Wolverine: Ill-18 12 vs 6 question

[Wolverine]

Have been working hard to add the Ill-18 to my game. Finished memorizing the DD indices today (s17) and passed numerous tests to confirm the memorization. First step taken. (And I didn't even pay SunRunner for his newly minted $35 flash cards! ;-) ).

I realize that a ton of research, math calculations, simulations, etc... have gone into the indices given on page 213 of BJA3. But, how can the index for 12 v 6 be 0? I realize that in the s17, DD game, the dealer is going to turn over an ace occasionally to make a "pat hand" but the number of busts with a ten value card on the 12 has got to eat into the value of the dealer busts with the 6 showing!?!?

I've done OK in math, but it has been a while since I attended school...so here goes nothing.

As I see it, hitting a hard 12 vs. dealer 6 is going to bust 4/13 times (p=.308). "Improving" that hard 12 into a 13 to 16 (still a loser unless a dealer bust occurs) will occur when another 4/13 cards hit the 12 (the ace, 2, 3, and 4) (p=.308). I don't have any other reference material to quote, except my T.J. Reynolds' "Complete Book of Blackjack" page 80 stating that dealers bust "42.08% of the time" with a 6 showing. It appears this data was cultivated from Braun and Baldwin.

That would leave 5 cards which helps the 12 to become a *possible* winning hand (p=.385).

If I bust and even if the dealer busts later, I lose. That should occur .308 of the time (thanks Tens, where were you when I doubled my 11?). I win when the dealer busts after I have hit 12 and gotten a lousy card that doesn't reach 17 the same amount of the time or .4208 x .308 = .1296. But I would have won without the hit, as the dealer broke, so I took a risk receiving that card. If I make a hand and the dealer busts, I win. That should happen .4208 x .385 = .162.

If the dealer breaks 42% of the time, they actually make a hand 58% of the time. Can I assume a 50-50% split of "making a hand" by both of us 17-21 including pushes? Then the 38.5% I make a 17-21 hand out of the twelve, the dealer will make a hand 58% of the time, for a p=.2233 expectation. Half of that (playing it even: win, lose, or push equally) would be roughly +.11 in wins for the player.

Possible outcomes:
Action Player Outcome
Hit 12 and player busts -.31
Hit 12 (stiff) and dealer busts +.13
Hit 12 (good) and dealer busts +.16
Hit 12 (stiff) and dealer makes hand -.18
Hit 12 (good) and dealer makes hand (win) +.11
Hit 12 (good) and dealer makes hand (lose) -.11

Lose 60% and win 40%

--OR--

No hit 12 and dealer busts +.42
No hit 12 and dealer makes hand -.58

It seems like this is a 50-50 play whether you hit it or stand on it. But if it is this close at 12 v 6 (and 12 v 5 would be nearly identical since dealer busts on fives is 42.89%) then to hit on 12 v 2, 3, **or 4** should be Basic Strategy. But BS says stay against the 4, 5, and 6. Why is that? Should BS be modified to be a hit 12 vs 2 through 6?

Thanks for the thoughts in advance.

[Don Schlesinger]

> Thanks for the thoughts in advance.

I hate to just "dismiss" your attempts at logic and analysis, but there is infinitely more math and combinatorial analysis going on for the hands you discuss than what you have offered.

The precise probabilities for hitting and standing on holdings of 12 v. dealer's 2-6 are given in Appendix A of BJA3. You can compare e.v.s there to see why hitting is right v. 2 and 3 and standing is right v. 4-6.

As for the 12 v. 4 DD index of 0, it is what it is, and it is correct. Note that, when you have received a 12 v. 4, no matter what the composition of your holding (T,2, 9,3, 8,4, or 7,5), your RC is positive, and, therefore, the count play (stand if TC is equal to or above 0) is consistent with the BS play to stand.

Don

[Wolverine]

[Wolverine]

Don,
The original question was 12 v 6, not 12 v 4 (I see why you are confused, we went over that earlier in the week/weekend). Do YOU hit 12 v 6 when the RC is negative in the DD, s17 game I described? Is that play tolerated in a casino? Or do they just shake their head at you like you are an idiot?!?

Thanks. I don't mean to be a pest, but these 12 totals just seem so wacky to me!

[Don Schlesinger]

> Don,
> The original question was 12 v 6, not 12 v 4
> (I see why you are confused, we went over
> that earlier in the week/weekend).

Right. Sorry. The advice was for 12 v. 6; I just wrote 12 v. 4 by mistake.

> Do YOU
> hit 12 v 6 when the RC is negative in the
> DD, s17 game I described?

Yes.

> Is that play
> tolerated in a casino? Or do they just shake
> their head at you like you are an idiot?!?

Same thing, right? The people most likely to shake their heads are the other players at the table.

> Thanks. I don't mean to be a pest, but these
> 12 totals just seem so wacky to me!

No problem. Hands have expectations. They are what they are. Some things seem logical, and others may seem less so. In the end, it's all just math. (And, some things seem more logical to some people than to others. :-))

Don