 (\$100 - \$10 + \$0), while the "House" has \$2.

Now, lets say they both play the exact same contest AGAIN but this time Player B wins. Their balances look like this now. Player A has \$98 (\$100 - \$10 + \$18 - \$10) and Player B has \$98 (\$100 - \$10 + \$0 - \$10 + \$18), while the "House" has \$4 (\$2 + 2\$).

If the two players continue to battle back and forth each winning every other turn, how long until the "take" catches up with them and they run out of money? Now...I know the answer is 100 contests because I modeled this process in Excel and cut & pasted until the balances for both reached \$0 and the house had all \$200. I then tried to create a formula to model how much the house will take in given X number of contests played...but I failed....terribly.

So the real question here is, how can I determine how much the "House" will make in 1,2...10...n number of contests? And how many contests would be required for the "House" to clean out say 2, 3, 4, 5, ....y competitors of all their money (assuming round robin wins, equal bank rolls and a 10% house "take"....I understand that if one person is dominant and wins every time, that will cut the contests short and the house will make less money because there will be less transactions...which actually brings up a good point....what would be the worst case scenario in that case??...this isn't critical but would be good to know)

Any help would be greatly appreciated!

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markr

1
Fri 8 Mar, 2013 11:12 am
@mas,
In a two player game, since the house takes \$2/game, after n games, the house will have won 2n dollars.
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markr

1
Fri 8 Mar, 2013 01:46 pm
@mas,
Worst case for the bank in an n-player game is one player winning 10 games. The bank would make only 10*n dollars.

Assumption: All n players play together in the 10 games. Perhaps that's not what you intended (round robin wins).
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markr

1
Fri 8 Mar, 2013 02:09 pm
@mas,
Quote:
If the two players continue to battle back and forth each winning every other turn, how long until the "take" catches up with them and they run out of money? Now...I know the answer is 100 contests because I modeled this process in Excel and cut & pasted until the balances for both reached \$0 and the house had all \$200. I then tried to create a formula to model how much the house will take in given X number of contests played...but I failed....terribly.

Chances are that one player will run out of money before the other.

I think you need to better define the problem that you seek a solution to. The game/payouts seem straightforward, but can more than two play in the same game? Do players always start with \$100? Are you looking for an expected value for the bank after n rounds, or until all players are broke except for one? Is this a game of skill or chance - do two (or more) players all have the same chance of winning?
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