dk
dk
Joined: Nov 2, 2009
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November 23rd, 2009 at 4:27:09 PM permalink
About 15 years ago, I took place in a free Casino Night. We started with play money and at the end of the night there was an auction where you use your remaining money to bid on prizes. The money had no value after the auction and each person could only walk out with one prize.

The "croupiers" running the casino night were volunteers and obviously not all of them knew the rules. In particular, roulette paid 2:1 for red/black and odd/even bets and 3:1 for 1-12/13-24/25-36 bets.

What is the best betting system for this scenario? Is this where the Kelly Criterion would be used? Would it matter if I knew the number of trials remaining before the end of the session?

I think I ended up betting 1/3 of my bankroll on red, 1/3 on black, and holding 1/3 in case green hit. At the end of the night I left with a nice golf bag, but I was far from the big winner.
The ratio of people to cake is too big.
JupiterJones
JupiterJones
Joined: Nov 23, 2009
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November 23rd, 2009 at 7:07:37 PM permalink
Quote: dk

About 15 years ago, I took place in a free Casino Night. We started with play money and at the end of the night there was an auction where you use your remaining money to bid on prizes. The money had no value after the auction and each person could only walk out with one prize.

The "croupiers" running the casino night were volunteers and obviously not all of them knew the rules. In particular, roulette paid 2:1 for red/black and odd/even bets and 3:1 for 1-12/13-24/25-36 bets.

What is the best betting system for this scenario? Is this where the Kelly Criterion would be used? Would it matter if I knew the number of trials remaining before the end of the session?

I think I ended up betting 1/3 of my bankroll on red, 1/3 on black, and holding 1/3 in case green hit. At the end of the night I left with a nice golf bag, but I was far from the big winner.



Given those payouts, the expected value of the dozens bets is 26.3% and the red/black and odd/even bets are a whopping 42.1%! Obviously the red/black/odd/even bet is optimal (and has less volatility too), given a choice between those two.

Based on Kelly criterion (which would apply in positive-EV situations like this... although I'm not sure either how the enforced short-run affects things), you'd bet 21% of your bankroll each time:

(2 * 0.473684 - 0.526316) / 2 = 0.210526

It wouldn't matter if you bet on red or black (or odd or even).

JJ


P.S. Also, I suspect the "auction" part of the problem, along with the short-term aspect, would introduce some gnarly game theory into the mix. Like in tournament play, betting decisions might be influenced by the bankrolls of your fellow players. This is beyond my ken... :-)

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