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Poker Math Question - Geek Squad Please Help

  
 
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Robb
Old 08-25-2008, 09:24 PM     Post subject: Poker Math Question - Geek Squad Please Help #1 (permalink)  
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 I'm trying to calculate the probability of flopping a straight or SD with various connectors. I started w/ T6. Here's my problem. I'm counting 2,816 possibilities, or a 14.37% chance. I think I must be too high.

Questions
1. Does anyone know the actual probability or odds? or where to get them?
2. I'm unsure of #4 below. Can you help?
3. I'm pretty sure of #1 - #3, but if I'm wrong point it out please.

19,600 possible flops
64 straights - 0.00327
512 OESD's - 0.02612
2,240 Gutshots - .11429

Check my thoughts here:

1. The only straight possible is 987, which can happen in 64 ways (4*4*4)

2. OESD's can only happen with 3 specific cards (also 64 ways each). Here are the 8 combo's:
KQJ - QJ9 - Q98 - J98 - 875 - 874 - 754 - 543

3. Gutshots can happen as 3 card combo's (64 ways each). Here are the 8 combo's:
AKQ - KQ9 - QJ8 - J97 - 975 - 854 - 743 - 543

4. Gutshots can happen as 2 card combo's
98 but no QJ7 (already counted). There are 4 9's, 4 8's then one card chosen from the 12 remaining T986's and the 24 cards from the 6 other values, so 16 * 36 = 576.
97 but no J85. Same calculation = 576.
87 but no 954. Same calculation = 576.

Any thoughts? BTW, unsure of where to post this, so I came here.
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oskar
Old 08-25-2008, 09:48 PM #2 (permalink)  
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 I would go at it slightly different.
The possibility of flopping 987 for example - in all permutations would be:
12/50, 8/49, 7/48

Are you sure you're adding probabilities the right way... because I'm getting crap right here too...
you would do something like 1-[(1-12/50)x(1-8/49)...]=x right?
but that doesn't turn out right.
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overflow
Old 08-25-2008, 10:08 PM #3 (permalink)  
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Since you've pointed out all the boards that give us straight draws, this is a bit easier. As you've said, the only way we can flop a straight is 987, so:
(12/50)(8/49)(4/48) = 0.00327, or 0.3% chance of flopping a straight.

QJ9, 457, 345, 875, 89J, JQK, Q98, 874 give us open ended draws:
(8)(0.00327) = 0.02612 = ~2.6% we flop open ended

3card Gutshots:
AKQ, AKJ, AQJ, KQ9, QJ8, J97, 975, 854, 743 (543 makes us open ended)
(9)(0.00327) == 0.02943 = ~2.9%

2 card Gutshots:
98x but no QJ7, 97x but no J85, 87x but no 954.
(3)((12/50)(8/49)(36/48) + (12/50)(37/49)(8/48) + (38/50)(12/49)(8/48) ) = 0.2718 = ~27.2%

So I get 33%
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overflow
Old 08-25-2008, 10:09 PM #4 (permalink)  
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Quote:
Originally Posted by oskar
I would go at it slightly different.
The possibility of flopping 987 for example - in all permutations would be:
12/50, 8/49, 7/48

Are you sure you're adding probabilities the right way... because I'm getting crap right here too...
you would do something like 1-[(1-12/50)x(1-8/49)...]=x right?
but that doesn't turn out right.
Nope, it's 12/50 * 8/49 * 4/48
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oskar
Old 08-25-2008, 10:22 PM #5 (permalink)  
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 Well D'OH!

but how do you add it up the right way?
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overflow
Old 08-25-2008, 10:23 PM #6 (permalink)  
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Quote:
Originally Posted by oskar
Well D'OH!

but how do you add it up the right way?
Like I did in the previous post.
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oskar
Old 08-25-2008, 10:40 PM #7 (permalink)  
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 D'OH again... you're correct. I was calculating OR and not AND probabilities.
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spoonitnow
Old 08-25-2008, 10:48 PM #8 (permalink)  
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 Some similar stuff on flop odds is listed here http://www.flopturnriver.com/Common-Flop-Odds.html
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Originally Posted by Ripptyde
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Robb
Old 08-25-2008, 11:26 PM #9 (permalink)  
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Quote:
Originally Posted by spoonitnow
Some similar stuff on flop odds is listed here http://www.flopturnriver.com/Common-Flop-Odds.html
Thanks, I don't mind reinventing the wheel if I have some way to see if I'm in the ballpark. Nice to find that I got the same answer as Pyroxene on both the number of straights and OESD's. Maybe that means my gutshot calculations are correct.
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Robb
Old 08-26-2008, 12:19 AM #10 (permalink)  
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Quote:
Originally Posted by overflow
2 card Gutshots:
98x but no QJ7, 97x but no J85, 87x but no 954.
(3)((12/50)(8/49)(36/48) + (12/50)(37/49)(8/48) + (38/50)(12/49)(8/48) ) = 0.2718 = ~27.2%

So I get 33%
You're double-counting possibilities here, not excluding enough cards to keep the sets disjoint.
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overflow
Old 08-26-2008, 02:04 AM #11 (permalink)  
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Quote:
Originally Posted by Robb
Quote:
Originally Posted by overflow
2 card Gutshots:
98x but no QJ7, 97x but no J85, 87x but no 954.
(3)((12/50)(8/49)(36/48) + (12/50)(37/49)(8/48) + (38/50)(12/49)(8/48) ) = 0.2718 = ~27.2%

So I get 33%
You're double-counting possibilities here, not excluding enough cards to keep the sets disjoint.
I see exactly what you mean. The correct calculation should be:

(3)((8/50)(4/49)(34/48) + (8/50)(36/49)(4/48) + (38/50)(8/49)(4/48)) = 0.08816 = 8.82%

So a shave over 14.62%?
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overflow
Old 08-26-2008, 02:36 AM #12 (permalink)  
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I keep second guessing myself .

Last time, this one should be right:
(3)((8/50)(4/49)(36/48) + (8/50)(37/49)((4/48)*(47/48)+(3/48)(1/48)) + (38/50)((8/49)(47/49) + (7/49)(2/49))((4/48)(47/48) + (3/48)(1/48)) = 0.090135 = 9.01%
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swiggidy
Old 08-26-2008, 02:39 AM #13 (permalink)  
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 I didn't dig through all the math, but I think your percentage is high because of gutshots, it looks like you might flop more gutshots with T6 then anyother hand.

#4 looks right to me
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Robb
Old 08-26-2008, 12:14 PM #14 (permalink)  
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Quote:
Originally Posted by swiggidy
I didn't dig through all the math, but I think your percentage is high because of gutshots, it looks like you might flop more gutshots with T6 then any other hand.
Yeah, I thought the gutshot % was too high, but the more I think about it, it makes sense. Gutshots just aren't that valuable. I found a few minor errors. I did the same calculation for 2-gappers, 1-gappers and connectors. Next, I summarized how many of possible straights are "nut" straight draws. Finally, I'm going to count how many are flush draws, how many are combo hands, and so forth. I hope to have the complete list of "flop odds" for connectors and gappers (sooted and otherwise) soon.

I will report back when I get through it all, and have had a chance to triple and quadruple check everything. The patterns were really cool, but it was near midnight when I hit pay dirt. So maybe I was just smoking crack.
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overflow
Old 08-26-2008, 07:37 PM #15 (permalink)  
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Quote:
Originally Posted by Robb
Quote:
Originally Posted by swiggidy
I didn't dig through all the math, but I think your percentage is high because of gutshots, it looks like you might flop more gutshots with T6 then any other hand.
Yeah, I thought the gutshot % was too high, but the more I think about it, it makes sense. Gutshots just aren't that valuable. I found a few minor errors. I did the same calculation for 2-gappers, 1-gappers and connectors. Next, I summarized how many of possible straights are "nut" straight draws. Finally, I'm going to count how many are flush draws, how many are combo hands, and so forth. I hope to have the complete list of "flop odds" for connectors and gappers (sooted and otherwise) soon.

I will report back when I get through it all, and have had a chance to triple and quadruple check everything. The patterns were really cool, but it was near midnight when I hit pay dirt. So maybe I was just smoking crack.
If villain is willing to stack off with one pair often enough, a gutshot and two overs on the flop has similar equity to a flush draw.
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Robb
Old 08-26-2008, 09:45 PM #16 (permalink)  
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 Here is a brief update. The list is Straights, 8-card straight draws, and 4-card straight draws.

3-Gap: S = 64 ; 8SD = 512 ; 4SD = 2624
2-Gap: S = 128 ; 8SD = 1024 ; 4SD = 3072
1-Gap: S = 192 ; 8SD = 1536 ; 4SD = 3648
0-Gap: S = 256 ; 8SD = 2048 ; 4SD = 4224

You can get each probability by dividing by 19600, the total number of flops possible.

Also, I'm working now on "nut" straights. Unless you have AT, it's impossible to have the nut straight draw. With a connector like 98, 75% of straights are the nuts, 5/8's of the 8-card straight draws are the nuts, and 2/3's of 4-card straight draws are the nuts.

I've always wondered why connectors are so much more valuable than gappers (understood the theory, but wanted to know the details). I'll start a new thread with the results when I'm (a) done and (b) sure they are correct.

For those math geeks interested, the number of straights and 8-card straight draws make a nice linear progression. 2-gappers have twice as many straights and 8-card draws as 3-gappers, and 1-gappers have 3x as many, and so on. It seems the 4-card ones should have a pattern, too, so I might have some errors. I'm rechecking everything.
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