First there's a 1/13 chance that your first card is an ace, and a 1/13 chance that your second card is a 7. So there's a 1/169 chance of getting A-7. Since 7-A counts too, the chances that you have a soft 18 is 2/169.

Given that you have a soft 18, the likelihood that the dealer has a 9 is 1/13. Based on the Wizard's appendix, the amount that you lose by standing instead of hitting is -0.1832 - (-0.1007) = 0.0825. So the total change in house edge for soft 18 against a 9 is 2/169 x 1/13 x (0.0825) = 7.5e-5.

Similarly for soft 18 against a 10 is 2/169 x 4/13 x (0.0335) = 1.22e-4.

For soft 18 against an ace the result is 2/169 x 1/13 x (0.0073) = 6.6e-6.

So the total for all these is the sum of the individual results = 1.98e-4, or about 0.02%.

In summary: given that you are facing a soft 18 against a 9, 10 or ace, you are giving up between 1 and 8% of the expected return for that hand by not playing basic strategy. However, this situation arises so rarely that the impact on the total house edge of the game is very small.

That is fine. Most players who knew the "exact answer" when they walked into the casino wouldn't be able to cite it after a few drinks and few chats with the waitress.

>In summary: given that you are facing a soft 18 against a 9, 10 or ace, you are giving up

>between 1 and 8% of the expected return for that hand by not playing basic strategy.

To me this is not a large amount but some of the blackjack players and counters on this board might dispute that.

>However, this situation arises so rarely that the impact on the total house edge of the game is very small.

Ah... here is the crux of the matter. If it is a very rare event then the burden on me for trying to remember the rule much less trying to apply it correctly and in a reasonable amount of time is very high even before the booze and the broads. That is why I often follow Ultimate Basic Strategy rather than Basic Strategy. I find it beneficial to jettison the excess baggage.

The difference between optimal play and reasonable play is a burden for the mathematically challenged but a fine tool for those able to utilize it.

Quote:IbeatyouracesWhat is the exact percent that a player gives up in a bj game that always stands on A-7 against a 9, 10 or A as opposed to someone who follows BS and always hit?. I'll use an 8 deck, H17, DOA, DAS as the game of choice.

Sorry I can't answer for the rules you gave. There's not a lot of information on this for H17. How about 6 deck S17 just to get an idea? This is what you lose for every $100 you bet. The lower amount is for hitting and the higher amount is for standing against these three up cards: against a 9 $9.85/$18.26, against a 10 $14.29/$17.96 and against the ace $9.53/$10.03. The ace is the close one. In H17 games, it is always a hit while in S17 games, it's a stay in plus counts.

This hand is not rare at all and is probably the most misplayed hand in blackjack. Add to that the lack of proper doubling and it becomes costly.

Quote:PapaChubbyI don't know about "exact", but here's an "engineering estimate" for an infinite deck, based on the Wizard's appendix #1.

First there's a 1/13 chance that your first card is an ace, and a 1/13 chance that your second card is a 7. So there's a 1/169 chance of getting A-7. Since 7-A counts too, the chances that you have a soft 18 is 2/169.

Given that you have a soft 18, the likelihood that the dealer has a 9 is 1/13. Based on the Wizard's appendix, the amount that you lose by standing instead of hitting is -0.1832 - (-0.1007) = 0.0825. So the total change in house edge for soft 18 against a 9 is 2/169 x 1/13 x (0.0825) = 7.5e-5.

Similarly for soft 18 against a 10 is 2/169 x 4/13 x (0.0335) = 1.22e-4.

For soft 18 against an ace the result is 2/169 x 1/13 x (0.0073) = 6.6e-6.

So the total for all these is the sum of the individual results = 1.98e-4, or about 0.02%.

In summary: given that you are facing a soft 18 against a 9, 10 or ace, you are giving up between 1 and 8% of the expected return for that hand by not playing basic strategy. However, this situation arises so rarely that the impact on the total house edge of the game is very small.

You forgot about the possibility of multi-card soft 18s, which can come after hitting a smaller soft hand or drawing an ace to a hard 7.

Quote:KellynbnfYou forgot about the possibility of multi-card soft 18s, which can come after hitting a smaller soft hand or drawing an ace to a hard 7.

You're right. I was specifically addressing the OP's stated problem of A-7 instead of the more general soft 18. I think that including all soft-18's increases the likelihood of occurance somewhere between 50 and 100%. So where a true A-7 against 9, 10 or A will occur once in 183 hands (on average), including all soft 18's will reduce this to something like 1 in 100. About once an hour. This will increase the effect on house edge from 0.02% to something in the range of 0.03-0.04%.

When I said the occurance is rare, I didn't mean that you're not likely to see it. I meant that it happens infrequently enough that the overall effect on the house edge of the game is drastically reduced. As opposed, for instance, to a player who doesn't always hit a 12-16 against a dealer's 7-A. This situation occurs about once every 4-5 hands, so playing it incorrectly will have a major impact on house edge.

Quote:IbeatyouracesWhat is the exact percent that a player gives up in a bj game that always stands on A-7 against a 9, 10 or A as opposed to someone who follows BS and always hit?. I'll use an 8 deck, H17, DOA, DAS as the game of choice.

not hitting A-7 vs a 9 cost you $9 out of your $100 bet on average.

not hitting A-7 vs a 10 cost you $3 out of your $100 bet on average.

I forgot what it cost you on an ace but I know it is better to hit it when the dealer hits soft 17.

Quote:cardcounternot hitting A-7 vs a 9 cost you $9 out of your $100 bet on average.

not hitting A-7 vs a 10 cost you $3 out of your $100 bet on average.

I forgot what it cost you on an ace but I know it is better to hit it when the dealer hits soft 17.

See my post above.