The theory is (when playing HEADS UP) instead of betting 1 unit at TC < 1, we bet 3 hands of .33 units at TC < 1. This accomplishes a higher expectation PER ROUND, because we metaphorically eat through the bad counts to get to the good counts quicker. Also, the concept is we move our max bet out to 1 hand of x units as to get more rounds in +EV situations.

RESULTS: Higher Win-rate, lower ROR bankroll restrictions, camouflage. (according to zengrifter)

Normal High-Low Inverse hand spreading difference 6d, S17, DAS, 3/4 PEN, 8-1 spread max bet at TC>3=8u (TOP)

(BOTTOM)

TC<1=3x1u

TC>=1, TC<2= 2x2u

TC>=2, TC<3= 2x3u

TC>=3 = 1x24u

Expectation

0.6172%

0.9028%

+46.2735%

Std. dev./round

$45.51

$46.25

+1.6157%

Avg. bet size.

$31.29

$32.16

+2.7934%

Win rate/hour

$19.31

$29.04

+50.3591%

5% ROR 8 hour trip bankroll

$2,392.50

$2,370.50

-0.9195%

5% lifetime ROR bankroll

$16,067.21

$11,033.94

-31.3263%

Does this look correct? I know the original spread is sub-optimal and you math wizards can find your optimal betting spread, I just wanted to introduce this concept for those who didn't know of it and to get comments on its validity.

EDIT: The information above assumes a $5 unit.

Next, the dealer is more likely to get good hands as we are in good counts, but if we play more hands than the dealer we're also more likely to get the hands like blackjack that are one of the biggest advantages we have in the game (getting paid 3:2 on it).

I also don't see how this would be less RoR. If you calculate out a max bet, whether you spread it across 1 hand or 2 or 3 that is still your max bet. While you do introduce covariance by playing more than one hand, I'd think you actually reduce variance by playing more than one hand overall. A simple small example as above, you're giving yourself more opportunities to get a BJ so even if the dealer pulls a good hand (which they will in good counts) you won't necessarily lose 2 hands.

Lastly, if you keep the number of hands (3 hands let's say) up even in good counts, you'll finish the shoe "faster" but that doesn't mean with less profit, AND, if you finish it faster doesn't that mean you're getting more hands per hour in general? Again, a good thing for any counters EV?

Example: TC=5, we bet 1x12u, our hand total is 12, dealer shows T, we hit and bust with a 22. The dealer flips over a 4 for a total of 14. Now because the hand is completed and we busted with 22 the dealer CANNOT take another card where the dealer otherwise would have on the 14 if there were more hands on the table due to the fact that it is more likely someone made a hand to where the dealer would be required to draw.

Quote:RomesThis is an interesting and debated topic. One thing I always discuss with it is one hand of max betting... I don't see it as a positive to "draw out" the shoe (theory). We don't know if the count will go up or down on the next hand, but given the TC +5, using a balanced count like Hi/Low, we know the count WILL go back down by the end of the show. So why not take advantage of what's KNOWN right now? Why not bet more and more hands right now instead of guessing whether or not the shoe will stay as positive for the next hand? Would you rather bet 2 hands of your max bet at a known TC +5 this hand, or 1 max of at TC +5 and then next hand at "unknown"? Maybe it dips to TC +4, well now that bet is not worth as much as it would be at TC +5. Yes, it could go up to +6, but it's more likely to go down.

Next, the dealer is more likely to get good hands as we are in good counts, but if we play more hands than the dealer we're also more likely to get the hands like blackjack that are one of the biggest advantages we have in the game (getting paid 3:2 on it).

I also don't see how this would be less RoR. If you calculate out a max bet, whether you spread it across 1 hand or 2 or 3 that is still your max bet. While you do introduce covariance by playing more than one hand, I'd think you actually reduce variance by playing more than one hand overall. A simple small example as above, you're giving yourself more opportunities to get a BJ so even if the dealer pulls a good hand (which they will in good counts) you won't necessarily lose 2 hands.

Lastly, if you keep the number of hands (3 hands let's say) up even in good counts, you'll finish the shoe "faster" but that doesn't mean with less profit, AND, if you finish it faster doesn't that mean you're getting more hands per hour in general? Again, a good thing for any counters EV?

Also the math geniuses have stated that it is actually higher EV to bet one hand of $150, than 3 hands of $50. This is counter-intuitive but that is what the math says.

This is where I disagree with this theory. First, it only truly applies heads up. Sure "everyone" could bust if you have 1 or 2 more players at the table, but as you're alluding to it's less likely to happen and thus the dealer will sometimes draw more cards. Though in a nice positive count such as the TC +5 example, the dealer will in general draw less cards.Quote:crazydazyI think from a theory basis we want one hand max bets ideally because we can literally see more rounds in +counts. This is solely due to the fact (IN HEADS UP) that we can lose the hand and the dealer is less likely to draw additional cards (effectively eating some of the good cards).

Example: TC=5, we bet 1x12u, our hand total is 12, dealer shows T, we hit and bust with a 22. The dealer flips over a 4 for a total of 14. Now because the hand is completed and we busted with 22 the dealer CANNOT take another card where the dealer otherwise would have on the 14 if there were more hands on the table due to the fact that it is more likely someone made a hand to where the dealer would be required to draw.

Next, I again circle back to the "more rounds" in a positive count. What's worth more... More rounds in a positive count or more bets at the same known positive count? Let's take this to an extreme and let's say we "know" the count will go down after 2 rounds. What's worth more:

1) Betting 1 hand 12 units for 2 hands.

2) Betting 2 hands 9 units (essentially 1 hand 12 units) for 1 hand.

Option 2 is both worth more, and reduces variance. Now let's get in to some fun theory. If the number of hands N until the count goes back down is ODD, then it's DEFINITELY our advantage to bet 2 hands as opposed to 1, because you'll get an entirely extra bet. Same example as above, but the count will go down in 3 hands:

1) Betting 1 hand of 12 units for 3 hands (3 bets).

2) Betting 2 hands of 9 units for 2 hands (4 bets).

It's a bit clearer in the case where the number of rounds before the count drops is odd.

No, that sounds quite correct. 2 hands of $50 is roughly the equivalent of 1 hand of $75, so it would make sense that 3 hands don't add up to the full EV of 1 hand unless you change your bet sizes. Wong writes about this in his book and refers to co-variance and bet sizing.Quote:crazydazy...Also the math geniuses have stated that it is actually higher EV to bet one hand of $150, than 3 hands of $50. This is counter-intuitive but that is what the math says.

1) Betting 1 hand 12 units for 2 hands (assuming positive count)

versus

2) Betting 2 hands 9 units for 1 hand (assuming positive count) this is the same as 1 hand of 12u in terms of EV

Scenario 1 is better because we effectively get more money down in a positive count.

Round 1 we get 12 units down, Round 2 we get 12 units down for a total of 24 units.

Scenario 2

We get 18 units down on 1 round split across two hands. (equivalent to the EV of one hand 12u, although with less variance).

Scenario 1 clearly generates more EV which is what I am isolating for this concept.

I do agree with your assessment of (1) vs (2) though. I think I was thinking higher bets in my head.

One thing you are forgetting though... Say there's TC +5 (as we've been saying all along) with 1 deck left... Say you get AJ vs dealer KQ... You bet 1 hand of 12 units, but now you're at TC +1 and you're not even raising your bet... You're betting 1 unit instead of 12. I still think there's more involved in betting KNOWN true counts because what you're doing is "hoping" the TC will be just as positive for your bet on the next hand, when mathematically speaking it WILL go down by the end of the shoe. So it's more probable to go down, but you're holding out for 2 hands in hopes of more EV but not guaranteed. The guarantee would be to bet 2x18 right now... that would get you 2 guaranteed bets at TC +5 right now.