Can someone tell me what are those 11 combinations?
I always come up with more than 11:
AQ3, AQ4, AQ5, AJ3, AJ4, AJ5, AT3, AT4, AT5, K95, Q84, J73, T62, 95A.
Please someone help me figure this out.

When you say flop with a double gutshot, do you mean a flop where 2 gutshots are possible or a flop where a double gutshot is possible with a Holdem hand? If the former, then a double gutter is obviously possible with the right Omaha hand.

As for the 11 combinations claim, which appears to be referring to flops with two gutshots possible (AQ3 mentioned) - it must be wrong in that basis, because any Ace + broadway + wheel card has two gutshots, so that is 16 right there (and there are more).


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I think I figured it out.
With double gutshot he is referring to flops giving a hand the chance to turn a straight in 2 ways, i.e 75 on 2-4-6.
Based on this, the list of 11 possible flop combinations is:

1. A,3,5
2. 2,4,6
3. 3,5,7
4. 4,6,8
5. 5,7,9
6. 6,8,T
7. 7,9,J
8. 8,T,Q
9. 9,J,K
10. T,Q,A
11. A,Q,3

You could argue that K2 on 3-4-5 can turn a straight in two ways and that's true, but that flop is in another category (3 to a wheel).
My previous examples (K95, Q84, J73, etc..) cannot turn a straight in two ways thus they are wrong.

P.S: I still can't understand why AQ3 is in that list.

75 on 642 is an open-ender.
85 on 642 is a double gutter (7 or 3)
75 on 963 is a double gutter (4 or 8)

There are 8 boards with the shape of 642 (A35-QT8) and 8 with the shape of 963 (A47-AJ8).

Also, 76 on 953 is a double gutter (4 or 8) as is 76 on T84 (5 or 9).

There are 8 boards with the shape of 953 (A37-AT8) and 8 with the shape of T84 (A57-AQ8)

So there's 32 board last right there.

I'm 100% sure that is not exhaustive but I'll leave it to you to work out some others, like the boards that T5 or 95 can have a double gutter on.

The only way to have a double gutter on AQ3 is to have an Omaha hand with both gutshots e.g. KJ54. Does this guy think you can make a straight Q-3??
Or maybe he is trying to say that you need to eliminate these?

I'm sure we are talking about NLHE and not Omaha.
At this point I'm really confused.
My question arised after reading this post: http://forumserver.twoplustwo.com/sh...37&postcount=3
Then I found this same question asked before: http://forumserver.twoplustwo.com/sh...70&postcount=1
Looks like this guy knew what he's talking about but I can't catch his reasoning behind the double gutshot flop type.

Then I found an article on his site http://www.spadebidder.com/flop-analysis/part7/ with some examples of double gutshot flops.

He's not active anymore so I can't ask him to clarify what he meant.
That's why I'm asking here.

Looking at his site again, he put AQ8 under the "other 1gaps" category while it should be put under double gutshot (JT) instead.

In the end I came up with this list for a total of 34 dbl gutshot flops:

1. A,3,5 74
2. 2,4,6 85
3. 3,5,7 96
4. 4,6,8 T7
5. 5,7,9 J8
6. 6,8,T Q9
7. 7,9,J KT
8. 8,T,Q 96
9. 9,J,K T7
10. T,Q,A J8
11. A,4,7 53
12. 2,5,8 64
13. 3,6,9 75
14. 4,7,T 86
15. 5,8,J 97
16. 6,9,Q T8
17. 7,T,K J9
18. 8,J,A QT
19. A,3,7 54
20. 2,4,8 65
21. 3,5,9 76
22. 4,6,T 87
23. 5,7,J 98
24. 6,8,Q T9
25. 7,9,K JT
26. 8,T,A QJ
27. A,5,7 43
28. 2,6,8 54
29. 3,7,9 65
30. 4,8,T 76
31. 5,9,J 87
32. 6,T,Q 98
33. 7,J,K T9
34. 8,Q,A JT

You’re missing a whole bunch. Take your first case: A,3,5 - 74. This results in A 345 7. So any two combinations of 3 cards and 2 cards using these 5 cards works. There are C(5,3)=10 such combinations, eg, A,3,4 -57 and 4,5,7 -A3 are two cases you don’t have.

For his analysis Spadebidder was trying to classify each possible flop. He called the following flops "double gutshots" because they have two one-card gaps between the three different ranks on the flop. Not really directly having anything to do with flopping a gutshot in the normal poker parlance:

A35
246
357
468
579
68T
79J
8TQ
9JK
TQA
QA3

These categories may not be perfect and his labels may not be perfect, but it is pretty clear what he did, why he did it, and what results he found.

Thanks for the explanation, I guess that explains everything. So his calcs are on point.
I really appreciate his work. I think those frequencies are very useful as they give some insight on what types of flop one should focus his studies (i.e focus more on high frequency flops).

It's sad to see he's not active anymore.

Right, but if he included the wrap of QA3, I wonder why he left out K24.

I know you know how poker hands are made. So I know you know the following:

AQ can make a straight with cards KJT.

A3 can make a straight with cards 245.

24 can make a straight with cards A35 or 356.

K2 cannot make a straight with any combo of three cards.

Edit: As I said above, Spadebidder needed to categorize flops for his analysis and this is one of the buckets he chose to construct. I am not attempting to defend the choice, but to explain the choice since there was a question about it.

My head is spinning from this (it didn't seem possible at first that 95 could flop a double-gutter!) and I've probably made a schoolboy error and double-counted or undercounted, but I've got up to 74 boards in total so far. If we include the 345 shape, then even 5-gappers like A7, 28 and 7K can be double-gutted!

The flop shapes I'm working from are:
A34 - 8TJ (8 possible flops for 1-gapper starting hands, 57-QA)
A35 - TQA (10 flops for 2-gappers, with some flops having two different holecard possibilities. e.g. on 579, both 36 and 8J have double-gutters.)
A37 - 8TA (8 flops for connectors 45-JQ)
A45 - 8JQ (8 flops for 3-gappers 37-TA)
A47 - 8JA (8 flops for 1-gappers 35-TQ)
A57 - 8QA (8 flops for connectors 34-TJ)
345 - TJQ (8 flops for 5-gappers A7-8A)
347 - TJA (8 flops for 3-gappers A5-8Q)
457 - JQA (8 flops for 1 gappers A3-8T)

Total: 74. Any more? (Apologies if I've made a stupid mistake somewhere. Double gutters always confused me).

I've not checked the numbers of each shape you mentioned but they all check out and I can't think of any more. They all also reassuringly take the form mentioned in this post:
http://forumserver.twoplustwo.com/sh...70&postcount=1
i.e. y(?)yyy(?)y where y are board cards or hole cards and (?) are outs to a straight. Namely:

x?xxo?o (A34)
x?xox?o (A35)
x?oxx?o (A45)
o?xxx?o (345)
x?xoo?x (A37)
x?oox?x (A57)
x?oxo?x (A47)
o?xox?x (357 - same shape as A35)
o?xxo?x (347)
o?oxx?x (457)

Numbers seem reasonable too - I'd be fairly confident that this is the lot.

Would be interesting to see how many are nut outs on different boards, whether you can be drawing to a chop vs the flopped straight, drawing to a lower straight vs an open-ender etc.

And yeh, I meant T4, not T5

You are all overcomplicating this.
All flopped double-gutters have the same form. ABAAABA.

A3457-8TJQA is 8 rank combinations of double gutters.

There appear to be 8*5C3 = 80 rank combinations of flops containing double-gutters. However, some flops are double-counted because there is enough transpositional overlap.

ABAAABAXX
XXABAAABA
XXAXAXAXX

There are six flop combinations of the form "XXAXAXAXX" which makes for 80-6 = 74
rank combinations of flops offering a double-gutter.

This is 74*4^3 = 4736 flop combinations offering a double-gutter.

There are 52C3 = 22100 total flop combinations.

The pre-deal probability of the flop offering a double-gutter is 4736/22100 = 1184/5525 = 21.4%