Question for Don: How much should you bet?

[MJ1]

So here is a question I seldom see discussed. Suppose a counter is in danger of tapping out his trip bankroll (oh no!). He is down to his last $600 and the count calls for a wager of $300. What fraction of his on hand capital should he bet? If you bet $300, then you risk losing EV if you have to split and double down on each split because you won't have enough money. There are other variations that would require 4x your initial bet, but you get the idea. Why is it such a big deal if you lose EV by not splitting or doubling? Is it really that much of a loss?

In theory, he could bet anywhere from 1/8, 1/6, 1/4, 1/2, or even the full amount of his leftover capital (maybe the count call for a $600 wager). Intuitively, I sense it would be either 1/2 over 1/4 of what he has left. Some of the big teams say the optimal bet is 1/6 of whatever you have on hand. Have you ever seen a mathematical treatment of this question or do you know of any simple math to justify wagering no more than 1/6th on hand capital?

Thanks,
MJ

[Freightman]

So here is a question I seldom see discussed. Suppose a counter is in danger of tapping out his trip bankroll (oh no!). He is down to his last $600 and the count calls for a wager of $300. What fraction of his on hand capital should he bet? If you bet $300, then you risk losing EV if you have to split and double down on each split because you won't have enough money. There are other variations that would require 4x your initial bet, but you get the idea. Why is it such a big deal if you lose EV by not splitting or doubling? Is it really that much of a loss?

In theory, he could bet anywhere from 1/8, 1/6, 1/4, 1/2, or even the full amount of his leftover capital (maybe the count call for a $600 wager). Intuitively, I sense it would be either 1/2 over 1/4 of what he has left. Some of the big teams say the optimal bet is 1/6 of whatever you have on hand. Have you ever seen a mathematical treatment of this question or do you know of any simple math to justify wagering no more than 1/6th on hand capital?

Thanks,
MJ

First comment is not to get stuck in that situation in the first place - however, there you are. I’ve been caught in that situation exactly once - I was playing out of town at a min $25 game. My wife called me to say that she found 20k in my pants while doing the wash. Whoops - I had only 2.5k on me - shit happens. Fortunately, a known and friend out of town player from a different locale than mine was also in town. We met for dinner and was I lent 10k. Even though I never went into that 10k, I most certainly leveraged it.

The first issue is the theoretical vs the practical. For sake of argument, theoretical should be optimal betting manicured to tolerance, bankroll, spread, rules, cut etc. Robotic betting on that formula usually assists one out the door in short order, provided competence is displayed. The second issue is to to modify approach that allows one to breathe for a longer period of time, assuming of course your approach is not slash and burn. Third, assuming of course that count is positive, no big deal if you lack funds for a double - you’re simply reducing EV. It is a big deal if you lack funds for split and a bigger deal if you lack funds for split after double. Too much EV lost - hence penalties paid for lack of funds. Provided backup funds are available elsewhere, it’s no shame to withdraw, regroup and come back fighting another day.

Now, how many bets should you have? Heads up, $350 bet, I once split to 4 hands all doubled. Now, that last double (for less, 8v6 true 3 or so remaining) - I could have easily reached into my pocket to maximize the bet, but that would have ruined the steam act. I recall another hand playing 2x75. Split to 8 hands with a couple doubled I’m sure.

My 2nd last comment on the subject - how serious are you and then make your own decisions. My last comment - I never run out of money - it’s there if I need it.

[aceside]

My last comment - I never run out of money - it’s there if I need it.

Interesting! I’ve never understood ROR but I am doing just fine in blackjack, but you seemingly don’t understand ROR either even though you are a veteran. Risk as much as you can afford to gain the max edge.

[Freightman]

Interesting! I’ve never understood ROR but I am doing just fine in blackjack, but you seemingly don’t understand ROR either even though you are a veteran. Risk as much as you can afford to gain the max edge.

Comprehension is a valuable skill. Suggest you reread.

[21forme]

Comprehension is a valuable skill. Suggest you reread.

You should know by now, aceside is hopeless.

[DSchles]

So here is a question I seldom see discussed. Suppose a counter is in danger of tapping out his trip bankroll (oh no!). He is down to his last $600 and the count calls for a wager of $300. What fraction of his on hand capital should he bet? If you bet $300, then you risk losing EV if you have to split and double down on each split because you won't have enough money. There are other variations that would require 4x your initial bet, but you get the idea. Why is it such a big deal if you lose EV by not splitting or doubling? Is it really that much of a loss?

In theory, he could bet anywhere from 1/8, 1/6, 1/4, 1/2, or even the full amount of his leftover capital (maybe the count call for a $600 wager). Intuitively, I sense it would be either 1/2 over 1/4 of what he has left. Some of the big teams say the optimal bet is 1/6 of whatever you have on hand. Have you ever seen a mathematical treatment of this question or do you know of any simple math to justify wagering no more than 1/6th on hand capital?

Thanks,
MJ

Somewhat shorter answer: always an interesting question, and I'm not sure what the right answer is from a purely theoretical point of view. Going to think about it. Given the somewhat low frequency of splits, I'd guess that close to $300 might be right, but again, I'm not sure.

Don

[Sharky]

assuming "calls for $300 bet" implies a relative high count, say, >=4...I'd probably play 2 spots of $200 each and pray for a BJ/20 on one of them...at least!

[MJ1]

Somewhat shorter answer: always an interesting question, and I'm not sure what the right answer is from a purely theoretical point of view. Going to think about it. Given the somewhat low frequency of splits, I'd guess that close to $300 might be right, but again, I'm not sure.

If the frequency of splits is low, then you are likely correct. What good does wagering $100 do if you do not split twice for a total of 3 hands and double on each split? How often does that really happen? In the meantime, you lose EV on the extra $200 that you could have wagered when the count called for a $300 bet!

In order to figure this out, one would likely have to look at the frequency of splitting and/or doubling, the EV for the various wagers that are a fraction of on hand capital, the EV lost by not splitting and/or doubling, and a whole bunch of math that is beyond me. Maybe a simulation comparing EV for certain fractions of on hand capital would provide the answer. Norm? In those instances when the counter lacks the money to split and/or double, he just violates basic strategy.

I would also think how many rounds are left to play is also a factor. If it is the final round, you would probably want to bet at least $300. If several rounds are left, I say bet no more than $150 (1/4). Why take a chance of tapping out when there are several rounds left when the count is high?

Note: The Church Team and MIT Teams adhered to the policy of betting no more than 1/6 of on hand capital when in danger of tapping out. I highly doubt that is a coincidence. All I can surmise is that one will win more money (in the long run) betting 1/6 than they would 1/2 in these types of situations. Then again, if this happens often you might want to increase the size of your trip BR.

MJ

[Mr. Ed]

I am surprised that there is not a straightforward answer. This is not something to be decided in the heat of the moment!

I just made up 1/3, since many splits require one more bet and I wanted to be prepared to do just that. But I never applied a rigorous analysis. Although 1/6 seems like overkill.

[Mr. Ed]

Actually, the following splits expect to have at least one more bet:
22v2-7
33v2-7
44v5-6
66v2-6
77v2-7

[DSchles]

I am surprised that there is not a straightforward answer.

No one said there wasn't a straightforward answer! I, for one, said I don't know what that answer is. In any event, it surely depends on a) the size of the proper bet compared to the total bank remaining, and b) the number of hands remaining to be played in the shoe. So, before we get the "straightforward answer," everyone has to agree on the conditions. For example, at high counts, I surely wouldn't be worried about the frequency of a pair split; it's minuscule ... unless you're splitting tens, which changes the dynamic yet again.

Don

[Mr. Ed]

Well now I am confused. I thought a session bankroll was…well…a session bankroll. Personally, I have never hit my session bankroll, since my first time when I brought $100 to play a $10 table. But if I ever did exhaust my session bankroll, my last bet would be 1/3 of whatever I had left (assuming I had 3 times the proper bet according to the count) regardless of how much of the shoe remains. And my proper bet is based on my total bankroll.

On a practical basis, I keep two max bets segregated in my wallet, and my last bet would actually be based on the chips I have on the table, so my last bet might just be my minimum bet. If I need to dip into my wallet to split and/or double my last bet, so be it. If I win/push, those chips literally go back into my wallet to support two max bets. If I lose, I go home.

So, just to be clear, are you suggesting it might be ok to bet your last session bankroll chip, and not be able to split or double?!

[DSchles]

So, just to be clear, are you suggesting it might be ok to bet your last session bankroll chip, and not be able to split or double?!

I don't think I said that anywhere. I said that there's a proper mathematical answer to the question, which I don't know. I further said that, depending on specified conditions, that answer would vary. Do you really think it makes no difference if this is the second hand of the shoe or the last??

Don