Effect of Ace Count On Hand Spread

[bj bob]

Just wondering about an issue that came to mind the other day. I don't know if anyone has directly addressed this head on, but here goes.
The prevailing thought is to play as few hands, especially in heads-up when the count is high so as to conserve the remaining high cards. That all makes perfect sense to me, however, I was also wondering, since I side count aces, that it might make more sense to spread to multiple hands when the count is Pos. and there is a substantial overabundance of aces remaining in the deck so as to take advantage of more possible BJ's paying 3/2, rather than the higher possibility of pairing them and thus getting only a 1:1 payoff. The situation came up the other night in practice when, in a DD game, with one deck dealt there were seven aces remaining with a TC of +4.
In that scenario, what would the optimal betting/spread strategy be, and moreover, has anyone ever done the math on this?

[Dopple]

Just from my experience on the table I would think that would be wise. In heads up you are getting more cards dealt to your side of the table for every dealer hand and you have more "safety" when you spread.

Just my opinion.

[Automatic Monkey]

Originally Posted by bj bob

Just wondering about an issue that came to mind the other day. I don't know if anyone has directly addressed this head on, but here goes.
The prevailing thought is to play as few hands, especially in heads-up when the count is high so as to conserve the remaining high cards. That all makes perfect sense to me, however, I was also wondering, since I side count aces, that it might make more sense to spread to multiple hands when the count is Pos. and there is a substantial overabundance of aces remaining in the deck so as to take advantage of more possible BJ's paying 3/2, rather than the higher possibility of pairing them and thus getting only a 1:1 payoff. The situation came up the other night in practice when, in a DD game, with one deck dealt there were seven aces remaining with a TC of +4.
In that scenario, what would the optimal betting/spread strategy be, and moreover, has anyone ever done the math on this?

A little bit of work has been done on this. In the SD scenario, being it is round-dependent instead of depth-dependent, you are always going to get the best deal when there are two hands in the game, regardless of whether or not you are playing one or both of them.

In multideck games it's a little different. In normal situations you want to play two hands, because the reduced variance allows you to increase your total bet 40-50% more than if you had one hand out there. The higher total bet increases your win rate more than the fewer number of hands decreases it, unless you happen to be playing heads-up with the dealer, in which case you are slightly better off playing one hand due to the additional rounds. (Did that make sense?)

Now whether the deck is rich in aces or in 10's is a little puzzling. If it's rich in aces there will be more BJ's but for the dealer as well as the player. And when the dealer gets a BJ it wipes everybody out regardless of how many hands you have out there. So off the top of my head I would think high ace density would increase the covariance between multiple hands, thus you would lose some of the benefit of multiple hands. Conversely, when the deck is rich in 10's the dealer is going to bust a lot and you will win all your unbusted hands, thus the value of multiple hands will increase.

So, without claiming to have done all the math, it looks like it's possible it may work the other way around from what you propose.

[Knox]

Without doing the math either, I would say that BJ plays 3:2 but if the dealer gets a natural you only lose 1:1 so you come out ahead. Having two hands to the dealer's one should give you better odds to catch a natural. Therefore play two hands, especially in heads up situations, regardless of number of decks.

[bj bob]

Originally Posted by Automatic Monkey

A little bit of work has been done on this. In the SD scenario, being it is round-dependent instead of depth-dependent, you are always going to get the best deal when there are two hands in the game, regardless of whether or not you are playing one or both of them.

In multideck games it's a little different. In normal situations you want to play two hands, because the reduced variance allows you to increase your total bet 40-50% more than if you had one hand out there. The higher total bet increases your win rate more than the fewer number of hands decreases it, unless you happen to be playing heads-up with the dealer, in which case you are slightly better off playing one hand due to the additional rounds. (Did that make sense?)

Now whether the deck is rich in aces or in 10's is a little puzzling. If it's rich in aces there will be more BJ's but for the dealer as well as the player. And when the dealer gets a BJ it wipes everybody out regardless of how many hands you have out there. So off the top of my head I would think high ace density would increase the covariance between multiple hands, thus you would lose some of the benefit of multiple hands. Conversely, when the deck is rich in 10's the dealer is going to bust a lot and you will win all your unbusted hands, thus the value of multiple hands will increase.

So, without claiming to have done all the math, it looks like it's possible it may work the other way around from what you propose.

I see what you're saying about covariance, Monk, but isn't it offset by the fact that in SD, DD, by increasing the number of your hands, in this case heads-up, that you are in effect compounding your opportunities of catching BJs, e.g. 3 player's hands vs. only one dealer hand and at the same time reducing dealer's chances of catching, all this at a 1:1 gain for the dealer vs. a 3:2 gain for the player, not to mention the probability of pushing BJ's with ins. in effect (since TC would warrant it).

[Automatic Monkey]

Originally Posted by bj bob

I see what you're saying about covariance, Monk, but isn't it offset by the fact that in SD, DD, by increasing the number of your hands, in this case heads-up, that you are in effect compounding your opportunities of catching BJs, e.g. 3 player's hands vs. only one dealer hand and at the same time reducing dealer's chances of catching, all this at a 1:1 gain for the dealer vs. a 3:2 gain for the player, not to mention the probability of pushing BJ's with ins. in effect (since TC would warrant it).

And I see what you're saying, and the effect of the 3:2 BJ payoff is already built into our advantage. It would be a terrible game without it.

Let's say you play 3 hands against the dealer's 1. Sure you will get 3 times more BJ's but when you get a BJ you win only that hand. The other two, who knows? Even at high counts if you don't have a BJ, chances are you don't have an advantage, so you can't think of non-BJ hands as winners. But when the dealer gets a BJ he will probably win all 3 hands. So you will get 3 times more BJ's but his BJ's will do 3 times more damage. (Disregarding the 3:2 of course.)

You can't consider insurance because insurance is just a sidebet, and you normally only have 5-10% advantage on it anyway (and that advantage is on half your bet, not the full amount.) Besides you are using an ace-neutral count, which means the ace-adjusted TC might be high enough to justify a max bet because of a lot of aces, but the main count might not be high enough to justify insurance. When I played HO2 sometimes I would have insurance on low bets and no insurance on high ones, which helps with cover if they are using good insurance bets to help ID counters because none of those guys understand ace-neutral counts.

[Knox]

What about the time I got blackjack on both of my hands? That was pretty sweet!



Seriously, I think if you work through the scenarios you can't go wrong playing multi hands. How many times have one or two ploppies at a crowded table caught the blackjack in high counts that was rightfully yours!??! That's what I thought!

[bj bob]

OK Monkman, I still can't tell if we're agreeing or arguing here, so let's get down to the nitty-gritty.
First, conventional BJ wisdom says to have as much $ on the table when the TC is at 4>, spreading to two hands if necessary. We OK on this?
Second, I remember a thread(s) stating that if you are ace tracking, you want to increase your bet by 50% if you are likely to get an ace dealt. That's how valuable an ace is.
So, let's put both of these into play at the same time:
The Monk is playing at his favorite gaming establishment, DD, real good pen. spreading $50-200x2, heads-up with(pendulous) dealer. One deck has been dealt and we know the following:1) 52 cards are left 2) 7 aces are left to deal 3) There are 4 extra X cards in the remaining deck(leaving 20 in all)- the 7 aces which leaves 25 non aces. Now, last hand played was with 2 hands at $200=$400 total. Since TC =+4(aces not reckoned) you will be taking insurance when dealer is ace-up. Would you, knowing this data, spread to more hands, and, to how many more under these circumstances?
And finally, in response to your getting wiped out X3 by a dealer's BJ, you are 3X more likely to wipe her out x3x1.5, ins. not withstanding. Same ratio, more bucks! Just cogitating here.

[Knox]

Additional comment is that you double down more in high positive counts. Several of the I18 indices are doubling down, e.g. 8 v 5 or 6, 9 v 2 or 7, 10-11 v everything. 7 indices right there, triggered in high + counts. The dealer can't double down.

Let's keep in mind, any dealer that beats an AP is just getting lucky anyway!

[Automatic Monkey]

Originally Posted by bj bob

OK Monkman, I still can't tell if we're agreeing or arguing here, so let's get down to the nitty-gritty.
First, conventional BJ wisdom says to have as much $ on the table when the TC is at 4>, spreading to two hands if necessary. We OK on this?
Second, I remember a thread(s) stating that if you are ace tracking, you want to increase your bet by 50% if you are likely to get an ace dealt. That's how valuable an ace is.
So, let's put both of these into play at the same time:
The Monk is playing at his favorite gaming establishment, DD, real good pen. spreading $50-200x2, heads-up with(pendulous) dealer. One deck has been dealt and we know the following:1) 52 cards are left 2) 7 aces are left to deal 3) There are 4 extra X cards in the remaining deck(leaving 20 in all)- the 7 aces which leaves 25 non aces. Now, last hand played was with 2 hands at $200=$400 total. Since TC =+4(aces not reckoned) you will be taking insurance when dealer is ace-up. Would you, knowing this data, spread to more hands, and, to how many more under these circumstances?
And finally, in response to your getting wiped out X3 by a dealer's BJ, you are 3X more likely to wipe her out x3x1.5, ins. not withstanding. Same ratio, more bucks! Just cogitating here.

It's right, you want to get as much money out there on the table in very high counts, but within the limits of your bankroll. What spreading to extra hands does is allow you to put more money out there at the same risk. I think the ratio is around 175% for 3 hands. So let's say with one spot available to play your max bet is $300, and with 3 spots available you'd put out 3 X $175, total $525. That's where you get your advantage. If you were to merely split the $300 up into 3 hands of $100, you wouldn't gain anything but you would actually lose money because you will be playing fewer rounds in this good count. And getting 3 x the number of BJ's on $100 hands is exactly like getting 1 X BJ's on $300 hands. But having the dealer get the BJ hurts worse with 3 X $175 than with 1 X $300.

But I wouldn't spread to more than 2 hands, because all the calculations show you don't gain very much leverage after the second hand, and because my max bet has already been calculated relative to my bankroll and risk tolerance and if I exceed that, I'm steaming. In the situation you describe, I'd just have my max bets out on two hands, sticking to the game plan.

About the 50% increase when ace tracking, there's a little bit of confusion there. Your advantage is 50% if you are 100% sure your first card will be an ace, and you know nothing else. But to have a reasonable RoR you have to bet a lot less than 50% of your available cash (probably more like 10-20%) and you have to be 100% sure, which means you have to have seen it before it is dealt. Any percentage doubt you have has to be reckoned into your bet. Now that's a 50% advantage only when you are sure you will be getting an ace. Having a bunch of extra aces in there that either you or the dealer can get is a whole different story, and yes that 50% advantage is calculated into the EOR of an ace, but the fact that everyone is equally likely to get that ace makes it no more valuable than the 10.