BJ immediately wins regardless of dealer's upcard . . .

[James989]

How much it worth in term of ev ? 6 deck, S17, DAS

[Meistro123]

Well chance of dealer having blackjack starting with T is 1/13 and with A is 4/13. Obviously it is irrelevant to other cards.

Dealer will start with a T 4/13 or 30.77% of the time. So the chance of the dealer starting with a ten and getting a blackjack is 30.77% * 7.7% or 2.37%

I guess should be the same for ace.

So about the complement of (%97.63 * %97.63%) of the time or 4.78% of the time that you get a blackjack this will end up with you getting paid 1.5:1 instead of even money. You get a blackjack 1 in 21 times.

So 4.78% of the time you will get a blackjack. So around (4.78% * %4.78) both you and dealer will get a blackjack.

So around .23% of rounds you will end up getting paid 1.5:1 instead of pushing.

So I estimate this to be +.345% for the player and more in higher counts and less in lower counts.

Actually ever so slightly higher, I suppose, because of the EOR of one ten from the shoe for getting an ace, and vice versa for the ace and getting a ten, although this is probably cancelled out in that your blackjack makes it less likely for the dealer to get a blackjack. So probably ever so slightly lower actually.

[DSchles]

The exact value for six decks is 0.325%.

Don

[Meistro123]

Gonna go out on a limb here and say 1 in 13

[DSchles]

When people ask what a rule is worth in blackjack, you start by stating its value to the basic strategist. That's what we've done here. It isn't possible to tell you what it's worth to a card counter unless you specify bet ramp and decks and penetration. And then, it would have to be simmed.

There are more tied naturals at higher counts than at lower ones, and you bet your biggest money at higher counts. So, clearly, the rule is more valuable to the wide-spreading counter than it is to the basic strategist. How much more valuable? That's why there are 139 charts in Chapter 10!

Don

[scroogemcduck]

The probability of BJ-BJ push increases as the fourth power of the proportion of hi cards in the deck, so at higher counts this could be a very big deal. Suppose you have TC+10 on infinite decks so that there are about 6 aces and 24 tens per 52 cards. Then the chance of a blackjack is (6/52)*(24/52) + (24/52*6/52) = 10.6%, and the chance of a blackjack push is 1.13%, so the advantage gained by the rule is 1.7% at TC+10.

At +15, the advantage is around (((7/52)*(28/52) + (28/52*7/52))^2)*1.5 = 3.15%.

[Dog Hand]

See it this sounds reasonable. There are 6 rounds straight up in single deck. This would mean approximately 3 Aces are in play every deck. Now one Ace could land in 4 places. Two are with me. One is the dealers up card. One as the dealers hole card. So I would be looking at a dealers Ace once in 3 out of 4 decks. If I play 100 hands, that's about 16 decks. So I should have an insurance decision to make 12 out of 100. Even if the decision is no. I came to this as it's how we used to schedule. But I don't know the algebra equation.

moses,

If your dealer has an Ace up 12% of the time on average, you are being cheated.

Naturally, the long-term average is 1 of 13, or about 7.7% of the time.

Dog Hand

P.S. Did your "scheduling" involve calculating the carrying capacity of airliners? ;-)

[DSchles]

The probability of BJ-BJ push increases as the fourth power of the proportion of hi cards in the deck, so at higher counts this could be a very big deal. Suppose you have TC+10 on infinite decks so that there are about 6 aces and 24 tens per 52 cards. Then the chance of a blackjack is (6/52)*(24/52) + (24/52*6/52) = 10.6%, and the chance of a blackjack push is 1.13%, so the advantage gained by the rule is 1.7% at TC+10.

At +15, the advantage is around (((7/52)*(28/52) + (28/52*7/52))^2)*1.5 = 3.15%.

The actual numbers aren't nearly this good. For a six-deck game, naturals occur about once in 14 at +10 and once in 11 for +15. The corresponding edges would be about 0.76% and 1.24%. Clearly higher, but not to the extent that you imagine.

Finally, good luck finding +10 and +15 true counts in six decks! Hardly worth discussing.

Don

[James989]

Thanks for your answer.

[DSchles]

"No two work together twice in 6 games."

What you meant to say was, "No two work together MORE than twice in six games." Everyone works with everyone else exactly twice in six games.

Don

[DSchles]

Sorry. I misunderstood the point. What you have is simply 4C2, which equals 6.

Don

[James989]

The exact value for six decks is 0.325%.

Don

Don, another special rule : 6DECK, S17, Split(A,A) only draw one card, Split (A,A) and draw a T is a BJ and immediately wins regardless of dealer's upcard ! How much it worth in term of ev ? My estimate is +0.031%, please help to check my estimate. Thanks