Since the dawn of card counting, blackjack players have been told that they must spread their bets in order to make any serious amount of money off their play. The only restriction has been the unknown, subjective, arbitrary, and post hoc limits imposed by casino management. Don Schlesinger has discovered that smaller spreads in backcounting simulations do not give up much versus larger ones in terms of SCORE, but a stronger observation results from use of certainty equivalent (CE) as the measure of risk-adjusted winnings.
It turns out that if optimal CE is used as the standard, the departure from canon is even more dramatic. I have used Norm Wattenberger’s CVCX site to note the results of his sims with six-deck games, and there is a point beyond which spreading one’s bets actually REDUCES risk-adjusted expectation.
As an example, let’s pick a semi-safe, prevalent six-deck game currently available at various minimums up and down the strip. It is particularly identified with one of the largest casino chains, appearing at several of their properties. Better games exist, but this one is common enough and safe enough that it can serve as a bread-and-butter game for shoe players and teams. We will disguise it by calling it the Moderately Good Money game. The rules are S17, DAS, LSR, 4.5/6.
According to Wattenberger’s data, the CE with the HiLo + I18 + F4 is maximized when the spread is 1-25 (with backcounting, of course). If you spread less than this, you give up some bucks in exchange for camo, but if you spread more than this, you are actually decreasing your CE!
The gain for tamer spreads can be expressed as a percentage of the maximum:
Spread CE CE/max
2 $25.54 0.890827
3 $26.87 0.937217
4 $27.40 0.955703
5 $27.70 0.966167
6 $28.11 0.980467
8 $28.48 0.993373
10 $28.65 0.999302
12 $28.66 0.999651
15 $28.66 0.999651
20 $28.66 0.999651
Wonging in was at +2 for spreads of 2 to 4 and at +1 for larger spreads; these values were of course chosen to optimize CE. Note that for a spread of 1-12, the player gives up only one cent versus the CE, establishing that this spread for the game in question is a lot more efficient than was perhaps realized previously. The 99% mark is achieved with a spread of 8 (and perhaps 7, which I was too lazy to check, although linear extrapolation implies 7 would be inadequate). If you have been swept up by the current emphasis on change in American political discourse, use a 1-5 spread: you will give up only 97c, less than a dollar, versus the theoretical maximum.
The pattern of a spread that maximizes CE persists in one-deck and two-deck games. However, the spreads that maximize CE tend to be in the hundreds for playable pitch games and are of less interest as a practical matter. I investigated the 1d, H17, NDAS, 0.6/1 game and the 2d, H17, DAS, 1.4/6 game on Wattenberger’s page and found that the CE-optimal spreads were between 200 and 400 in each case.
I haven’t bothered to check yet to see if anyone else has “discovered” this tendency, so if I’m inventing the telephone for the second time, so be it. Regardless of how “original” my insight is, however, shoe players who have taken pride on having such a good “act” that they can spread 1-100 or more can stop working on their act now: they’ve overdone it.
It turns out that if optimal CE is used as the standard, the departure from canon is even more dramatic. I have used Norm Wattenberger’s CVCX site to note the results of his sims with six-deck games, and there is a point beyond which spreading one’s bets actually REDUCES risk-adjusted expectation.
As an example, let’s pick a semi-safe, prevalent six-deck game currently available at various minimums up and down the strip. It is particularly identified with one of the largest casino chains, appearing at several of their properties. Better games exist, but this one is common enough and safe enough that it can serve as a bread-and-butter game for shoe players and teams. We will disguise it by calling it the Moderately Good Money game. The rules are S17, DAS, LSR, 4.5/6.
According to Wattenberger’s data, the CE with the HiLo + I18 + F4 is maximized when the spread is 1-25 (with backcounting, of course). If you spread less than this, you give up some bucks in exchange for camo, but if you spread more than this, you are actually decreasing your CE!
The gain for tamer spreads can be expressed as a percentage of the maximum:
Spread CE CE/max
2 $25.54 0.890827
3 $26.87 0.937217
4 $27.40 0.955703
5 $27.70 0.966167
6 $28.11 0.980467
8 $28.48 0.993373
10 $28.65 0.999302
12 $28.66 0.999651
15 $28.66 0.999651
20 $28.66 0.999651
Wonging in was at +2 for spreads of 2 to 4 and at +1 for larger spreads; these values were of course chosen to optimize CE. Note that for a spread of 1-12, the player gives up only one cent versus the CE, establishing that this spread for the game in question is a lot more efficient than was perhaps realized previously. The 99% mark is achieved with a spread of 8 (and perhaps 7, which I was too lazy to check, although linear extrapolation implies 7 would be inadequate). If you have been swept up by the current emphasis on change in American political discourse, use a 1-5 spread: you will give up only 97c, less than a dollar, versus the theoretical maximum.
The pattern of a spread that maximizes CE persists in one-deck and two-deck games. However, the spreads that maximize CE tend to be in the hundreds for playable pitch games and are of less interest as a practical matter. I investigated the 1d, H17, NDAS, 0.6/1 game and the 2d, H17, DAS, 1.4/6 game on Wattenberger’s page and found that the CE-optimal spreads were between 200 and 400 in each case.
I haven’t bothered to check yet to see if anyone else has “discovered” this tendency, so if I’m inventing the telephone for the second time, so be it. Regardless of how “original” my insight is, however, shoe players who have taken pride on having such a good “act” that they can spread 1-100 or more can stop working on their act now: they’ve overdone it.
. 