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Risk-Averse Betting

In Lesson 14 of my Blackjack School, I make this reference to the index numbers I use in the Basic Strategy variations presented therein: "...a few have been modified based upon the theory of 'risk averse' play which was developed about 15 years ago. These numbers work well; they have been proven in thousands of hours of actual casino play by me and my students."

Basic Strategy variations cause us to modify the play of a hand according to the count. For example, Basic Strategy for my "school" game (6-decks, S17, DA2, DAS) tells us to always hit a hand of 9-7 or 10-6 (sixteen) against a dealer's 9. But the variation is to stand if the True Count (TC) is 5 or more. That makes sense; as the count increases on the plus side, the probability of receiving a 10 as the hit card increases proportionately. On the other hand, Basic Strategy says to hit a hand of 9 versus a dealer's up card of 7, but the variation is to double 9 vs. 7 when the TC is 6 or higher. As the count increases in our favor, we will not only bet more, but will also stand more, surrender more often (if possible), double more and split pairs more often. All of those variations are primarily a function of the mathematics involved - if you will make X $$$ hitting 9 vs.7 when the count is 0 (the count a Basic Strategy player effectively uses), when the TC is 6 or higher you will make X+ if you double. My index number for 9 vs.7 is 6, but most counting systems show an index of 3 for that play. My index is a "risk-averse" number, whereas the 3 is an "expected value" (EV) number. Why the difference?

Hopefully you understand that expected value for each hand is the means by which we determine the Basic Strategy. For example, if you hit a hand of 9 versus a dealer's up card of 7, the EV is +17.61%; if you double, the EV is +11.60%, so the proper play - if you're not counting the cards - is to hit. But if the TC is 3 or more, the EV for doubling is +17.95%, which is a higher return than just hitting. But you can also see that the EV gained is very small; 17.95 versus 17.61. However, to get that additional 0.34%, you must risk an extra bet (remember that the EV for doubling is based upon the original bet, but the play requires you to place another bet that typically matches the original.) To further clarify this, let's say you've bet $1000 on a hand because the True Count's up to 3 (you're a high roller) and you receive a 9 against the dealer's 7. You double your bet to $2000 and take just one card. Now your risk is $2000, but your expected gain is 0.0034 x $1000 = $3.40. That's fine, it's what we do in this business, take every opportunity and exploit it to the max. It's an extra $3.40, which is good. But it's only good, if...

Making Basic Strategy variations based solely upon the EV assumes that a loss will not affect how you will play the next hand. I'm not talking psychology here - none of us like losing $2000 doubles - but what impact will that have on your bankroll? Obviously, your bankroll will be smaller. (All together now: $2000 smaller.) But will that loss require you to change your bet size? If you're truly rich and such a loss will have no impact, then the EV play is the way to go. But, if you're like most of us, your bankroll is finite, so 2, 3 or 4 such losses might require us to change the bet schedule from, say. $350 times the TC - a $1000 bet at TC 3 - to $250 times the TC or $750 at TC 3. The idea that we should bet in proportion to our advantage (the Kelly Criterion) is what creates the need for risk-averse indices for those plays where extra bets are risked, namely splitting and doubling. If your bet-to-bankroll size is just a small fraction of "Kelly", as opposed to the 75% of Kelly that I always recommend, risk-averse indices aren't as important. But, if you - like most beginners - are basically funding your play from current income, then you should use the numbers I show in lessons 14-16, which are available here: http://www.gamemasteronline.com/BlackjackContent.shtml

In those lessons, there are several numbers that I omitted on purpose, like doubling your hand of 10 versus a dealer's up card of 10 and splitting 10-10 vs. a dealer's 5 and 6. In the case of 10 vs. 10, the EV number is 4, but the risk-averse number is much higher, so I just left it out because you'll likely never see that high a count in a 6-deck game. In the case of splitting 10s, I left that out not so much because of the risk of losing, but more because of the risk of getting barred from the casino. For those of you who want to do it, the risk-averse number for splitting 10-10 vs. 5 is 6 and for 10-10 vs 6, it's 5. Easy to remember, but don't say I didn't warn you.

I'll see you here next time.

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