A Serious and important question

The following question is addressed to knowledgeable counters who have
kept track of blackjack news. As background, I recently returned from
Las Vegas and have been rereading a number of books both before and after the trip.

Upon reflection after rereading "The Theory of Blackjack" for the
upteenth time, I was nearly floored when I realized that the change
in strategy numbers provided in many popular books are horrendously
inaccurate for practical double down and pair splitting situations.

My question is whether this issue has been addressed by others over
the years. Since I'm not a heavy gambler, I don't follow the news
and wouldn't know. For this reason, I will refrain from providing
a lengthy analysis demonstrating the above at this time.

Are you referring to risk-averse indices? Why don't you tell us what you mean by your remarks. The books are correct, for the most part, for EV-maximizing indices. They aren't meant to provide any means of comparing extra gain to extra risk taken on.

I would imagine that's what you're referring to.

Don

"...after rereading "The Theory of Blackjack" for the
upteenth time"

Why don't you just read it once and understand it the first time? Don't read it fast, like an airport novel, but slowly, advancing only as each point is comprehended?

"Why don't you just read it once and understand it the first time? Don't read it fast, like an airport novel, but slowly, advancing only as each point is comprehended?"

BECAUSE you would finish a chapter once every decade using your method. And you would probably still not fully understand some things. Much easier to forget about blackjack and come up with the Grand Unification Theory.

No good, my dear SotSog...Grand Unification cannot be contemplated while there is an impotent question....

TYPOS?

I have wandering the some thing.

First, I'd like to thank you for your serious response to my question and for restraining yourself from commenting on my obvious typo.

I don't gamble very often, but I've always been intrigued with blackjack. I don't recall risk-averse strategy as being referenced in any of the books I've read, which include "Theory of Blackjack",
"Million Dollar Blackjack", The World's Greatest Blackjack Book",
"Blackjack Secrets and "Blackjack Essays".

Actually, after further reflection I realize that the problem at hand is too obvious to have been missed, even though it never previously occurred to me. Therefore, I feel somewhat foolish in proceeding, but I'm very curious to know about the accuracy of the change in strategy indices found in some of the above mentioned books. Here goes:

I am assuming the following assumptions (which may be wrong) as to how change in strategy indices are determined:

- A change in strategy occurs if such change maximizes a players expectation.
- An infinite bankroll.
- In a double down situation, a player will hit if the expectation is negative. A player will double down if the expectation is positive, and it is greater than the expectation for hitting.

Now, the problem as I see it is that I would think a change in strategy should be a function of both a player's percentage advantage for the hand in question, and the percentage of his bankroll that has been wagered.

If my analysis up to now makes sense, then it is easy to provide examples showing why some change in strategy indices for doubling down (and maybe pair splitting?)found in many popular books are dangerous. For instance, on a players large bets, he could be wagering 4% of his bankroll (after the double down) when having only a 0.5% advantage. Obviousy, this type of consistent betting pattern greatly increases the likelihood of ruin (in practice, if not in theory).

Put another way, as a player wagers a greater percentage of his bankroll, it becomes less likely that the player should change strategy by doubling down. Indeed, there may be situations where a player shoudn't double down even though basic strategy says otherwise. This result is contrary to the familiar change in strategy rules, which indicate that a player should be more willing to double down as the count increases.

Again, assuming my analysis is accurate, I'd be bery curious to know how and where this problem has been addresses.

Thanks

Congratulations! You've just been in a time-warp for 21 years and have emerged to "discover" risk-averse indices all on your own! :-)

The problem was first studied by Joel Friedman in a paper he wrote at the University of North Carolina at Chapel Hill in 1980.

You are correct about its total absence from the books on blackjack. I rectified that in the second edition of BJA, Chapter 12, Part II. I suggest you have a look at that.

You may also want to reference Karel Janecek's "Statistics of Blackjack," which he provides with his SBA software.

Don

P.S. Without giving much explanation to the process, Bryce Carlson, in his "Blackjack for Blood," actually tried to generate risk-averse indices for his Advanced Omega II count. I don't think they're 100% accurate, but he is to be commended for at least incorporating the idea in his overall strategy, which hadn't been done by any other author before him.

"I have wandering the some thing."

Did it ad up rite?

For the most important indices, it seems that greates % error in his "RA" indices are for 10 vs 10 and 9 vs 2. He underestimate the 10v10 index and overestimates the 9 v 2. He states in his book "This point occurs (RA index) when the added gain from bet doubling, expressed as % of original bet, is equal to the player's overall edge". That is when "doubling or splitting will not only win more money (or lose less), but will no dilute the player's overall edge."
"That is what we have don with AOII" Out of curiousity, what specifically is faulty with this thinking and why did it underestimate 10v10 and overestimate 9v2.

In defense of Bryce, he also stated "Another valid approach, that of calculating these indices so as to maximize the log of the expected win, is not really feasible due mainly to real-world betting constraints necessitated by camouflage considerations" That is it seems he was aware of more correct approach but did not take it on because of complications (for example different RA indices for different betting). Thanks for any answers.

All you need to do is come up with an example where maximizing expected log of bankroll is different from matching the player's overall edge. I think you have the talent for that.

It should be pointed out that expected log of bankroll isn't the only utility (nor even the only risk averse utility). Lefty pointed out to me once that even risk athirst strategies can be "rational" as defined by a mathematician. You define a utility, you define a whole new set of indices.

ETF

Is gambling writers who talk about "advantage", which is a percentage of money wagered. This is really a meaningless statistic. Trying to optimize your "Percent advantage" serves no purpose.

As you and ET Fan have notified, the correct method would be to maximize your utility. In other words, you should pick the strategy which gives you the highest Certainty Equivalent. Now for games like BJ, you can approximate your CE very well by looking at Mean and Variance (and Bet Size, of course.)

If you maximize your CE in this way, you will also be generating the strategy which optimizes your SCORE. I think there are some posts of mine on BJ-Math that discuss this point.

In case you are wondering why I add the qualification for "games like BJ" the key properties of BJ are relatively small bets, and relatively small higher moments (Skew, Kurtosis,etc.)

PS1: Let me thank you for your remarks on Bryce's indexes. I had know that Bryce used an incorrect method in his approach, but I did not know what specific indexes he had mis-computed.

PS2: I really think the best explanation of this whole theory is in Don's BJA-2, which I highly recommend.

I had written

"I have wandering the some thing"

Obviously I meant to say

"I have been wandering the some thing"

It is really bad when you can't keep typos out of your typos.

Obviously you meant to say:

"I have been wondering about the same thing."

"I have been wandering the some thing"

Shouldn't it be: "I've BIN wandering...?"

Obviously we were not wondering about the same thing...