Optimal betting considering future opportunity

[David Spence]

Kelly betting is what many of us use as at least one factor (OK, usually it’s not the most important factor, but bear with me) in determining how much to bet. One shortcoming it seems to have is that it only takes into account the present situation. I realize that it considers the future by preserving current wealth, but this doesn’t take into account that future opportunities may be much better than the present one.

For a trip I plan to take, I’ll first be playing a very marginal game with a ~3% edge for about 10 hours. After that, I’ll be playing a much better game with a ~20% edge for about 10 hours (travel logistics prevent me from playing the better game first, or for all 20 hours). Should I consider the potential opportunity cost of not being able to bet as much at the better game resulting from losing money at the marginal game?

Consider a simpler(?) case: you first play one round of Game A. In Game A, you have a .9 probability of losing your wager, and a .1 probability of winning 1000 times your wager. You then play one round of Game B. In Game B, you win 10,000 times your wager with certainty. How much of your $10,000 bankroll would you wager on Game A? Even though Game A has an astronomical ev, most APs probably wouldn’t wager anything close to full or half or whatever Kelly fraction with which they might normally feel comfortable. Instead, they’d likely save virtually all of their bankroll for Game B and the $100,000,000 guaranteed win. Here, you could treat each dollar as being worth $10,000, since that’s exactly what you’ll get in Game B. So when you risk $1 in Game A, you’re really risking $10,000. This could be an argument for wagering 1/10000 Kelly in Game A, and similar reasoning could be used for the more complicated situation mentioned in the previous paragraph.

I realize this discussion is a little muddled, and it’s not entirely clear whether I’m asking a question or just rambling. But I suspect I’m not the first to consider this common situation, and I was wondering what others’ thoughts might be.

 

[FLASH1296]

Not only are you rambling somewhat, but your figures re: advantages
of 3% and 20% are from way out in the vicinity of the Twilight Zone.

 

[sagefr0g]

Kelly betting is what many of us use as at least one factor (OK, usually it’s not the most important factor, but bear with me) in determining how much to bet. One shortcoming it seems to have is that it only takes into account the present situation. I realize that it considers the future by preserving current wealth, but this doesn’t take into account that future opportunities may be much better than the present one.

For a trip I plan to take, I’ll first be playing a very marginal game with a ~3% edge for about 10 hours. After that, I’ll be playing a much better game with a ~20% edge for about 10 hours (travel logistics prevent me from playing the better game first, or for all 20 hours). Should I consider the potential opportunity cost of not being able to bet as much at the better game resulting from losing money at the marginal game?

Consider a simpler(?) case: you first play one round of Game A. In Game A, you have a .9 probability of losing your wager, and a .1 probability of winning 1000 times your wager. You then play one round of Game B. In Game B, you win 10,000 times your wager with certainty. How much of your $10,000 bankroll would you wager on Game A? Even though Game A has an astronomical ev, most APs probably wouldn’t wager anything close to full or half or whatever Kelly fraction with which they might normally feel comfortable. Instead, they’d likely save virtually all of their bankroll for Game B and the $100,000,000 guaranteed win. Here, you could treat each dollar as being worth $10,000, since that’s exactly what you’ll get in Game B. So when you risk $1 in Game A, you’re really risking $10,000. This could be an argument for wagering 1/10000 Kelly in Game A, and similar reasoning could be used for the more complicated situation mentioned in the previous paragraph.

I realize this discussion is a little muddled, and it’s not entirely clear whether I’m asking a question or just rambling. But I suspect I’m not the first to consider this common situation, and I was wondering what others’ thoughts might be.

i haven't read your full post, lol, just enough to get somewhat a sense of what you are saying, sorta thing.
but whatever, i hope this thread goes on and we learn something, cause whatever i believe there are some real serious issues that your post points to.
things like kelly betting and frequency of plays in the real world, sorta thing. then there is the fact that we attack all sorts of games, different games or the same games of various flavors, sorta thing.
so yeah, this is an important topic.
and as i believe you allude, who the heck plays kelly betting full throttle anyway. then too, isn't kelly betting have really when you get down to the nitty gritty, all kinds of ways of thinking about it? like how much groceries cost, lol.
whatever, this is a rush job for me, gotta get going, but i hope this thread goes on.
just would add, these kinds of questions, to me point to the idea that one definitely needs to think stuff out, not just go blindly without full understanding of all the issues, lol.

 

[aslan]

Not only are you rambling somewhat, but your figures re: advantages
of 3% and 20% are from way out in the vicinity of the Twilight Zone.

Unless he's talking about a good counting situation (great rules, great pen) versus a hole card/shuffle tracking opportunity with counting thrown in to boot. The latter should occur somewhere this side of the twilight zone, don't you think, although it wouldn't do me much good except for the the most blatant form of hole carding opportunity?

 

[David Spence]

Thank you for the thoughtful responses so far. I hope the discussion remains focused on the original issue of how to bet considering future advantage, rather than on the mechanism or plausibility of obtaining the given advantages. If it helps, pretend the games are 1% and 7% (or .3% and 2%, or whatever numbers you won't object to). I do, however, think the absolute magnitude of the numbers is relevant. For example, in the .3% and 2% case, the best advice would be, "Don't play the first game!" or, depending on your standards, "Don't play at all!"

 

[blackjack avenger]

Kelly or Not

If you have a 1% advantage you bet it.
If you have a 3% advantage you bet it.
If you have a 5% advantage you bet it.

Perhaps be sure to not overly fatigue yourself on the marginal game before the better opportunity.

Now, Kelly starts to break down with large advantages, and given the uncertainty of our real world advantage it's best to bet a fraction of kelly. Also, we cannot decrease our bets below table minimum, so another reason to bet fractional kelly.

:joker::whip:

 

[sagefr0g]

If you have a 1% advantage you bet it.
If you have a 3% advantage you bet it.
If you have a 5% advantage you bet it.

Perhaps be sure to not overly fatigue yourself on the marginal game before the better opportunity.

Now, Kelly starts to break down with large advantages, and given the uncertainty of our real world advantage it's best to bet a fraction of kelly. Also, we cannot decrease our bets below table minimum, so another reason to bet fractional kelly.

:joker::whip:

yeah, ok, that was something i meant to mention, like wouldn't the idea be to understand each scenario piece by piece or play by play sorta thing, set yourself up properly for each. then wouldn't it all just be additive?
so i guess maybe the question on the matter is the question of devoting ones time to the various scenario's in the most efficient way possible.
but whatever, far as going full kelly on some rare play, my guess is probably not, or at least not with one's full bank.
whatever this stuff is something to think over for sure.
still in a rush here, sleepy too, lol, i hope i'm even in the same ballpark as the OP.

 

[21forme]

A 3% advantage is nothing to sneeze at. I would play it. In this case, I would bet so my ROR is in the 1-2% range.

Based on the edges you give, you're probably HCing. If it's 3CP, don't neglect the significantly higher variance of the game compared with BJ in your ROR calcs.

 

[assume_R]

Firstly, Avenger, what do you mean by:

Now, Kelly starts to break down with large advantages

?

Secondly, now you could think of an analogous situation in card counting, where the TC is +2, and you have a 1% advantage. Should you bet a bit less, waiting for the TC of +10, when you have a 5% advantage so you can be more then? In my understanding, the answer is no; for a given present situation, you bet proportional to EV/Var. Don't save $$ for possible future situations with a higher EV/Var.

If you have a choice at the current moment between 2 games, play the game with the higher EV/Var value. But saving for the future higher EV situations would be like only minimum betting at TC of +1, +2, and +3 so that you can place a higher wager when the TC reaches +4. Seems incorrect.

Just my 2 cents.

 

[blackjack avenger]

Kelly Breakdown

Kelly assumes a simple plus 1 minus 1 payoff
with bj we have the variance due to spl and dbl
so
If you place a large bet due to a large advantage then the following spl dbl situations that may arise; which will have a smaller advantage, will influence how you would play your hand.

Regular smaller advantage hands in bj we can account for the variance.

:joker::whip:

 

[assume_R]

Ah, thanks avenger.

 

[David Spence]

Firstly, Avenger, what do you mean by: ?

Secondly, now you could think of an analogous situation in card counting, where the TC is +2, and you have a 1% advantage. Should you bet a bit less, waiting for the TC of +10, when you have a 5% advantage so you can be more then? In my understanding, the answer is no; for a given present situation, you bet proportional to EV/Var. Don't save $$ for possible future situations with a higher EV/Var.

If you have a choice at the current moment between 2 games, play the game with the higher EV/Var value. But saving for the future higher EV situations would be like only minimum betting at TC of +1, +2, and +3 so that you can place a higher wager when the TC reaches +4. Seems incorrect.

Just my 2 cents.

I agree with what you've said above with regard to card counting. But I'm not sure it's analogous to the situation I originally described. There, you know you're going to have an edge of ~20% for 10 hours. That is, it's not just a possible future situation with a higher ev/var; it's a (near) certainty. With card counting, even if you play long enough to be assured of a future TC of +10, it certainly won't last for more than the remainder of a shoe, or for a few hands in a pitch game.

Now the answer might still be the same in both cases: don't worry about the future. But I'm not sure the analogy proves this answer.

Say the best game you'll ever find is 1%, and that's the game you're presented with today. Now pretend that you can find a 10% game every day but today. I think most people would be more likely to play today in the first situation than in the second. Granted, bankroll preservation might not be the only concern here--wanting to maintain a high hourly wage could be a factor. However, this does illustrate that it might be reasonable to consider the future when making a present decision.

 

[blackjack avenger]

Subjective vs Objective?

I agree with what you've said above with regard to card counting. But I'm not sure it's analogous to the situation I originally described. There, you know you're going to have an edge of ~20% for 10 hours. That is, it's not just a possible future situation with a higher ev/var; it's a (near) certainty. With card counting, even if you play long enough to be assured of a future TC of +10, it certainly won't last for more than the remainder of a shoe, or for a few hands in a pitch game.

Now the answer might still be the same in both cases: don't worry about the future. But I'm not sure the analogy proves this answer.

Say the best game you'll ever find is 1%, and that's the game you're presented with today. Now pretend that you can find a 10% game every day but today. I think most people would be more likely to play today in the first situation than in the second. Granted, bankroll preservation might not be the only concern here--wanting to maintain a high hourly wage could be a factor. However, this does illustrate that it might be reasonable to consider the future when making a present decision.

Wanting to maintain a high hourly wage is subjective, matter of opinion. A player may also not want to sit out a day and lose income, even if a smaller amount. Neither opinion is wrong.

The math or objective answer is you bet ev/var with whatever game you are confronted with or choose to play.

Now if the weaker game has a much higher variance and one is concerned that a big negative move would hurt their bank for the better game that may be something to consider.
However,:joker::whip:
Better games often have higher variance because we bet more.


:joker::whip:

 

[sagefr0g]

.....
Say the best game you'll ever find is 1%, and that's the game you're presented with today. Now pretend that you can find a 10% game every day but today. I think most people would be more likely to play today in the first situation than in the second. Granted, bankroll preservation might not be the only concern here--wanting to maintain a high hourly wage could be a factor. However, this does illustrate that it might be reasonable to consider the future when making a present decision.

from your perspective above it just seems following the wizard of odds commandments fits the bill: (especially #8)
http://wizardofodds.com/gambling/tencom.html

8. Thou shalt covet good rules.

(8. Rules vary from casino to casino. To improve your odds know good rules from bad and then seek out the best rules possible. )

so from the exact scenario mentioned, it seems you would wait a day and play the better conditions.
thing is how based in reality is the situation, would more complicated real world scenarios change the answer?:whip:

whatever still to me this thread i think points to really interesting issues and questions.

 

[blackjack avenger]

Saving For A Rainy Day, But Never Rains

So we should not bet TC1 because a better opportunity is in the future?
So we should not bet TC2 because a better opportunity is in the future?
So we should not bet TC3 because a better opportunity is in the future?
So we should not bet TC9 because a better opportunity is in the future?
So we should never bet because a better opportunity is in the future?

:joker::whip:

 

[sagefr0g]

So we should not bet TC1 because a better opportunity is in the future?
So we should not bet TC2 because a better opportunity is in the future?
So we should not bet TC3 because a better opportunity is in the future?
So we should not bet TC9 because a better opportunity is in the future?
So we should never bet because a better opportunity is in the future?

:joker::whip:

wong it how you wanna wong it?
never say never?
:whip:

 

[blackjack avenger]

Is Optimal Discretionary?

wong it how you wanna wong it?
never say never?
:whip:

Sure bet how you want
but
The original ? was about betting optimally.

:joker::whip:

 

[Pro21]

As a practical matter this seems an easy problem. Figure out what the approx worst loss you can take in both games and bring that much cash.

 

[David Spence]

As a practical matter this seems an easy problem. Figure out what the approx worst loss you can take in both games and bring that much cash.

Done and done.

 

[zengrifter]

If you have a 1% advantage you bet it.
If you have a 3% advantage you bet it.
If you have a 5% advantage you bet it.

That is not exactly correct, as pertains to BJ. The optimal K-bet would be more like 60-70% of the edge. zg