Lucky
Lucky
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January 1st, 2023 at 1:21:25 PM permalink
Dear Wiz,

What is the probability that a player will win a final hand of 17? Assume a 6-deck H17 shoe game. Thanks.
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gordonm888
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January 1st, 2023 at 1:34:13 PM permalink
Quote: Lucky

Dear Wiz,
What is the probability that a player will win a final hand of 17? Assume a 6-deck H17 shoe game. Thanks.
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Edited with additional info.
I get that a 9-8 has a net EV of -0.2945 with a win probability = 0.3002.

A T-7 has a net EV of -0.2960 with a win probability = 0.3001.

An A6-T has a net EV of 0.2933.with a win probability = 0.3001.

A T-4-3 vs 2-A has a net EV of -0.2957 with a win probability = 0.2998.

A 6-6-5 vs 2-A has a net EV of -0.2962 with a win probability = 0.2995.

A T-2-A-A-A-A-A has a net EV of -0.2820 with a win probability = 0.3036. Because the odds of the dealer having a faceup card that is an Ace is significantly reduced. However, it does include T2AAAAA vs 2-6, hands which will almost never occur if the player is playing basic strategy. The EV of T2AAAAA vs 7-A is approximately EV= -0.37947, with a win probability = 0.23523

I realize these are not all the possible hands of 17, but I hope you find them helpful.
Last edited by: gordonm888 on Jan 1, 2023
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charliepatrick
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January 1st, 2023 at 1:52:39 PM permalink
^ There are many 17s one can get to playing basic strategy, some which aren't obvious. So you could get A2AAAAT unless you would normally double A2, and even A2AAAAA9 vs 9/A/T. You can also get to A6 if you split Aces, or things like A42/A5A if you doubled.

Note if you're only trying to win, i.e. a standoff is of no help, refer to Freebet Blackjack for a strategy; for instance hit 17 vs 7.
aceside
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January 1st, 2023 at 5:22:03 PM permalink
The OP probably meant to ask the probability of a player win with a hard 17 hand. Based on the above posts, we can safely say it is about 30%.
Ace2
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January 1st, 2023 at 10:01:13 PM permalink
Quote: charliepatrick

^ There are many 17s one can get to playing basic strategy, some which aren't obvious. So you could get A2AAAAT unless you would normally double A2, and even A2AAAAA9 vs 9/A/T. You can also get to A6 if you split Aces, or things like A42/A5A if you doubled.

Note if you're only trying to win, i.e. a standoff is of no help, refer to Freebet Blackjack for a strategy; for instance hit 17 vs 7.
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regarding A2AAAAA9. I believe an 8-card hand is probably immaterial
It’s all about making that GTA
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