Casino Whoring; Risk of ruin question

[MrMon]

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It doesn't take that much longer and given enough hands, you should trend back to where you belong, providing you are playing correctly.

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Nonsense. There is no restoring force.

Betting tiny amounts is a waste of time. By betting $2/hand instead of $4/hand, you saved the equivalent of taking a coin-toss for $60, and you required an extra 360 hands. It's hard to imagine that this was a good trade for you.

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You are correct. There is no restoring force. But there is a trend toward the average. Wild swings either way will even out over a large number of hands. I'm not a statistician, so I can't tell you if the number of hands difference between $2 and $4 is a large enough number of hands. But you know what I mean.

As for it being a waste of time, an extra 360 hands at 3 hands per round is 120 rounds. I doesn't take that much time, say 45 minutes. A coin toss for $60 is worth $30, so if it takes me 45 minutes, that's $40/hr. Not bad.

Besides, it was more fun that way.

[pzhon]

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As for it being a waste of time, an extra 360 hands at 3 hands per round is 120 rounds. I doesn't take that much time, say 45 minutes. A coin toss for $60 is worth $30, so if it takes me 45 minutes, that's $40/hr. Not bad.

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You misunderstood. The amount of variance you saved by betting at $2/hand rather than $4/hand was about the same as the variance of a fair coin-toss for $60. How much would you be willing to pay to avoid winning or losing $60 with probability 50%? I'd pay less than $1, but however much you are willing to pay is what you saved with that extra 45 minutes.

By the way, for someone winning 2 BB/100 at $2-$4, playing 100 hands is like getting $8, then taking a coin-toss for $60, then wasting 90 minutes (or less, for a multitabler). If you ignore the time spent and entertainment value, such a $2-$4 player should be unwilling to give up $8 to avoid a fair coin-toss for $60.

By the way, the above analysis ignores the fact that you were playing 3 hands at once, which has a greater variance than playing 1 hand at a time.

[pzhon]

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EV = 50 - (0.0019*3000) = 44.3
SD = sqr(3000*2) = 77.5
Bankroll > 77.5^2/44.3 = 135

So with a bankroll of more then £135 I would likely clear the £3000 WR with £2 bets despite SD fluctuations.


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I said that you need to worry if SD^2/EV>B, but not that you don't have to worry if your bankroll is larger. You may want to set a comfort level c, and only accept wagers where SD^2/EV > c*B. Many people seem to prefer a value of c between 2 and 4, and this can correspond to the oft-repeated figure of 300 BB for limit Hold'em. These people would prefer to have a bankroll of 270-540.

It's a slightly more complicated problem to optimize your bet size given that you are risk averse but you value your time.

By the way, the variance is slightly greater in Pontoon than in blackjack.

Ok. Thanks for the input.

Best,

Ralf