Probability question
January 23rd, 2013 at 3:58:01 PM
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Hi all. I'm wondering what the probability of being dealt a total of 10 or less in an 8 deck blackjack game is? Also, a hand of "A9" will also be counted as a 10. No real specific reason for asking, just curious. Thanks!
January 23rd, 2013 at 6:01:42 PM
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Okay.
You have specified that A+9 would count as a total of 10, so can I assume that A + A,2,3,4,5,6,7,8, would count as 2, 3, 4, 5, 6, 7, 8 and 9, respectively?
You have specified that A+9 would count as a total of 10, so can I assume that A + A,2,3,4,5,6,7,8, would count as 2, 3, 4, 5, 6, 7, 8 and 9, respectively?
https://wizardofvegas.com/forum/off-topic/gripes/11182-pet-peeves/120/#post815219
January 23rd, 2013 at 6:47:42 PM
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Yes. I forgot to mention that.
January 23rd, 2013 at 7:12:00 PM
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Possibilities that are less than 10:
AA, A2, A3, A4, A5, A6, A7, A8, A9
22, 23, 24, 25, 26, 27, 28
33, 34, 35, 36, 37
44, 45, 46
55
Possibilities:
Non-pairs: 20
Pairs: 5
Number of Combinations per possibility:
Non-pairs: 32*32 = 1024
Pairs: 32*31/2 = 496
Total combinations 10 or less:
20*1024 + 5*496 = 22,960
Total combinations for any 2-card blackjack hand:
416*415/2 = 86,320
Probability of a blackjack starting hand of 10 or less:
22,960/86,320 =26.60%
AA, A2, A3, A4, A5, A6, A7, A8, A9
22, 23, 24, 25, 26, 27, 28
33, 34, 35, 36, 37
44, 45, 46
55
Possibilities:
Non-pairs: 20
Pairs: 5
Number of Combinations per possibility:
Non-pairs: 32*32 = 1024
Pairs: 32*31/2 = 496
Total combinations 10 or less:
20*1024 + 5*496 = 22,960
Total combinations for any 2-card blackjack hand:
416*415/2 = 86,320
Probability of a blackjack starting hand of 10 or less:
22,960/86,320 =26.60%
