Kelly and optimal bet sizing

[ARK]

Sorry in advance if this has been discussed before, or if I'm just completely off base.

Has anyone calculated what the optimal Kelly % of betting? I'm curious that the negative edge we sometimes have in blackjack isn't factored into betsizing.

So if I understand Kelly criterion correctly:

1) Kelly betting = Whatever your current edge in a game is, your bet size should be that %-size of your bankroll
2) Kelly betting is the optimal betting strategy for bankroll growth (in a vacuum)
3) Overbetting Kelly increases the chance of bad outcomes while decreasing the chance of good outcomes. Overbetting is much more dangerous than underbetting.

This all makes sense to me EXCEPT that Kelly betting dictates that we should have a bet size of zero when our edge is 0% or less. Practically speaking, that's not what we usually do. Even if we wong out at TC-1 we are likely to still play at TC 0,1,2 (Zen Count) with minimal bet sizes but if I remember correctly this will be about 50% of the hands we play!

My question is has anyone quantified this effect? I would think that this would easily make full Kelly an overbet. I'm guessing that this is the reason I've seen recommendations 1/2 or 1/4 Kelly but is there actually an optimal percentage? I'd like to maximize my bet sizes without overbetting or unnecessarily reducing my win rate.

Maybe I'm thinking about this completely the wrong way so please feel free to tell me. I understand Kelly from an independent bet standpoint but it seems flawed to base you betsize purely on bankroll when you're bankroll is going to experience extra fluctuation and downward pull from slightly negative or zero player edges.

 

[blackjack avenger]

a ?

What literature do u have?

 

[ARK]

What literature do u have?

Blackbelt in Blackjack is the only blackjack book I own. Other than that just I've done additional reading at these forums, snyders web site, and some basic Kelly stuff on Wikipedia.

 

[blackjack avenger]

snyder is fine

If his book tells u how to bet? That is fine.

I think he recommends .5 Kelly.

If u are happy with your betting limits I would not raise stakes until 1/4 to 1/8 Kelly.

In bj we can consider negative bets and Kelly. Snyder does this.
The reason betting less then Kelly is due to crushing variance which can beat down you bank.

 

[MangoJ]

In principle, you can calculate a true Kelly bet based on a larger scale of a shoe (rather than a hand). Given a bet spread, wong in&out points, and rules, you can not only simulate your EV of that game, but also the exact distribution of your game.

With that distribution, you can then maximize CEV with regard to your unit bet and given bankroll). The ratio of this optimal bet and your bankroll will be the "generalized Kelly bet".
You can then of course choose to play 1/2 or 1/4 of that amount.

 

[ARK]

In principle, you can calculate a true Kelly bet based on a larger scale of a shoe (rather than a hand). Given a bet spread, wong in&out points, and rules, you can not only simulate your EV of that game, but also the exact distribution of your game.

With that distribution, you can then maximize CEV with regard to your unit bet and given bankroll). The ratio of this optimal bet and your bankroll will be the "generalized Kelly bet".
You can then of course choose to play 1/2 or 1/4 of that amount.

I think this is where I was going, that your actual "bankroll" that you use for calculating Kelly needs to be adjusted for the conditions of the shoe (number of decks and penetration)

It looks like maybe Casino Verte does these calculations? As a Mac user I can't use that program. Is there anything else out there I can use? Or am I just overanlayzing this and should just stick with 1/2 Kelly.

 

[blackjack avenger]

depends on how much u value your bank

Kelly if u can add to bank.
.5 Kelly is the most risky if can't add to it.
At least .25 Kelly with a larger bank.

The more conservative the fraction the less large bet resizing down on losses, the shorter the long run & the more certainty of winning.