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#1
04-28-2007, 03:01 PM
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I invented a new gambling game
I just "invented" a new gambling game.
I say "invented" because I just thought it up, and I've never heard of it, but I'm sure someone else has run this game long before I was born. It's a variation of the old "Matching Quarters" game. I call it "Throwing Pennies." It work like this: I have a cup and three pennies (or any other coin). I charge my customer one dollar to "throw the pennies." This is the key point - The customer doesn't wager a dollar, I charge him a dollar. The customer throws the pennies. If they come up all heads or all tails, then the customer wins three dollars. If one of the pennies is odd, then they don't win anything. Simple as that. Since I keep the customer's dollar if he wins or if he looses, then I have a "house edge." My expectation is $0.25 per throw. So after 100 throws, I could expect to "win" 75 throws, "loose" 25 throws and have a net win of $25.00. Or I should say "per 100, over the long run." My question for you math-types is what would be my standard diviation and risk of ruin? Or more specificly, how much money will I need to have (in one dollar bills) to make it unlikely someone will "break the bank?" 
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#4
04-30-2007, 01:39 PM
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Re: I invented a new gambling game
[ QUOTE ]
This is the key point - The customer doesn't wager a dollar, I charge him a dollar. [/ QUOTE ] Yes he does wager a dollar--he wagers it getting 2-1 odds. He's getting 2-1 odds on an event that is 3-1 to occur, so of course you tend to make a large profit with such a game. I would worry about finding 'customers' for such a shallow game more than risk of ruin. Most gamboooling games need to be complex enough so that players cannot quickly or easily compute the chances of winning, but simple enough so they can understand the rules. This game fails the first requirement IMO.
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#7
05-08-2007, 06:06 PM
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Re: I invented a new gambling game
Your win rate is $0.25/throw
your std dev is sqrt{[(-2-0.25)^2 + 3*(1-0.25)^2]/4} = $1.30/throw On a per 100 throw basis this works out to: winrate = $25/100 throws std dev = $0.13/100 throws In poker, your std dev per 100 hands is usually 2 to 5 times higher than your win rate. Here your win rate is almost 200 times higher than the std dev. So this game will have 400 times less variance than even the most reliable poker games. Your risk of ruin is basically zero (I doubt you'd need more than $50). To make this game comparrable to poker, you'd have to give them $3.98 when they win. That should put your "risk" in perspective.
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#8
05-12-2007, 12:29 AM
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Re: I invented a new gambling game
well, if your stdev per throw is $1.30 your stdev per 100 throws is $1.30 * sqrt(100) = $13 - don't divide by 100.
[ QUOTE ] Your win rate is $0.25/throw your std dev is sqrt{[(-2-0.25)^2 + 3*(1-0.25)^2]/4} = $1.30/throw On a per 100 throw basis this works out to: winrate = $25/100 throws std dev = $0.13/100 throws In poker, your std dev per 100 hands is usually 2 to 5 times higher than your win rate. Here your win rate is almost 200 times higher than the std dev. So this game will have 400 times less variance than even the most reliable poker games. Your risk of ruin is basically zero (I doubt you'd need more than $50). To make this game comparrable to poker, you'd have to give them $3.98 when they win. That should put your "risk" in perspective. [/ QUOTE ]
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#9
05-12-2007, 03:37 AM
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Re: I invented a new gambling game
[ QUOTE ]
well, if your stdev per throw is $1.30 your stdev per 100 throws is $1.30 * sqrt(100) = $13 - don't divide by 100. [/ QUOTE ]Quite true...variance always INCREASES with larger samples, which is a counterintuitive result. A good way to remember it is to square the SD to get variance per game (or 100 hands, etc). Variance is more convenient than SD since variance can be added to compute variance for the sum of independent events (then taking the square root to get back to SD terms). This does, of course, have the same effect as multiplying the SD by the square root of the sample size, but it's a little less cryptic.
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