Optimal hand spread

Hello, What is the optimal hand spread, both when you are playing by yourself and with others? Despite cover, I just want to know what hand spread is most effective. 

I have an idea of the hand spread when you are playing by yourself, but correct me if I'm wrong. My idea is to play as many hands as possible at the minimum bet when the true count is negative to eat all the bad cards fast and play as few hands as possible when the true count is positive to eat few small cards (including bet spread). The thing I don't get is why you should play more hands if you are not by yourself at the blackjack table, why not just play one hand with a higher bet?

I know I'm asking many questions, but I have a lot on my mind right now about different things in blackjack that I have read which I have a hard time finding the logic in right now.

First of all, let's make sure were on the same page with respect to the term "spread". As a noun, it's your maximum bet divided by your minimum bet. So, if you bet between $25 and $300, that's a 1-12 spread. You might see this referred to as your vertical spread. We also use "spread" as verb, as in "I spread from one to two hands". You might see this referred to as your horizontal spread.

You seem to be referring to spreading from one to several hands in your post. This topic is covered in BJA3. The logic is that, when there are others at the table, play one hand at low counts to reduce your own exposure to low cards and play 2 hands at high counts to increase your own exposure to high cards. When playing alone, playing one hand always turns out to be more effective.

The last line..."when playing alone, playing one hand always turns out to be more effective"... WHY?

If you can, why not play 1 hand in negative counts, 2 in positive?  I have often started out with two hands, dropped to one if the count is negative, played two hands with min bet on each for neutral or TC+1, and stayed with two hands through positive decks.  Trying to understand why it's not more effective than simply playing one hand?

I would have to re-read the chapter to properly explain it all. I do recall that it was the overall effect of exposure to high and low counts, average number of cards used per-round and expected rounds per-hour which resulted in an expected win rate per hour. It turned out that, when playing heads up, this was maximized by always playing one hand.

If you bet perfectly optimally, each of two hands has 73% of the optimal one-hand wager.  So, for each round, playing two hands, you bet 146% of the amount you'd bet playing one hand.  But, you use up 150% of the cards required for one hand (three total hands, including the dealer, instead of two, head-up).  So, playing one hand gets out slightly more money per unit of time.

Don

The question Fabian brings up is a question I've asked myself many times.  I've also been a little confused as to why it doesn't make sense to spread out to two hands in positive shoes when playing heads up. I've read the section on this topic in BJ Attack a couple times, and I'm still a little confused.  By they way, I've read BJ Attack at least 3Xs and still refer to it when I have questions. It's my go-to bj book, and I think I own most of them.  Don's explanation finally brings some clarity to this question. The key appears to be optimum betting, which I know I don't do.  I've found it's easier and provides more cover to spread to two hands in a head's up DD game and at the same time raise my bet significantly on both hands.  I usually do this after a loss and the count has got more positive. I act like I'm steaming and fan out to two hands with fairly big bets...at least for me.  I do this because I've seen other players do this that I know don't count. It pretty much fits in with what this casino expects to see.  I expect this increases my ROR (which isn't a concern for me since I have pretty much an unlimited bankroll) but it also should increase my EV.  Am I right in thinking this way?  I'm a recreational weekend $10 to $80 player but I still want to play with as big advantage as possible. Thanks for any help you can give me here!  

"I expect this increases my ROR (which isn't a concern for me since I have pretty much an unlimited bankroll) but it also should increase my EV.  Am I right in thinking this way?"

Short answer:  yes. 

But, what you have to understand is that, when making comparisons as to which way is "better," we have to keep the math rigorous and make sure to compare apples to apples.  If your total bet for the two hands far exceeds what is optimal with respect to the one-hand bet, we're now comparing apples to oranges.  So, if you do that, your ROR will increase as will your e.v., as you mention.  But that doesn't make your way "better," as I have tried to explain.

In the investment world, "better" is often measured by the Sharpe ratio.  Just because one investment returns more than another doesn't necessarily make it "better," if the first investment requires a disproportionate amount of risk in order to attain the return.  As risk doesn't seem to matter to you, then you're right to bet as much as you can get away with.

Don

Thanks for your quick reply.  That somewhat clarified the issue for me.  I understand your apple to apple vs apple to oranges analogy.  I probably brought up something that wasn't my main point.  The way I play is more for cover but I wanted to make sure my thinking was correct.  When I'm head's up and I win a hand and the count goes up, I stay with one hand and increase my bet.  When I lose a hand and the count goes up, I spread to two hands with larger bets, saying something like I want to "change up the cards".  This looks more natural than increasing a bet on one hand after a loss.  Believe it or not, I have been backed off at two local casinos and my maximum bet never got over $50.  I've got smarter since then (which was about 7 years ago) by reading books, including yours, and acting more like a gambler.  I've only got two local casinos left to play in so I want to make sure they don't back me off.  I'm playing bj more for fun then money but I still want to make sure I'm playing a winning game.

With this said, I still don't quite understand the logic - or math - for why it makes sense to spread to two hands when there are other players at the table but it doesn't make sense to do this when playing head's up.  Isn't the dealer like another player?  In positive shoes shouldn't we always try to play more hands then the dealer, regardless if there is 0 players at the table or 1 to 5 players at the table?  For example, in a head's up game if the count if positive and there are enough cards left for 6 hands then I would think the correct strategy would be to spread to 2 hands.  This would allow the player to get 4 hands, while the dealer would only get 2 hands in the positive counts.  If the player stayed with one hand then he would only get 3 hands, while the dealer got 3 hands.  What am I missing?  Why does the logic - or math - change when playing head's up vs with other people?

Again, I know I'm splitting hairs here and it in reality it probably doesn't matter much.  

" I've found it's easier and provides more cover to spread to two hands in a head's up DD game and at the same time raise my bet significantly on both hands.  I usually do this after a loss and the count has got more positive. I act like I'm steaming and fan out to two hands with fairly big bets...at least for me."

In the second post you wrote:
" The way I play is more for cover but I wanted to make sure my thinking was correct.  When I'm head's up and I win a hand and the count goes up, I stay with one hand and increase my bet.  When I lose a hand and the count goes up, I spread to two hands with larger bets, saying something like I want to "change up the cards".  This looks more natural than increasing a bet on one hand after a loss." 

" Believe it or not, I have been backed off at two local casinos and my maximum bet never got over $50.  I've got smarter since then (which was about 7 years ago) by reading books, including yours, and acting more like a gambler.  I've only got two local casinos left to play in so I want to make sure they don't back me off.  I'm playing bj more for fun then money but I still want to make sure I'm playing a winning game."

I am very surprised about the two back offs you received, but for a completely different reason than what you are most likely thinking. Although there is a good lesson to be learned here, it just goes to show the extreme differences in accepted tolerance levels among various casinos. When frequenting a casino you need to observe the average level of play that is taking place in the pits and do not exceed.
In my opinion of your cover play as acting like a gambler "what happens at the end of the shoe, or if or when the count dropped, especially if you just won a few hands? You can not just turn it on and off on a dime, a gambler often keeps gambling on tilt without rhyme or reason." after a losing bet followed up with two hands making larger, and bigger bets, is all the wrong approach, especially on a double deck game, and more than likely going to get you tossed in the last two remaining joints you have left. All you are doing is drawing attention to yourself, instead of trying to blend in. Changing the number of hands played also upsets the flow of the cards, and gets the plops angry, I also do this last part. Anyway, if a casino is willing to toss you at your level of play it was not worth worrying about to begin with.  

"With this said, I still don't quite understand the logic - or math - for why it makes sense to spread to two hands when there are other players at the table but it doesn't make sense to do this when playing head's up.  Isn't the dealer like another player?  In positive shoes shouldn't we always try to play more hands then the dealer, regardless if there is 0 players at the table or 1 to 5 players at the table?"

Both hands face the exact same dealer up card, and subsequently the outcomes of each hand have more of a tendency for results to co-incide together. When playing two hands heads up the trade off is almost a wash. When playing two hands you are getting 50% more money on the table, which is 75% bet on each hand of what a one hand normal wager would be called for, "not steaming large gambling bets that your act calls for" at the expense of eating more cards, resulting in almost no difference. Only when you know that the cut card is going to come out in the next round should you take advantage to spread to two hands in a good count situation.  

I believe I answer this fairly clearly in BJA3, pages 24-26.

Don

You did. Since I sent my last email I've spent more time rereading this section in your book and your forum answers.  This is the part in BJ3 that has me questioning the optimum strategy for head's up (it's on page 26):  "Now, there is one instance, even when playing alone, when spreading to a second hand is a must.  If you are proficient in eyeballing the discard tray and "know" when the last hand in the shoe is about to be dealt, then by all means, spread to a second hand.  It doesn't matter anymore that you are using up more cards."

Why wouldn't this same logic apply in the middle of the DD game when the count becomes positive.  I've many times spread out to two hands in a positive count and then had the count go back to negative.  In this case, I wouldn't think that taking the extra cards is a negative; in fact, it could be seen as a positive since I'm eating up more high cards by playing more hands.  When the count goes back to 0 or negative, I move back to one hand.  The point being is that once the deck becomes positive doesn't it make sense to take as much advantage of this situation as possible, which in some cases means taking more cards in the middle of the shoe?  Said another way, taking 150% more cards in positive counts might not reduce the number of big bet opportunities in a head's up game relative to playing one hand.  This is why I don't understand the calculations shown in Table 2.4 on page 26.  You show 100 big bets with 1 hand and only 67 with 2 hands. Why?  If we only spread out to two hands in high positive counts with our maximum bet, then why wouldn't we be able to also make 100 big bets - or close to 100 big bets - with two hands?  I'm sure I'm missing something here but I don't know what it is. And I know my antidotal experiences at the bj table is not a good way to analysis this problem

With all this said, I agree with your last sentence on page 26 of BJ3:  "As is often the case with blackjack questions, sometimes we become so enamored of the theory that we lose sight of the practical, bottom-line implications."  Which you point out is very small.

I understand that this is not that important in terms of winnings but it's how I'm wired, being anal about things like this.  I might be totally off base - or comparing apples to oranges again - in my thinking but I wanted to at least give you some of my thoughts on this.   
  

I'm not sure how else to explain this to you.  People don't usually have trouble with the concept.  There are only a finite number of cards in a deck, or two, or six.  When you play a hand, you use up cards.  If you play, say, 24 rounds with the dealer head-up, then you use up 24 x 5.4 cards, or about 130 cards.  Now, starting with those same 130 cards, if you spread to two hands, for a total of three, with the dealer, you now are using 8.1 cards per ROUND, and will get in only 16 rounds, instead of 24, with those same 130 cards.

So what's the difference if, head-up, you make 24 $100 bets, for $2,400, or if you make 16 bets of $75 on each hand, for 16 x $150 = the same $2,400?

Your turn!

Don

"So what's the difference if, head-up, you make 24 $100 bets, for $2,400, or if you make 16 bets of $75 on each hand, for 16 x $150 = the same $2,400?"

Don, if I am interpreting the op correctly when he jumps to two hands both of his individual bets will now exceed what his one unit wager would have been. He is using a steaming for camouflage approach and is also based on having some kind of unlimited bank. 




 

Don, thank you for your reply.  I'm trying to understand this from strictly a mathematical standpoint.  The cover play and steaming also plays into it but this isn't my main reason for asking this question.  I fully understand how playing two hands uses up more cards than one hand and why this is not the optimum strategy for head's up play, if it's done thoughout the shoe.  I'm saying play one hand most the time (when the count is negative to say let's say +1) in a head's up game and only spread to two hands when the count if positive, or highly positive.  This is also what I think the person who asked this question in BJ3 is saying.  Since a true count of +5 - or any high positive count - doesn't happen very often, then most of the time I'll be playing one hand, and using up about the same number of cards as if I played one hand at all counts.  Correct me if I'm wrong, but I think your analysis is assuming two hands for all counts in a head's up game.  In this case, I agree with your calculations.  This player is using up a lot of cards and making less big bets with optimum betting strategy than if they played one hand in a head's up game.

Also, in DD game most of the time a high count will come toward the end of the shoe, where you've recommended spreading to two hands.  My question is why not always spread to two hands in high counts in a head's up game, even if this occurs in the middle of the shoe?  Why does it make mathematic sense to do this at the end of the shoe but not the middle?  Since we don't know the composition of the cards left in the deck, the middle of the shoe could be our only opportunity to spread to two hands.  Said another way, what's the difference in spreading to two hands in the middle of the shoe to take advantage of a high count, and then going back to one hand vs playing one hand during the whole shoe and only spreading to two hands at the end of a shoe in a positive count?  In both cases I've used up the same number of cards (I understand this isn't totally correct since having more hands in at the end of the shoe will probably use up a couple more cards).  And in both cases, I've taken advantage of a high count with optimum betting strategy.

You're right I am having trouble understanding this, and I truly appreciate your patience.  I you don't reply to me again, I understand.  And I know this isn't that important, it's just something I'm trying to understand.  Even before I saw this question on the bj21 forum, I struggled with understanding this part of your book.  That's why I was excited when I saw someone ask the same question I've struggled with. 

 

The difference is because, for the last hand of the shoe, the dealer is required to play the round to its completion.  He can't run out of cards; rather, he uses as many as necessary to finish the hands.  So, there is no concern for how many cards are used up.  If the stop card is poised to come out, you try to win as much on that last round as possible.

If you do this in the middle of the shoe, you don't win any more, on a profit-per-card basis than if you played a single hand.  You use 50% more cards to win 50% more money.  There's no edge in doing that.

Can't explain it any differently, so if this time doesn't work, I'm afraid I'm out of approaches to make you understand.

Don

Got it!  That does make sense now! What I was thinking you were saying in BJ3 is that spreading to two hands in a head's up game meant I would win less money, not the same amount, when I bet optimally.  This is what I struggled with.  I understand why the last hand is different.  Also, your first answer to my question where you said "Short answer: yes." also made total sense.  I also liked the answer given by the Bishop (Arnold Snyder) in your book BJA3 on page 24: "When the count is high, you'd theoretically like to have as much money on the table as your bankroll can afford.  If you can get more on the table with multiple hands, then multiple hands are your best strategy, provided, of course, that multiple hands do not hurt you in some other way - notably, tipping off the casino that you may be a card counter."

There is no question that the reason I got backed off by two local casinos about 7 years ago was due to spreading to two hands. This definitely brings attention to a player, even when playing low stakes red chip bj.  Today, I'm smarter and rarely spread out to two hands unless I know it's acceptable at the casino I'm playing at. If ploppies don't spread out to two hands then I don't either, no matter what the count is.  If I'm playing with ploppies that spread out occasionally then I will too, but only in positive counts (and I don't do this very often)...and I only do it after a loss.  I understand now why this doesn't make sense in a head's up game, unless it's a way to get more money on the table after a loss and I know it's acceptable play at a casino.  There is one local casino here and one further away (4 hour drive) that does not allow spreading.  If you start with one hand, you can not spread in the middle of the shoe.  This is another reason I figured this type of play is probably an advantage to a counter.  It's good to know that playing more hands in a positive count is not that big of an advantage since it definitely gets the wrong type of attention.

As far as the casinos that backed me off, I went back to one of them about a month ago since they were giving out good comps. I figured it had been about 7 years since my backoff so I might be okay trying it again and getting some promotional chips.  After I gave them my license for a card, I got a tap on the shoulder in less than 10 mins to step away from the table.  This guy, along with several security guards, and the manager informed me - away from the table - that I wasn't welcomed there.  They told me I was in their computer system as being barred from their casino in 2010 (I think they might have actually said 2008).  They also informed me that they own casinos throughout NA and I would not be allowed to play in these casinos either.  This shows that casinos have long memories (or good computer systems) and even a low stakes red chip counter can get banned, pretty much for life.  As far as the other casino that barred me around the 2008 - 2010 timeframe, they were friendly and said I could continue to come to their casino and play any game but bj.  I actually had a long talk with the manager after I got backed off since this was the first time it happened to me and he was very friendly.  He said they had been watching my play for a while.  My barring was not due to my play for only that day.  He said they finally determined I was counting and they didn't want my action.  Again, I was never betting more than $50 at this casino.  My spread was pretty much from $10 to $40.  I've learned a lot from those days and haven't been backed off since.

Thanks again for being patient with me!
 

Fabian wrote:

"I have an idea of the hand spread when you are playing by yourself, but correct me if I'm wrong. My idea is to play as many hands as possible at the minimum bet when the true count is negative to eat all the bad cards fast"

If I appear to be nit picking I am sorry, but I do not want new players to get mixed up on interpretations. 
I know what you meant to say Fabian but it did not come out right. In reality you want to play the least amount of hands possible betting the minimum when the true count is negative. Accomplished by either wonging in and out and finding another table, or let others eat up the bad cards while you sit out hands.

" and play as few hands as possible when the true count is positive to eat few small cards (including bet spread)."

In this case you want to play as many hands as possible when the true count is positive, but avoid playing two hands when you are playing heads up, even if the TC is positive. 

"The thing I don't get is why you should play more hands if you are not by yourself at the blackjack table, why not just play one hand with a higher bet?"

Because, when you are not playing alone more cards are already being eaten anyway, it is not as big a factor. With others at the table by you spreading to two hands in positive counts enables you to get 50%  more  money on the table betting  75% on each of both hands of what your one hand wager would have been, with the same variance as playing the one hand with the higher bet.   

"With others at the table by you spreading to two hands in positive counts enables you to get 50%  more  money on the table betting  75% on each of both hands of what your one hand wager would have been, with the same variance as playing the one hand with the higher bet."

No, not the same variance.  The same risk of ruin.  Higher e.v., higher variance, same ROR.

Don 

Thank you Don, I messed that up.