9,9 VS. 7

I am very loyal and have much faith when it comes to basic strategy. However, I've always been curious about how the gears to everything works...

When you've got a pair of 9's (Split to 2-9 accept for 7...that's the multi-deck strategy, at least) against a dealer's 7 why don't you split? When I get that hand, I stand of course because basic strategy says so...but this is one of the only plays that's made me think WHY DAMNIT?! =)

You split them if the dealer shows an 8 or 9 or 6...so why not a 7? I must be thinking too hard. Hmmm...

As always, replies are greatly appreciated as there is much wisdom to be soaked in here.

-Pard Pounter

The "simple" answer is that splitting 9s increases your EV against 2-6,8,9.

The "intuitive" answer...
First, remember that an 18 is not a particularly strong hand. If the dealer does not bust, you will lose more than half the time.

2-6 are potential bust cards. With a split, you can double your winnings on a bust. With a "2", you get a double down opportunity. With a 10 or Ace, your hand has improved. Nearly half the time, something very good happens after the split.

7 Is a special case. The dealer's most likely hand with a 7 showing is a 17. 7,8,9,A, the dealer is less likely to bust, but you win outright if the face down card is a 10.

If an 8 is showing and you split, you will "improve" your hand with a 2,10 or A on the first card nearly half the time. If you do not, and you hit until you are at 17 or more, your average hand goes up to about 18.5... In summary, your expectation goes up substantially if your first card is solid (6/13 times), and you about break even if it does not (higher average hand, offset by busting about 1/4 of the time).

So why do you split against 9's? Again, your 18 is a "weak" hand. You have the same math against the 9 as 8 for hitting, except the cost of standing is much higher.

As Daringly has pointed out, the simple and most intuitive answer for 9,9 v 7 is that you have 18 and the dealer likely has 17.

Epstein, in the "Theory of Gambling and Statistical Logic," provides a table (Appx A) with these numbers:

Expectation of standing w/ 9,9 v 7 = 0.9665

Expectation of splitting 9,9 v 7 = 0.4011

So, you are more than twice as likely to "win" by standing. (NOTE: These are single deck numbers and not count-dependent.)

Whoh, dude, something is out of whack. :) I wouldn't even buy .9665 for twenty v 7.

Check again. ;-)

ETF

I tried to do this too quickly, I think. So, let me try this again:

1) The expectation by drawing minus the expectation by standing (when holding 9,9 v 7) = -0.9665.

2) The expectation by splitting this pair = 0.3611.

3) The expectation from optimal strategy (which is stand) is 0.4011.

Sorry for any confusion I may have caused-- the conclusion is still the same (standing is better), but I misreported the numbers.

Personally, it would have to be a TC of at least +4 for me to split these up.

SnowE.

From Wong's Professional Blackjack (tables in appendix E, page 314)

Single deck

9-9 vs. 7

Stand: +.401
Split: +.341 (NDAS)
Split: +.363 (DAS)

--Mayor