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Flop Combos
To start, this post is aimed at identifying how hand combinations change in relation to board texture.
For example, how many combos are made hands on a AKQ rainbow flop?
— 3 combos of AA, KK, QQ — 9 total for sets
— 16 combos of JT — 16 combos for nut straight
Now, you might argue that not all JT combos will see every flop. True, I’m simply trying to find out the maximum risk according to the board texture of possible hand combinations. Then, I can reduce hand combos when necessary.
When dealt two cards, there are:
13 ways to dealt no-gap (AK, KQ, QJ, JT, T9, 98, 87, 76, 65, 54, 43, 32, A2)
12 ways to be dealt one-gap (AQ, KJ, QT, J9, T8, 97, 86, 75, 64, 53, 42, A3)
11 ways to be dealt two-gap (AJ, KT, …, 52, A4)
10 ways to be dealt three-gap (AT, K9, …, 62, A5)
Below, I’m going to look at different flops and their connectivity.
No-Gappers & Well Connected
AKQ — 9 sets (AA, KK, QQ) — 16 straights (JT)
A23 — 9 sets (AA, 22, 33) — 16 straights (54)
These type of flops are “on the edge” because they always contain an ace and you can’t go higher or lower. There are at most (9 + 16 = ) 25 hand combos that make a set or straight.
KQJ — 9 sets (KK, QQ, JJ) — 32 straights (AT, T9)
234 — 9 sets (22, 33, 44) — 32 straights (A5, 65)
These type of flops are “near the edge” because they are one spot away from an ace. At most, you will need (9 + 32 = ) 41 hand combos that make a set or straight.
QJT — 9 sets (QQ, JJ, TT) — 48 straights (AK, K9, 98)
345 — 9 sets (33, 44, 55) — 48 straights (A2, 62, 76)
These type of flops are in the middle. Not shown (JT9, T98, 987, 876, 765, 654). All of these flops have at most (9 + 48 = ) 57 hand combos that make a set or straight. As mentioned, maybe I can reduce this number by eliminating hands like 62 or 76o thus making your total smaller
One Gappers & Well Connected
AKJ, AKT, AQJ, AQT, AJT — each has 9 sets, 16 straight combos
A24, A25, A34, A35, A45 — each has 9 sets, 16 straight combos
These one-gap flops are less connected than the no-gappers. There are fewer ways to flop a straight because it requires you to have the missing gap card in your hand. There are some double one-gap flops like (AQT, KJ9) that only offer one way to flop a straight. These will always have 25 combos
KQT, KJT, QJ9 — each has 9 sets, 32 straight combos
These flops are more “middle”. They offer two ways to flop a straight. This means 41 hand combos are sets or straights.
Next, what if the board is paired?
one pair on flop
AAK — this board has 1 combo of quads, 3 of KK for boat, 6 for AK boat
772 — this board is the same
trips on flop
333 — this board has 12 hand combos that could contain a 3 for quads, there are 12 pocket pairs (6 combos each) for full-houses.
To be continued…
ARW
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Recap
1) No Gap
There will be 9 combos of sets and between 16 – 48 combos of straights
i.e. – AKQ — only one way to flop a straight (JT) — 16 combos
i.e. – 987 — two ways to flop a straight (JT, 65) — 32 combos
2) One-Gap
There will be 9 combos of sets and between 16 – 32 straight combos
i.e. – AKJ — only one way to flop a straight (QT) — 16 combos
i.e. – T97 — two ways to flop a straight (J8, 86) — 32 combos
3) Two-Gap
There will be 9 combos of sets and only 16 straight combos
i.e. – AKT — only one way to flop a straight (QJ) — 16 combos
4) Pair on Flop
There will be 1 combo of quads and 9 combos of full-house.
i.e. – AA2 —
There are 3 combos of 22 full-house and 6 combos of A2 full-house
5) Trips on Flop
To analyze this flop, I look at starting hands. There are 12 pocket pairs that have flopped a full-house. To have quads, you can’t have a pocket pair. Thus, of the 2 dealt cards, one way to deal quads and 12 other cards possible for the 2nd card. Thus, there are 12 specific hands that can flop quads. This means there are (12 * 16) = 192 hand combos. This number is large but remember, it can be reduced.
i.e. – Let’s say you open with AA from the button and the bb defends. The flop is KKK. There are only 12 specific hands that the bb defends with that contain a K. However, we can reduce 192 combos by eliminating some hands based on their tendencies. I would argue that AK and maybe KQ would re-raise, not defend. It’s more likely that suited Kx will be defended and off-suit Kx might fold. Also, Kx with low kickers are more likely to be folded than higher kickers.
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Ummm, what about suited-ness?
With 13 ranks (A, K, Q, J, T, 9, 8, 7, 6, 5, 4, 3, 2),
– There are 12 ways to be dealt a suited ace like AK, AQ, or A2 where each has 4 suited options (AKss, AKhh, AKdd, AKcc). Thus, there are a total of 48 combos of Ax suited that can be dealt to a player.
6) Monotone flops
When the flop is all one suit, there are 48 combos of suited Ax however only 1 suit is on the board, this means only (48 / 4) = 12 combos of the flopped nut flush.
7) Two-tone flops
These flops are common and they cause havoc on counting combos. Let’s say that you open from the button and the bb 3-bets. Here are some talking points:
i.e. — The flop is QcTc3h
Our opponent CANNOT have top pair and have a flush draw. (AQcc not possible)
i.e. — The flop is QhTc3c
Our opponent CAN have top pair and a flush draw. (AQcc is a strong hand)
Lastly, your hand might have blockers that reduce the combos for connectedness and suitedness.
If the flop is QcTc3c, the most dangerous hands are (QQ, TT, 33, QT, AQ, KQ, KJ, J9). If you’re holding AhJc, the number of dangerous combos is reduced for hands like (AQ, KJ, J9). Specifically, the opponent can’t hold AJcc, KJcc or J9cc.
By knowing the combos, you will simply make better decisions at the poker table.
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