Count to Predict a Blackjack

[gronbog]

I'm not posting in order to revive the debate on whether counting cards in general is beneficial in tournaments or not. The arguments for and against using traditional counts have all been made. However, there is a thread over at blackjacktheforum.com discussing using a count for the purpose of predicting increased odds of a blackjack being dealt in what the poster is calling a "modified tournament format".

https://www.blackjacktheforum.com/showthread.php?38251-Count-to-predict-blackjack#post215268

I think that in some tournament situations, this might be useful. For example, an event local to me has an accumulation format for which one can advance with high probability if you win one all-in bet followed by a 2 stage progression. Lately I've been counting the cards while waiting to make my move, solely for the purpose of perhaps gaining an increased chance of being dealt a blackjack. This makes the subsequent progression unnecessary.

Using a count specifically designed to detect this situation might make more sense.

Thoughts? Other ideas?

 

[London Colin]

Although EV is not the issue, there is still an EV-like consideration - how much increased probability of blackjack do you choose to require before making your move?

There is also the issue of whether or not there will be a shuffle between now and the end of the tournament round. If not, or if it will occur very late, then delaying making your move is as likely to hurt you as to help you. See this previous discussion about the merits of counting in general :- Hi Lo when the count is negitive

 

[gronbog]

Yes. The round is 25 hands, and there is usually a shuffle somewhere between hand 15 and 18. I generally like to make this move late because, if successful, other players tend to copy it. If I wait, then some players will have busted out and others will already be engaged in whatever strategy they had originally planned on. However, if near the end of the first shoe, the count is favorable, I will make the initial all-in bet at that time instead. The progression can wait a little longer, if needed.

As for how favorable, I don't have a hard figure. The few times I have done this, the true count ended up being greater than +4, which I thought was good enough to make the all-in bet. I guess I'm just thinking out loud about whether a more customized count would be more valuable for this kind of move

 

[London Colin]

Yes. The round is 25 hands, and there is usually a shuffle somewhere between hand 15 and 18. I generally like to make this move late because, if successful, other players tend to copy it. If I wait, then some players will have busted out and others will already be engaged in whatever strategy they had originally planned on. However, if near the end of the first shoe, the count is favorable, I will make the initial all-in bet at that time instead. The progression can wait a little longer, if needed.

That makes sense. If the non-counting default is to wait until after the shuffle anyway, then there's no downside to counting (other than the mental effort).

As for how favorable, I don't have a hard figure. The few times I have done this, the true count ended up being greater than +4, which I thought was good enough to make the all-in bet. I guess I'm just thinking out loud about whether a more customized count would be more valuable for this kind of move

I'm not sure if it would really be worth the effort involved in using a customised count. As it happens, I recently had cause to try and devise such a count for a different purpose. I came up with the slightly impractical -
A: -16, T: -2, Other: +3 (or equivalently -8, -1, +1.5).

It seems to work quite well in sims, but, if I understand things correctly, to truly track the probability of a blackjack you would need to count the aces and tens separately, and come up with some way of combining them that I presume would have to involve multiplication.

Rather than use +/- count(s) to track the change in probability, it might be more straightforward to simply keep track of the number of tens, aces and others left in the deck and calculate the probability directly.

Or just track the aces and tens, use the usual deck estimation techniques to get 'tens-per-deck' and 'aces-per deck' figures for the remaining cards. Multiply those two numbers and the result is proportional to the BJ prob. (1326 times bigger, in fact.) So you could decide on a target value for this product, corresponding to the BJ probability at which you make your move.

Does that all sound right? [I'm by no means sure of myself on this subject.]


The 'linear' count I can up with comes from looking at EORs, scaling them to convenient integers, and then adjusting them so that the count is balanced.

The EORs I calculated for BJ prob. are -

1D
ace: -0.01062
ten: -0.00121
other:+0.00193

6D
ace: -0.00169
ten: -0.00019
other:+0.00031

So the ratio is roughly -5.5 : -1 : +1.5 (or -11 : -2 : +3), and I changed the 5.5 to 8 (11 to 16) to make it balance.