Hi-Lo or 10-Count?

Hi,

I�d like to ask how much could I win (or lose) if I switch from Hi-Lo to 10-Count to achieve a better (100%) IC. The game is 6D, S17, DA2, DAS, ES10, ENHC, but it has one weird rule � one is offered insurance every time the dealer�s first card is 7 through Ace. This is 8/13 or 61.5% of the time. Thus, using the insurance bet can be very profitable when the proportion of tens is high. That happens about 12% of the time. So, the absolute percentage is 0.615x0.12=0.074 or 7.4%. I am flat-betting and using a bonus that gives me an advantage over the house anyway. So, I am not interested in BC. Using 10-Count for insurance decisions is explained by Stanford Wong in his Professional Blackjack. Every ten card is assigned -2 value and any other card is given +1 value. Thus when RC is more than 24 (for 6D) it is profitable to take insurance. Will my playing decisions suffer a lot if I use the obsolete10-Count? I could recalculate 10-Count RC to Hi-Lo TC to find the critical indices. Playing Efficiency (as defined by Griffin) is not relevant to unbalanced counting systems and is only an estimate. But how bad an estimate? So, what is better? Hi-Lo with PE=51% and IC=76% or 10-Count with PE=?% and IC=100%, taking in account how often the insurance is offered?

Blackjack Rookie

Blackjack Rookie,

Although you didn't say explicitly, I assume that, when you take insurance against a 7, for example, you're placing a sidebet that the dealer's second card will be an X, rather than that the dealer will draw to 21. I further assumed that the insurance wager pays 2:1, and that you could take it regardless of whether or not you surrendered your hand... is this in fact the case, or must you choose between ES10 and insurance?

I used the "insurance count" you mentioned (X = -2, all other cards = +1), but I started at an IRC of -24. Thus, the insurance wager EV is 0 at a RC of 0, and +EV at all positive RC's.

I simmed this problem as a sidebet in CVData, which is just a bit "off" for the situation, since in CVData we have to place the SB before we know that the dealer has a 7-A, and we have to decide to place the SB before the dealer starts dealing the round. In the actual situation, of course, you could take insurance only when the dealer shows a 7-A, and would calculate the RC at that exact moment (and so have an up-to-the-minute RC).

I ran one 400-million-round sim, and found that, if you could take the SB on EVERY round (that is, regardless of the dealer's upcard) for which the RC>=0, then you would place the SB on 11.5% of the rounds (46,037,577 times out of 400,000,000 rounds) and your SB EV would be 4.832% (16,087,337 times won out of 46,037,577 SB wagers).

Of course, you can only take insurance if the dealer shows 7-A, so I ran another 400-million-round sim to see how often the dealer shows a 7-A when the RC>=0. Here, I found that the percentage of a dealer showing 7-A is 63.82% (29,370,448 times out of 46,018,604 total rounds with RC>=0), which is a few percent higher than 8/13 = 61.54%.

This means that you would be able to take insurance (with +EV) approximately 11.5%*63.82% = 7.34% of the rounds, and enjoy an edge on those SB's of about 4.832%. Thus, using the 10-count would add 7.34%*4.832% = 0.3546% to your BS EV. I would venture to guess that this is a lot more than the gain you would realize by using HiLo to vary your play while flat-betting.

Hope this helps!

Dog Hand

Dog Hand,

Thanks for your help.

Your assumptions are correct. Insurance is a sidebet that the dealer's second card will be an X and this bet pays 2:1. Insurance can be taken regardless of whether or not the player surrenders his hand.

The sim results are close to what is expected. But I am afraid I�ll have to revise the sentence �Thus, using the 10-count would add 7.34%*4.832% = 0.3546% to your BS EV.� I think the number 0.3546% should be reduced by half because the insurance wager is not allowed to be more than half the initial stake. Perhaps using the 10-count instead of Hi-Lo is a moot point because with Hi-Lo I�ll take insurance bets also, just my decisions will be correct 76% of the time.

Thanks again and, as Mr. Schlesinger says, good luck and good cards!

Blackjack Rookie

Thus, using the insurance bet can be very profitable when the proportion of tens is high. That happens about 12% of the time.

Where did you get that number from?It seems pretty high to me.What kind of pen do you get?

I am flat-betting and using a bonus that gives me an advantage over the house anyway. So, I am not interested in BC.

This requires some further explanation.Do you mean that if you accept flatbetting you get a bonus that is more valuable than the benefits of varying your bets?

Francis Salmon