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View Full Version : Hypothetical Casino running/risk of ruin equation question.

ohgeetee
10-23-2004, 02:20 AM
Lets say I were running a casino game where on a computer, i pressed a button that gave a random number from 100-1000, and the sucker pressed a button that gave a random number between 1-1000, and if his roll beat mine, I paid him 1:1 and if I won i kept his bet. I have \$100k in funds to run this casino, and more than enough suckers to play the game.

What should my range of allowed bets be to avoid risk of ruin, and what is the equation to come up with this?

please assume there is no trickery, all numbers are whole and perfectly random, etc. Its a clean game except for the exceptional odds in favor of the casino.

reid savid
10-23-2004, 04:44 AM
\$0.00 You cannot avoid risk of ruin, only minimize it. Hope this helps.

dogmeat
10-23-2004, 01:03 PM
\$100,000 = -{SD^2/(2*WR)}*LN(ROR)

\$100,000 is your bankroll
ROR is your accepted (desired) risk of ruin

Leo99
10-23-2004, 02:17 PM
That's a good question. Yeah, what Dogmeat said. First you need to state your ROR. If it's zero then you can't play. Just like any casino in the world, there's a risk you'll go bankrupt. The lower the risk you're willing to take the higher the bankroll you'll need to ensure the law or large numbers works in your favor. The casino commisions make sure the casinos have a certain bankroll sufficient to payoff the customers should the casino have a run of bad luck.

ohgeetee
10-23-2004, 09:52 PM
What are LN and WR in the above equation? SD is standard deviation?

Avoiding ROR was bad wording, but what I was looking for was an equation that Ic ould plug in different RoR% and see the changes.

BruceZ
10-24-2004, 07:24 PM
[ QUOTE ]
What are LN and WR in the above equation? SD is standard deviation?

Avoiding ROR was bad wording, but what I was looking for was an equation that Ic ould plug in different RoR% and see the changes.

[/ QUOTE ]

LN is the natural logarithm, WR is the win rate, and SD is the standard deviation. Here is an easier equation you can use which is also exact:

ror = (0.451/0.548)^B

where B is the bankroll size in bets. For example, if you want a ror of 1%, B = 23.64 bets. So if your bankroll is \$100,000, each bet can be 100,000/23.64 = \$4230.

0.548 is your probability of winning a bet since you always win 99/1000 times that he picks 1-99, and you win half the time that he picks 100-999 unless you tie, so your probability of winning is 99/1000 + 900/1000 * (.5 - 1/901) = 0.548. His probability of winning is 0.451

Solving for B gives:

B = ln(ror) / ln(.451/.548)

where ln is the natural logarithm (or you can use base 10 logs here too). For a derivation, see the first part of my derivation of the full ror formula in this post (http://forumserver.twoplustwo.com/showthreaded.php?Cat=&amp;Number=683150&amp;page=0&amp;view=ex panded&amp;sb=5&amp;o=14&amp;fpart=2#Post682045683150).

ohgeetee
10-25-2004, 04:24 PM
Bruce, as always, you are the man.

Thank you for a succinct explanation in easier to grasp terms than the raw probability formula.