Optimal betting considering future opportunity
- Thread starter David Spence
- Start date
It doesn't matter the order of the games. If you play a great game first, then a decent game later, or vice versa, you'd still bet the optimal percentage of your bankroll. You get a certain percentage, you earn a certain percentage of that, and your overall expected end result is essentially BR*bet_percentage*edge, and that becomes your new bankroll. If you play two different games/bets then BR*bet_percentage1*edge1*bet_percentage2*edge2 is the same thing as BR*bet_percentage2*edge2*bet_percentage1*edge1. It doesn't matter which you play first. Obviously the math looks slightly different if you are comparing the log utility or whatever for Kelly betting, but the end result is the same: it doesn't matter which bet comes first. If you know you are going to bet more than once, you still calculate the optimal bet for each independently.
If you bet $991, you have a 10% chance of winning $991,000 on game A and having a final bankroll of $10,010,000,000, and a 90% chance of ending up with $90,090,000. The expected utility of that result is 0.1*log(10,010,000,000)+0.9*log(90,090,000)=8.159. With no bet on game A, we end up with a final BR of $100,000,000 with probability 1. The expected utility of that is 1*log(100,000,000)=8.000, so if your utility function matches the assumptions that go along with the Kelly betting theory, then you should still bet the first positive EV game without regard for possible better games in the future. Think of it this way: yes, you are risking your capital that might be better utilized in a later game, but if you win (and you do have an edge), then you will have even more money to attack that next game.
The caveat here would be if you are sizing your bets based on a total bankroll, but your trip BR is smaller and you can't get any more cash in time to play the better game. Similar issues apply if you are concerned about CTRs or other buy in limits.
If you bet $991, you have a 10% chance of winning $991,000 on game A and having a final bankroll of $10,010,000,000, and a 90% chance of ending up with $90,090,000. The expected utility of that result is 0.1*log(10,010,000,000)+0.9*log(90,090,000)=8.159. With no bet on game A, we end up with a final BR of $100,000,000 with probability 1. The expected utility of that is 1*log(100,000,000)=8.000, so if your utility function matches the assumptions that go along with the Kelly betting theory, then you should still bet the first positive EV game without regard for possible better games in the future. Think of it this way: yes, you are risking your capital that might be better utilized in a later game, but if you win (and you do have an edge), then you will have even more money to attack that next game.
The caveat here would be if you are sizing your bets based on a total bankroll, but your trip BR is smaller and you can't get any more cash in time to play the better game. Similar issues apply if you are concerned about CTRs or other buy in limits.
ok optimal.talking about one day circa 10hrs, a not so great game
then till yer pushing up daisies a much better game, sorta thing is how i thought it was clarified from the original post.
so i guess that sort of a wild ( but not so unreal life like) scenario is what gets my interest.
heck i dunno, just to me maybe, is a billionaire wall street banker gonna have his limo pull over at the side of a road so he can get out and pick up some discarded aluminum cans that he can later convert into cash at some recycling center? well, maybe the oracle of Omaha would, lol, he's lived in a thirty one grand house since 1957. lol.
but whatever, i guess really when it comes to advantage and frequencies, even if some advantage is not so frequent while another is really, really frequent, then i guess it really doesn't matter play it all if it floats your boat, lol. long as you really have an advantage, sorta thing, i guess.
just me maybe, i feel really confident when i'm faced with an advantage play field that has lots and lots of plays.
on the flip side, when i'm faced with an advantage play field that has only the likelihood of a few plays, i feel less confident.
One Man's Aluminum is Another's Gold
Maybe his niece is with him and he wants to show the importance of recycling, perhaps how he made his money? Its a matter of choice what one want's to do with their time and money, but once they decide to gamble there are optimal or near so ways to do it.
Sure, many plays are better from a realization of EV perspective, but an advantage play is an advantage play. If your local casino was closing in a week would you not play because of variance? If you have a rare occasion for a very high EV situation would you not play it? Let's say you play that very rare high EV situation and lose. Then what? if you play a lot that one play will diminish in importance to your overall results over time. Also, if you keep playing you will probably have that rare high EV event happen again and if you get enough of them you will probably come out ahead.
:joker::whip:
Maybe his niece is with him and he wants to show the importance of recycling, perhaps how he made his money? Its a matter of choice what one want's to do with their time and money, but once they decide to gamble there are optimal or near so ways to do it.
Sure, many plays are better from a realization of EV perspective, but an advantage play is an advantage play. If your local casino was closing in a week would you not play because of variance? If you have a rare occasion for a very high EV situation would you not play it? Let's say you play that very rare high EV situation and lose. Then what? if you play a lot that one play will diminish in importance to your overall results over time. Also, if you keep playing you will probably have that rare high EV event happen again and if you get enough of them you will probably come out ahead.
:joker::whip:
Out of action is a cardinal sin in this game.
One extremely important variable that hasn't yet been mentioned in this thread is the $10K CTR rule. Many AP's are loathe to risk more than that amount in a 24 hour period, due to the fact that they're often playing under an assumed identity.
Suppose my BR is enough to be able to afford a 10K bet on a 1% advantage. If I lose the hand, (which I WILL about half the time); I can't play in that casino for 24 hours. This is an obvious case in which I would be CRAZY to bet the amount which is optimal to my BR.
Unless they have a line of credit, or have chips in their pocket, or some OTHER way to legally go over 10K, most HC'ers will end up playing to an imaginary BR of only 10K rather than to their ACTUAL bankroll. So as you can see, deciding upon the optimal bet size CAN often be a balancing act.
Anyways; in answer to the question presented by the OP: In the REAL world, future betting opportunity is very often the deciding factor when calculating optimal bet size - MUCH more often than you might think!
One extremely important variable that hasn't yet been mentioned in this thread is the $10K CTR rule. Many AP's are loathe to risk more than that amount in a 24 hour period, due to the fact that they're often playing under an assumed identity.
Suppose my BR is enough to be able to afford a 10K bet on a 1% advantage. If I lose the hand, (which I WILL about half the time); I can't play in that casino for 24 hours. This is an obvious case in which I would be CRAZY to bet the amount which is optimal to my BR.
Unless they have a line of credit, or have chips in their pocket, or some OTHER way to legally go over 10K, most HC'ers will end up playing to an imaginary BR of only 10K rather than to their ACTUAL bankroll. So as you can see, deciding upon the optimal bet size CAN often be a balancing act.
Anyways; in answer to the question presented by the OP: In the REAL world, future betting opportunity is very often the deciding factor when calculating optimal bet size - MUCH more often than you might think!
this is sort of the thing that really gets my interest about the original post.
the original post reminds me of these sorts of situations.
i'll probably be roasted, toasted and put out to dry over this one, but here goes, and at least i have as an out of an excuse as i'm no professional and if i was working for a pro i wouldn't do what i'm gonna describe.
there are various scenarios, but here is one.
i have an advantage play that i don't fully understand. what i think it has is a relatively modest expected value with a relatively high standard deviation.
the nature of the plays are such that they are relatively few and far between but sometimes fast and furious when they present. additionally near the end of a night they tend to dwindle down to a trickle.
and so here comes my sin, lol, pretty much i will base my decision on whether to stay in the casino and make those last few plays (which are uncertain if they will even present) on how my actual results of the previous plays have measured up with respect to what i think is expected value and standard deviation.:whip:
the original post reminds me of these sorts of situations.
i'll probably be roasted, toasted and put out to dry over this one, but here goes, and at least i have as an out of an excuse as i'm no professional and if i was working for a pro i wouldn't do what i'm gonna describe.
there are various scenarios, but here is one.
i have an advantage play that i don't fully understand. what i think it has is a relatively modest expected value with a relatively high standard deviation.
the nature of the plays are such that they are relatively few and far between but sometimes fast and furious when they present. additionally near the end of a night they tend to dwindle down to a trickle.
and so here comes my sin, lol, pretty much i will base my decision on whether to stay in the casino and make those last few plays (which are uncertain if they will even present) on how my actual results of the previous plays have measured up with respect to what i think is expected value and standard deviation.
:whip: