Quote from: dooglus on June 18, 2014, 08:43:59 PM

Quote from: PacoMartin on June 18, 2014, 08:32:05 PM

Quote from: dooglus on June 18, 2014, 07:32:49 PM

Quote from: dooglus on June 18, 2014, 07:12:06 PM

When a player risks 1 unit at 33% for a 3x payout for example, the house is risking 2 units for a 1.5x payout with a 67% chance of winning. If you apply the Kelly Criterion on those numbers you'll see that it's still optimal to risk 1% of the bank.

f = (bp - q) / b

where f is the fraction to risk,
b is the payout multiplier minus 1
p is the probability of the house winning
q is the probability of the house losing

So your saying these are the optimum bets for the player, and not the house?
edge 1%
1-'edge' 99%

b	1	2	0.5
p	49.5%	33.0%	66.0%
q	50.5%	67.0%	34.0%
q/b	50.5%	33.5%	68.0%
f	-1.0%	-0.5%	-2.0%

Yes. You need to consider how much the house should risk, considering the odds the house is getting.

That is different than considering how much the player should risk, considering their odds.

It's not symmetrical, which is somewhat counter-intuitive.

Kelly criterion says that no players should ever play just-dice, nor should they go to vegas (except blackjack if you card count). However, Kelly criterion says casinos and Doog should allow players to play.