Average Standard Deviation

[DSchles]

Hi, Don,

Thanks so much for the detailed reply!

1) Yes, sorry, negative $1.85, not +$1.85.

2) Above you use 1.15 for s.d., but in your book you use 1.1. Please explain.

You haven't read very far in the book, have you. Depending on rules, one-hand s.d. can be as low as 1.12 (no DAS or resplitting of pairs). I used 1.1 just to make the math easy in the beginning of the book. All the chapter 10 charts have s.d.s, by the true count for every conceivable game. Use those. Don't use anything from the very early chapters.

3) If I am getting a higher number of blackjacks, that is (obviously) good. How can something so GOOD reflect POORLY on my standard deviation? (By the way, by not playing alone while sitting at first base, I am hoping to reduce the chance of the dealer getting 'my' Ace,' which should 'preserve' my edge of about 5%. Is this sound reasoning? I need to ask such a question because the .51 edge that I used in the calculation to arrive at my 5% edge has not taken into account that I may NOT receive the Ace that I claim I am certain of receiving by using .51, correct?)

Getting e.v. from blackjacks doesn't excuse you from the increased s.d. that comes along with them. Variance is, basically, the average squared result of a hand. If you square the global s.d. of 1.15, you get 1.32. Meanwhile, what's the average squared result of getting a 3:2 payoff? Obviously, it's 1.5^2 = 2.25. Hence the extra variance when your e.v. is derived from naturals. Variance isn't good or bad. It's just variance!

Can't help with the uncertainty of getting the ace. That's up to you to determine. I don't know what you're doing, so I can't tell you how likely or not you are to get an ace. But I can tell you with certainty that your overall variance, and hence s.d., is larger than what I calculated, as I warned you it might be.

4) How do I go about calculating a more appropriate s.d. for the 3 hands, or is that question 'outside the scope' of this thread?

Yes, it's somewhat outside. You may have read the recent reference to James Grosjean's 42.08% article. It refers to the optimal percent of one's bank to wager given one card in the hand will be an ace. But it requires playing a different BS than normal, to be more risk-averse, given such a large wager.

5) Above, where you indicate that you arrived at a different s.d. than I, did you forget to multiply the square root of 3 by 1.1?

Actually, no, I didn't; I just forgot to write that I did! Sorry about that. But the answer is right.

7) OK, yes, that's interesting about how one cannot average standard deviation. In the above, you added the E.V.s together. But could we also have used ONE E.V. (not 2 initially) as a result of using one edge ("Average Advantage"?) that results from appropriate weighting and averaging of the two edges (1 edge for the 37 hands and 1 edge for the 3 hands)? But if we do that, won't that low edge not accurately represent this shoe containing a very high on 3 hands of its hands? And how does one determine bet size for each hand with the use of an average (and not a specific-to-the-hand) advantage?

I don't see the point in one e.v. But, you have it. You play 40 hands and you win $1.15. So the per-hand global edge is $1.15/40 = $0.02875. But, it isn't really pertinent or useful for anything.

8) Using the numbers you arrived at, how can I, without computer software, calculate the ideal bet size given a specified Risk of Ruin and bankroll? Can I algebraically manipulate one of the Risk of Ruin formulas in Chapter 8 of your book "Blackjack Attack" (3rd ed.)?

You can use Norm's calculators, at the top, all based on my formulas. But there's no point. You really shouldn't be betting $10 on all the losing hands and then $20 for the aces. That makes no sense at all. You should be betting table minimum for the bad hands and whatever you can afford and get away with for the good ones. You have -0.5% edge on 37 hands and 5% edge (not sure where that comes from) for the other three, and all you want to bet is twice as much? Not very logical.

Don