MJ: BJ In Color: Playing Multiple Hands

[MJ]

Ok, I have some questions about this part of the study (see link below). If there are other players at the table it is no surprise always playing two hands is better than always playing one hand. But if you can switch back and forth between one hand at negative and neutral counts to two hands at positive counts, then why wouldn't that be optimal?

Why wouldn't it be better to bet the bare minimum of one hand with low counts rather then betting double that on two hands?

Karl Janeck wrote the post below a while back in response to a question I posed on this topic. In point #1 he says you should only switch to two hands when there are other players at the table and when the count is positive.

Additionally, the point Karl makes about spreading to three hands when there are 5 other players at the table contradicts what is stated in BJA3. I can't recall how many other players need to be at the table to spread to 3 hands, but it is less than 5 (I don't have my copy of BJA3 on hand). Any thoughts on this one, Don?

MJ

Karl wrote:

"As discussed, you should never play more than 2 hands. (It would be correct to switch to 3 hands on positive counts if there were at least other 5 more players at the table.)

When is it optimal to play two hands:

The effect of playing 2 hands is twofold. On the positive side, the player gets more money on the table for the same risk. The downside is the card-eating effect since two hands take more cards. The card eating effect is less significat if there are more players at the table. After performing analytical calculations it follows that

1) If there is at least one extra player at the table, it is optimal to spread to two hands with proper bet size (75% each hand) as soon as the count is positive. Thus, theoretically it is not necessary to wait for a large positive count.

2) If the counter plays alone, the two effects (card eating and extra money) roughly cancel out and there is no advantage in spreading to two hands (while it does not matter either).

Note that the optimal number of hands is completely unrelated to how much positive the count is. For example, one should spread to 3 hands with another 5 players at the table regardless if the count is +1 or +15.

The analysis above does not include any cover-related or other practical considerations."

Link

[Don Schlesinger]

> Ok, I have some questions about this part of the study
> (see link below). If there are other players at the
> table it is no surprise always playing two hands is
> better than always playing one hand. But if you can
> switch back and forth between one hand at negative and
> neutral counts to two hands at positive counts, then
> why wouldn't that be optimal?

What are you betting on the hands? Do you continue to bet optimally? What does "optimally" mean in negative counts? How many players are at the table?

> Why wouldn't it be better to bet the bare minimum of
> one hand with low counts rather then betting double
> that on two hands?

It would be better to bet noting at all! So, we bet as little as we can get away with, without making ourselves look painfully obvious.

But, to answer in the spirit of the discussion: because cards get used up with more hands. If I play alone, and bet $100, that's $100 for two hands per round, or $50 spent per round, trying to get rid of cards. If, instead, I bet, say, $75 on each of two hands, then that's $150 bet and three hands used, or the same $50 per hand. And, some will argue, the shoe is depleted faster, which is good, since the count is negative.

> Karl Janeck

Close! KarEl JanecEk. Missing a couple of e's!

> wrote the post below a while back in
> response to a question I posed on this topic. In point
> #1 he says you should only switch to two hands when
> there are other players at the table and when the
> count is positive.

Well, that's what I wrote in BJA3, no? So, it must be true! :-)

> Additionally, the point Karl makes about spreading to
> three hands when there are 5 other players at the
> table contradicts what is stated in BJA3.

It contradicts the rules of blackjack, because, it would be very hard to squeeze that total of EIGHT hands into seven betting circles!! :-) I'll explain below what, obviously, he really meant, but you should have understood yourself that what he wrote was impossible.

> I can't
> recall how many other players need to be at the table
> to spread to 3 hands,

Three.

> but it is less than 5 (I don't
> have my copy of BJA3 on hand). Any thoughts on this
> one, Don?

Sure. If I wrote it in BJA3, then it's probably correct.

> Karl wrote:

> "As discussed, you should never play more than 2
> hands. (It would be correct to switch to 3 hands on
> positive counts if there were at least other 5 more
> players at the table.)

When there are three other players at the table, if you play two hands, that makes five player hands. Add one for the dealer, and that makes six. If the optimal bet was $100 for one hand, then the optimal bet is, say, $74 on each of the two hands, and you have $148 worth of action for six hands, or $24.67 per hand. If you play three hands of optimal $58 each, that's $174 for the now seven hands on the table, or $24.86 per hand, which, clearly, is slightly more.

But we're just rehashing p. 26 of BJA3. It's all there.

> When is it optimal to play two hands:

> The effect of playing 2 hands is twofold. On the
> positive side, the player gets more money on the table
> for the same risk.

Certainly true.

> The downside is the card-eating
> effect since two hands take more cards. The card
> eating effect is less significant if there are more
> players at the table.

True.

> After performing analytical
> calculations it follows that

> 1) If there is at least one extra player at the table,
> it is optimal to spread to two hands with proper bet
> size (75% each hand) as soon as the count is positive.

Still true.

> Thus, theoretically it is not necessary to wait for a
> large positive count.

Right.

> 2) If the counter plays alone, the two effects (card
> eating and extra money) roughly cancel out and there
> is no advantage in spreading to two hands (while it
> does not matter either).

Right again.

> Note that the optimal number of hands is completely
> unrelated to how much positive the count is. For
> example, one should spread to 3 hands with another 5
> players at the table regardless if the count is +1 or
> +15.

I can only reiterate what I wrote above. Since doing what Karel suggests, literally, is physically impossible at the table, let's cut him some slack and understand that what he meant was that, if you're already playing two hands with three other players (total of five player hands, at the table), then it would be better to spread to the third hand for yourself.

> The analysis above does not include any cover-related
> or other practical considerations."

Right.

Finally, if you really want to get on someone's case, go after Wong, who writes, on p. 210, of PBJ: "... increasing to three hands of optimal-sized bets will not win you more money no matter how many other players are in action at your table." His own numbers on p. 204 belie what he wrote.

But, as I've often said, I wouldn't play three hands at a table for cover reasons, although that wasn't the spirit of what Wong wrote. In the end, it just is so close that it doesn't matter.

Don

[MJ]

> What are you betting on the hands? Do you continue to
> bet optimally? What does "optimally" mean in
> negative counts? How many players are at the table?

Say the table minimum is $10, 1 other player at the table. Ideally, you would want to bet nothing at all (in negative counts)as you stated, but this is play all so we bet the minimum of $10 for 1 hand. When the count becomes favorable, we then place two hand wagers adjusted for covariance. My point is that it wouldn't make any sense to play two hand at the $10 minimum for negative counts, correct?

Going back to the BJ in Color study that I linked to in the above post, the chart shows the highest SCORE for ALWAYS playing two hands. I would think that by 'switching' back and forth between 1 and 2 hands, we are getting the best of both worlds. On the downside, we bet the table minimum of 1 hand for negative counts and then on the upside we play 2 hands (adjusted for covariance) at the positive counts. Wouldn't switching back and forth have a higher SCORE then always playing two hands (assuming you cannot bet below the table minimum on the two hands and that we bet the minimum on one hand)?

> It would be better to bet noting at all! So, we bet as
> little as we can get away with, without making
> ourselves look painfully obvious.

Makes sense!

> But, to answer in the spirit of the discussion:
> because cards get used up with more hands. If I play
> alone, and bet $100, that's $100 for two hands per
> round, or $50 spent per round, trying to get rid of
> cards.

I think you meant to write $50 spend per hand.

> If, instead, I bet, say, $75 on each of two
> hands, then that's $150 bet and three hands used, or
> the same $50 per hand. And, some will argue, the shoe
> is depleted faster, which is good, since the count is
> negative.

That all makes sense, but SCORE does not take into account the time factor. In your example, you are assuming the counter can place two hand wagers below $100. What if the table minimum was $100? Then I guess in this case the best option (assuming play all) would be to bet 1x$100 in the negative counts? Playing it at 2x$100 would be foolish, right? That would be losing twice as much EV, while only eating 50% more cards.

> I can only reiterate what I wrote above. Since doing
> what Karel suggests, literally, is physically
> impossible at the table, let's cut him some slack and
> understand that what he meant was that, if you're
> already playing two hands with three other players
> (total of five player hands, at the table), then it
> would be better to spread to the third hand for
> yourself.

Fair enough.

MJ

[Don Schlesinger]

> Say the table minimum is $10, 1 other player at the
> table. Ideally, you would want to bet nothing at all
> (in negative counts)as you stated, but this is play
> all so we bet the minimum of $10 for 1 hand. When the
> count becomes favorable, we then place two hand wagers
> adjusted for covariance. My point is that it wouldn't
> make any sense to play two hand at the $10 minimum for
> negative counts, correct?

Mathematically, right. But, it has been mentioned many times that playing one hand only in the bad counts and then switching to two hands in the good is, unfortunately, one of the tell-tale signs of a card counter. So, when Norm or someone says that it's better to play two (optimal) hands all the time (and the minimum you can get away with on negative counts), it's in comparison to playing one hand all the time.

> Going back to the BJ in Color study that I linked to
> in the above post, the chart shows the highest SCORE
> for ALWAYS playing two hands. I would think that by
> 'switching' back and forth between 1 and 2 hands, we
> are getting the best of both worlds.

Right. See above. Until they throw you out. Then, you have no world at all! :-)

> On the downside,
> we bet the table minimum of 1 hand for negative counts
> and then on the upside we play 2 hands (adjusted for
> covariance) at the positive counts. Wouldn't switching
> back and forth have a higher SCORE then [than] always > playing two hands (assuming you cannot bet below the
> table minimum on the two hands and that we bet the minimum
> on one hand)?

Yes. And not betting at all in the negatives would be even better still. All you're saying is that back-counting is better than playing all, and that, forced to play all, betting as little in the negative counts as possible is the most desirable. But, that doesn't mean that you should play that way, or that you will get away with it.

> I think you meant to write $50 spend per hand.

Yes, right. sorry.

> That all makes sense, but SCORE does not take into
> account the time factor. In your example, you are
> assuming the counter can place two hand wagers below
> $100.

Just using a round number for illustration. In general, it's not great for the table to dictate your minimum bet to you, if, in fact, you'd prefer to bet less.

> What if the table minimum was $100?

Then, I'd find a table with a lower minimum! :-)

> Then I guess
> in this case the best option (assuming play all) would
> be to bet 1x$100 in the negative counts?

See above. Beating a dead horse.

> Playing it at
> 2x$100 would be foolish, right? That would be losing
> twice as much EV, while only eating 50% more cards.

Mathematically, yes.

Don

[MJ]

> Mathematically, right. But, it has been mentioned many
> times that playing one hand only in the bad counts and
> then switching to two hands in the good is,
> unfortunately, one of the tell-tale signs of a card
> counter. So, when Norm or someone says that it's
> better to play two (optimal) hands all the time (and
> the minimum you can get away with on negative counts),
> it's in comparison to playing one hand all the time.

But what you are saying is not in agreement with the chart. You are saying that mathematically it is better to switch back and forth between 1 and 2 hands (assuming optimal betting) vs playing 2 hands all the time (assuming optimal betting). Yet, the chart is indicating that playing 2 hands all the time is mathematically stronger than switching back and forth between 1 and 2 hands.

Take another look at the chart (link below).

MJ

Chart

[Norm Wattenberger]

As it states, the charts are based on one particular set of circumstances. No way to create charts for all situations.

> But what you are saying is not in agreement with the
> chart. You are saying that mathematically it is better
> to switch back and forth between 1 and 2 hands
> (assuming optimal betting) vs playing 2 hands all the
> time (assuming optimal betting). Yet, the chart is
> indicating that playing 2 hands all the time is
> mathematically stronger than switching back and forth
> between 1 and 2 hands.

> Take another look at the chart (link below).

> MJ

[Brick]

> As it states, the charts are based on one particular
> set of circumstances. No way to create charts for all
> situations.

Norm the only possible way I see playing 2 hands(play all) can have a higher score is if TOTAL min bets in neg counts are lower than than min bet when playing one hand in negative counts,or max bets are higher,otherwise how can this be possible)*%? It is my understanding SCORE is based on same ror and bankroll.

thanks,
Brick

[Norm Wattenberger]

It's important to understand that when comparing two hands play all with one hand at 0 and lower and two hands at +1 and higher, I don't just simply change the min bets. The entire betting ramp must be recalculated to maintain the same risk and spread.

> Norm the only possible way I see playing 2 hands(play
> all) can have a higher score is if TOTAL min bets in
> neg counts are lower than than min bet when playing
> one hand in negative counts,or max bets are
> higher,otherwise how can this be possible)*%? It is my
> understanding SCORE is based on same ror and bankroll.

> thanks,
> Brick

[MJ]

> It's important to understand that when comparing two
> hands play all with one hand at 0 and lower and two
> hands at +1 and higher, I don't just simply change the
> min bets. The entire betting ramp must be recalculated
> to maintain the same risk and spread.

given how the bet schedules are set-up. I had to go on CVCX and compare the bet schedules to see what was going on. When spreading from 1 to 2 hands, CVCX provides a MUCH higher minimum bet than that for playing 2 hands all the time. I don't think players would increase their minimum bet on 1 hand like that if they could bet the same minimum as the 2 hand play all bet schedule on 1 hand. The 1 to 2 hand schedule also puts out less money for the max bet to conform to using the same spread and risk as the 2 hand schedule.

Bottom line: The best option is to switch from 1 to 2 hands so long as the 2 hand bet is adjusted for covariance (and the minimum bet on 1 hand is the same as that for 2 hand play-all). Mathematically, this is far stronger than playing 2 hands all the time, as Don stated above. I think the chart is a bit misleading, as most people will not understand how the bet ramps were set-up (I know I didn't).

MJ

[Norm Wattenberger]

Of course if you do that, you are increasing the spread. So of course the SCORE goes up.

> given how the bet schedules are set-up. I had to go on
> CVCX and compare the bet schedules to see what was
> going on. When spreading from 1 to 2 hands, CVCX
> provides a MUCH higher minimum bet than that for
> playing 2 hands all the time. I don't think players
> would increase their minimum bet on 1 hand like that
> if they could bet the same minimum as the 2 hand play
> all bet schedule on 1 hand. The 1 to 2 hand schedule
> also puts out less money for the max bet to conform to
> using the same spread and risk as the 2 hand schedule.

> Bottom line: The best option is to switch from 1 to 2
> hands so long as the 2 hand bet is adjusted for
> covariance (and the minimum bet on 1 hand is the same
> as that for 2 hand play-all). Mathematically, this is
> far stronger than playing 2 hands all the time, as Don
> stated above. I think the chart is a bit misleading,
> as most people will not understand how the bet ramps
> were set-up (I know I didn't).

> MJ

[Don Schlesinger]

> Of course if you do that, you are increasing the
> spread. So of course the SCORE goes up.

No, the SCORE stays the same. The hourly win rate increases! :-) :-)

Don