Bonaqua: One stupid question to Don Schlesinger

[Bonaqua]

Dear Mr. Schlesinger,
please explain one thing. I read your book "BlackJack Attack" 3-rd ed. On the pages from 394 to 474 You gave the Complete Basic Strategy EVs. Lets look, for example, on the page 395, column freq. In the case Hand 3,2 frequency is 0.00065011
How You obtain this number?
My calculations show that the frequency of this situation will be 4/52*4/51*4/50*2=0,000965309

I no doubt that You and Mr. Cacarulo right in your calculations.
But please tell me where is my mistake?

Thanks.

[Don Schlesinger]

> Dear Mr. Schlesinger,
> please explain one thing.

With pleasure.

> I read your book
> "BlackJack Attack" 3-rd ed. On the pages
> from 394 to 474 You gave the Complete Basic Strategy
> EVs. Lets look, for example, on the page 395, column
> freq. In the case Hand 3,2 frequency is 0.00065011
> How You obtain this number?
> My calculations show that the frequency of this
> situation will be 4/52*4/51*4/50*2=0,000965309

> I no doubt that You and Mr. Cacarulo right in your
> calculations.
> But please tell me where is my mistake?

> Thanks.

Unfortunately, you picked the first chart, where the dealer's upcard was an ace. Had you gone to a different chart, with upcard 2-9, you would not have encountered this apparent problem, and your calculations, no doubt, would have been correct.

The frequencies that you see are for playable aces. The assumption is that the dealer has already checked for a natural, and that he doesn't have a ten underneath. Otherwise, none of the plays -- stand, hit, double, etc. -- would make any sense.

Now, using your numbers, above, there are 49 cards left for the dealer's hole card, and 16 of them are tens, so the chance of having a playable ace would be 1 - 16/49 = 33/49. Try multiplying your 0.000965309 by 33/49, and see what you get.

It should make you happy! :-)

Don