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Probabilities of certain Blackjack hands ?
| September 23rd, 2011 at 1:07:40 PM permalink | |
| PlayHunter Member since: Sep 16, 2011 Threads: 13 Posts: 32 | Heya! I would like to know what are the percentages for each of the following in any blackjack given hand: 1. Any two card 20 ? (this include sotf A+9 and from what I know is ~ 10,5%) 2. Any two card hard 20 ? (ie. 10+10, 10+J, Q+K) 3. Pair including all ten value cards ? (ie. 2+2, or A+A, or J+J) 4. Pair excluding all ten value cards ? PS: I know that the percentage differ slightly depending on the number of decks used, but a roughly +/-1% approximation would be just great for my needs. Thanks ! |
| September 23rd, 2011 at 1:42:43 PM permalink | |
| miplet Member since: Dec 1, 2009 Threads: 3 Posts: 552 | For 6 decks with formula for permutations given d decks. The denominator is 52*d(52*d-1) . 1. Any two card 20 ? (this include sotf A+9 and from what I know is ~ 10,5%) 10.5861984 % 16*d*(d*16-1) + d*4*d*4*2 2. Any two card hard 20 ? (ie. 10+10, 10+J, Q+K) 9.3989612 % 16*d*(d*16-1) 3. Pair including all ten value cards ? (ie. 2+2, or A+A, or J+J) 7.3954984 % 52*d*(d*4-1) 4. Pair excluding all ten value cards ? 5.1199604 % 36*d*(d*4-1) |
| September 23rd, 2011 at 11:00:42 PM permalink | |
| PlayHunter Member since: Sep 16, 2011 Threads: 13 Posts: 32 | Thanks a lot ! Great info ! But, seems I still need a bit more help with something similar. What is the percentage of being dealt: 1. Any soft hand ? (including a Blackjack and a pair of aces) 2. Any soft hand ? (including a Blackjack but excluding pair of aces) 3. Any soft hand ? (excluding both: blackjacks and pair of aces) |
| September 24th, 2011 at 6:29:25 AM permalink | |
| ChesterDog Member since: Jul 26, 2010 Threads: 0 Posts: 199 |
Using miplet's reply as a template, I get: For 6 decks with formula for permutations given d decks. The denominator is 52*d(52*d-1) . 1. Any soft hand ? (including a Blackjack and a pair of aces) 14.8157309% 4*d*48*d*2 + d*4*(d*4-1) 2. Any soft hand ? (including a Blackjack but excluding pair of aces) 14.2468464% 4*d*48*d*2 3. Any soft hand ? (excluding both: blackjacks and pair of aces) 9.4978976% 4*d*32*d*2 |
| September 24th, 2011 at 10:47:47 AM permalink | |
| PlayHunter Member since: Sep 16, 2011 Threads: 13 Posts: 32 | Thanks a lot man ! |
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