Simple Kelly Problem

[cero_z]

Hi All,

Probably a ridiculously easy math question, but please help me out by calculating my average advantage in these blackjack scenarios:

a)I place 100 bets, betting the same amount each time. For half of the bets, I have a 1.5% advantage, and for half of them, I am at a .5% disadvantage.

b)Again I play 100 hands, but this time I wager 5x when I have a 1.5% advantage, and just x when I'm at a .5% disadvantage.

According to my gorilla math, my EV in the first scenario is 1.05 x my total action, for an average advantage of .5%
In the 2nd scenario, it's 1.07 x total action, for an average advantage of .7%.

Is this right, in terms of me determining my bet sizes according to some Kelly Criteria (1/2, full, etc.)? Does it matter in terms of the swings that the hands enjoy different
degrees of advantage/disadvantage? In other words, would the bankroll considerations be any different from scenario 2, if I played all hands at a .7% advantage?

Thanks in advance.

[AaronBrown]

(a) Correct, except you meant to write 1.005 instead of 1.05. The 0.5% is correct.

(b) Almost correct. Let's do it in dollars instead of percentages, it's easier to get it right. You bet $200 with the 0.5% disadvantage, for an expected loss of $1. You bet $1,000 with the 1.5% advantage, for an expected gain of $15. If you do one of each, you win an average of $14 on $1,200 bet, $14/$1,200 = 1.1667% advantage. It doesn't matter whether you do it 2 times or 2 million, it's still 1.1667%.

Kelly tells you to bet a fraction of bankroll, not a fixed amount. So as you win money, you increase your bet sizes. With any disadvantage you bet a negative amount (that is, you take the other side of the bet). If that's impossible, you bet zero. With a positive expectation, the fraction of bankroll you bet depends on the variance of the outcome.

I assume this is blackjack you're trying to model. In this case, the variance is essentially constant, so all that matters is edge. Your bet should be proportional to edge times bankroll, and you should make the minimum possible bet when you have a disadvantage.

As a practical matter, you make the minimum bet when the count is against you, then ratchet up the bet as the count moves more in your favor, until you hit the maximum. This assumes that you are not trying to disguise your counting. As you are more successful, you move to higher limit tables.

[cero_z]

Hi Aaron,

Thanks so much for your thoughtful reply. I was thinking of applying it in a shuffle-tracking situation where I'd be flat-betting the first 3 decks, and then employing a different flat bet (smaller) for the remainder. Upon some analysis, though, it looks like I'll have to develop more precise tracking skills than I have now, in order to find a risk/reward tradeoff that's remotely palatable for a poker player.

[creedofhubris]

[ QUOTE ]
Upon some analysis, though, it looks like I'll have to develop more precise tracking skills than I have now, in order to find a risk/reward tradeoff that's remotely palatable for a poker player.

[/ QUOTE ]

Yeah, gl with that.

I hear lots of fun blackjack stories that start out,

"We had $20K of EV last night!"

and end with "... so we lost $15K."

[DWarrior]

I'm pretty sure you can earn more multi-tabling online poker than you can ever hope to as a blackjack card counter. And with a fraction of the risk.

[cero_z]

[ QUOTE ]
I'm pretty sure you can earn more multi-tabling online poker than you can ever hope to as a blackjack card counter. And with a fraction of the risk.

[/ QUOTE ]

Agreed, but I said "palatable for a poker player," not "as good as poker." I like Blackjack, I think playing it helps my poker game, and I'm pretty sure there are some sweet opportunities to put down some big-edge plays in the podunk casinos I play in.