Blackjack Basic Strategy Logic Question

[Dov]

I was reading 'Blackjack for Blood' by Bryce Carlson again yesterday and noticed something interesting regarding basic strategy.

As I understand it, basic strategy assumes that the dealer has a T in the hole because it is 4 times more likely that he has a T,J,Q, or K than any other card. However, it occured to me that it is still twice as likely that he DOESN'T have a T down. This is because there are 9 other cards he could have as hole cards as well.

So why does basic strategy assume a T when it is actually 9-4 (2.25-1)against the dealer having a T in the hole?

I have some ideas but I want to see if anyone actually knows this before I start guessing.

Dov

[knightunner]

This is due to precisely the reason you mentioned. It is 2.25:1 that the dealer has a ten. It is more likely that he has a ten than any other number, so it is easier to calculate odds for this. Of course this is assuming that the count is even. Variations on basic strategy occur once the count changes. I haven't read the book you are talking about, but I assume it tackles this topic...

~knight

[Dov]

Yes, it is a book on counting. The point is, though, that if you hold hard 16 facing the dealer's 7, it is twice as likely that his hole card is NOT a ten than it is. (with a neutral deck)

Why does basic strategy still assume that he has a ten there?

[Ed Miller]

Why does basic strategy still assume that he has a ten there?

Basic strategy doesn't assume anything about the denomination of the hole card. It calculates the highest EV play for the entire domain of possible hole cards.

Sometimes when people try to logically explain basic strategy, they do it in terms of "assuming a ten," but that's not how basic strategy is derived.

[cardcounter0]

Basic Strategy does not assume the dealer has a Ten in hole.
It assumes the dealer hole card is equally likely any of the remaining cards after the two cards you have in your hand and the dealer's up card is removed from the deck.

[cardcounter0]

It doesn't assume the dealer has a Ten in hole with a 7 upcard. It also assumes the dealer has a 3 or a 4 in the hole with a 7 upcard. It also assumes the dealer has a 9 in the hole, and will get a 5 when he hits his 16.
Basic Strategy takes into account every combination of hole card, and every combination of possible player and dealer hits, and sums them.

[pzhon]

Here are some situations in which basic strategy does not assume the dealer has a 10:

/images/graemlins/spade.gif Stand with hard 17 versus 8, 9, 10, and A.

/images/graemlins/spade.gif Hit with 12 versus 3. If the dealer has 13, improving to 18 is unlikely to make a difference, and is too risky.

/images/graemlins/spade.gif Split 88 versus 10. If the dealer has 20, this is horrible. It is not only worse than hitting, it is worse than standing and taking a sure loss.

/images/graemlins/spade.gif Double down with 10 versus 9: If the dealer has 19, doubling down wins roughly 5/13, tie 1/13, and loses 7/13, so you are better off hitting.

/images/graemlins/spade.gif Don't split with TT vs. 6. In Double Exposure (http://wizardofodds.com/games/doubleexposure/doubleexposure.html), the rules are slightly different (you lose ties), but it is right to split tens against a dealer 13-16.

/images/graemlins/spade.gif Don't double down with 8 versus a dealer 2-6. If the dealer has 12-16, you would want to double the stakes. In reality, the dealer is always an underdog to bust.

I don't think it is bad to say that you should imagine the dealer probably has a ten in the hole. That may help people to avoid some common mistakes, like standing on a stiff hand versus a dealer 7-A, or hitting a stiff hand versus dealer 2-6.

[Dov]

Thanks for your replies everyone. I Finally Get It!

[knightunner]

Me too! (And I thought I got it before)

[CORed]

Blackjack basic strategy does not assume anything. It is simply the play with the best EV for each combination of player total and dealer upcard. Because there are more 10 value cards in the deck than any other value, it happens that assuming the dealer's hole card is a 10 gives a fair approximation of basic strategy.