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#1
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Hi,
I'm trying to figure out what the odds of flopping any of the following are, given that we are holding 67s (or any suited connector like 89s, JTs) - two pair(using both hole cards, not a pair on board), trips, full house, quads - OE straight draw or double belly buster - flush draw - made straight or made flush It's been a while since I've done anything like this, so I'm afraid I wouldn't trust whatever results I did get. Anyone able to do this calculation? |
#2
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I will try this but hopefully someone will check my flush draw and open ended straight draws to insure I didn't double count anything. I will use 67 suited.
Straight Flush There are four different combinations of three cards that give you a straight flush. They are 10,9,8 and 9,8,5 and 8,5,4 and 5,4,3. So straight flush flops are 4*1*1*1 = 4 flops or .0204% Four of a kind = 2*(3c3) = 2 flops or .0102% Full house with 6 and 7 = 2*(3c1)*(3c1) = 18 flops or .0918% Flush = (11c3) = 165 - 4 = 161 flops or .8214% (note you must subtrat out the straight flushes) Straight As mentioned before a straight will come with four different combinations of three cards. = 4*4*4*4 = 256 - 4 = 251 flops or 1.2806% Three of a Kind = 2*(3c1)*44 = 264 flops or 1.3469% Two pair with 6 and 7 = (3c1)*(3c1)*44 = 396 flops or 2.0204% Flush and an eight out straight draw The combinations that allow an eight out straight are as follows: 89x, 85x, 54x, 4810, 953. The easiest way to count these combo's is to insure the x doesn't create a straight and it is not the same as one of the other cards. For example: 89x were x is not a 10,5,8 or 9. Now in this combination we need to have two and exactly two of a specific suit. It can be 89 s, x not or 8x s, 9 not or 9x s, 8 not. 89/x = 1*1*27 = 27 8x/9 = 1*7*3 = 21 9x/8 = 1*7*3 = 21 89/9 = 1*1*3 = 3 89/9 = 1*1*3 = 3 Total for 89x is 75 * 3 total combo's = 225 Now for the 10,8,4 and 9,5,3 95/3 = 1*1*3 93/5 = 1*1*3 53/9 = 1*1*3 For a total of 9 flop * 2 combo's = 18 Total of 15 out hands = 225 + 18 = 243 flops or 1.2398% Flush draw ( 9 outs) Note some of these have 12 outs to a gutshot straight = (11c2)*39 = 2145 - 243 = 1902 flops or 9.7041% Eight out straight draw We use the same combinations as discussed above but we then subtract out the flops that have a flush already and the flops that have two of our suit. These are already counted. For 89x = 4*4*34 = 544 + 2*(4c2)*4 = 544 + 48 = 592 There are three combo's = 1776 flops for 9,5,3, = 4*4*4 = 64 * 2 combo's = 128 for a total of 1904 flops Now there is a total of 26 flops above that give a flush and 243 that have 2 of your suit. Therefor there is 1904-26-243 = 1635 clean flops or 8.3418% Summary Straight Flush.......4.......4 Four of a kind.......2.......6.....1 in 3266 Full house..........18......24.....1 in 817 Flush..............161.....185.....1 in 106 Straight...........251.....436.....1 in 45 Three of a Kind....264.....700.....1 in 28 Two Pair w (6,7)...396....1096.....1 in 17.9 15 outs............243....1339.....1 in 14.6 9 outs............1902....3241.....1 in 6.0 8 outs............1635....4876.....1 in 4.0 Cobra |
#3
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Excellent post, thank you!
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#4
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In the eight-out straight problem, where did
2*(4c2)*4 come from for 89X? I have only the 544 number as necessary. |
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