BJ Count

Does anyone know of a formal (mathematical) yet practicable way to correlate BJ true count with mathematical expectation (which could be practically used while playing, if only approximately)?
Thx.

Quote: APEppink

Does anyone know of a formal (mathematical) yet practicable way to correlate BJ true count with mathematical expectation (which could be practically used while playing, if only approximately)?
Thx.

Yes.
Others can elaborate, I'm still undercover as the village idiot ,-)

Quote: TwoFeathersATL

Yes.
Others can elaborate, I'm still undercover as the village idiot ,-)

I've seen through your charade for a while now!

Quote: APEppink

Does anyone know of a formal (mathematical) yet practicable way to correlate BJ true count with mathematical expectation (which could be practically used while playing, if only approximately)?
Thx.

I guess I'd want to know exactly what you're looking for. Are you essentially asking "How much money could I expect to win at X true count?" Yes, there is a pretty easy way to do that:

1) Get the house edge of the game given the rules.
2) Get the penetration, as this will effect frequencies... But for simple averaged math for the ever changing PEN, you can use the 75% mark which the following responses I have all follow.
3) Understand that each True Count effects the house edge by APPROXIMATELY .5%. You will have to SIM your game/etc to get more refined numbers, but I've worked from .5% and never had an issue. The following is based off each TC being worth ~.5%.
4) Figure out your Bankroll/Spread to get your RoR < 1% (If you're trying to be pro, <5% or whatever you're comfortable with if you're a weekend warrior / part time player).
5) Given the Overall Advantage you have at any true count, one could use the information above to calculate how much a bet at that true count is worth.

In counting this commonly carries the mathematical terminology of "Gain Per Hand" in association with each True Count. I discuss Gain Per Hand in my A-Z articles as well as the A-Z thread where I post spread sheets showing all the math available for you to download and tinker with (I think page 7?).

If I am understanding your question right perhaps you are asking about the Kelly Criterion? A lot of Blackjack books include a Kelly Criterion table and there are some KC calculators on the web.

Quote: TwoFeathersATL

Yes.
Others can elaborate, I'm still undercover as the village idiot ,-)

I thought you were the court jester.

Quote: Acender

If I am understanding your question right perhaps you are asking about the Kelly Criterion? A lot of Blackjack books include a Kelly Criterion table and there are some KC calculators on the web.

No. Got Kelly pretty well down. Romes answered my question pretty well.
Thx.

I am guessing your question might be in two parts. The first, which is more academic, is how to derive an efficient counting mechanism. The second, is how to determine what the House Edge might be for specific counts.


Being only a deputy village idiot my answer to the second is to create your count (for argument sakes HiLo) and run simulations. The method is to run millions of shoes of BJ keeping a running count and storing each result in an array depending on that running count (I actually used one decimal place). This then gives an approximation on the EV at different counts - and typically I found it flipped positive at about 0.9.

One could even improve on this by varying the strategy at every stage (e.g. standing on some 12's etc.). However I was just trying to investigate the impact of countability so I could compare it to another game I was designing.


Now your first question is more interesting - how does one create the most accurate count. I'm not really sure how to do this so all I could do is to adjust the deck by removing one card of each rank and seeing how the House Edge changed. In theory you can do this mathematically but I found it easier just to run ten long simulations. You can then try out different counting methods as see how accurate each one is. What I did is to create factors based on the change in HE e.g. -1.1 .... 1.6 1.2 .9 .8 -1.2 which I called "Count 8".

I used Eliot's idea - which is that a person watches 100 hands, bets $100 whenever it's in the Player's favour, otherwise bets $0 - and determine how much profit is made from the 100 hands.
Using simple Hi Lo, 6 decks, 83% pen UK rules gave a figure of $27.20 profit.
Using a "Count 8" which had different figures for each ranked card, including 8s and 9s, gave $28.73.

So it is worth using a more complicated count, probably not.

Quote: Greasyjohn

I thought you were the court jester.

Well yes, that too. They go hand in hand.
CharliePatrick has stated he is 'only the deputy village idiot' below, after actually working on these numbers.
Kudos to him.
Don't know if he should be promoted or demoted. I'm still thinking, I'm slow.......;-)