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How To Read Hands by Ed Miller
Exercise #2:
Suppose our reg opener's range after the turn in the hand from ex1 is:
[88, A9s, KTs-K9s, QJs-JTs, 98s-87s, J9s-86s, T7s, Ad8d-Ad2d, Kd8d, 7d6d-5d4d, 7d5d-5d3d, A9o, KQo, KTo-K9o, QJo-JTo].
The board on the river is Qd Td 9s 2c 8c.
Determine the different strength hands the reg could have, how many hand combos make up each type of hand, and the percentage of the time he has that hand when he gets to the river.
First let's count the number of hand combos in his range on the river:
- 88 -> 3 combos
- A9s -> 3 combos (As9s is not possible)
- KTs-K9s -> 3+3 = 6 combos (KdTd and Ks9s are not possible)
- QJs-JTs -> 3+3 = 6 combos (QdJd and JdTd are not possible)
- 98s-87s -> 2+3 = 5 combos (9s8s, 9c8c, and 8c7c are not possible)
- J9s-86s -> 3+2+3+3 = 11 combos (Js9s, Td8d, Tc8c, 9s7s, and 8c6c are not possible)
- T7s -> 3 combos (Td7d is not possible)
- Ad8d-Ad2d -> 8-2+1 = 7 combos
- Kd8d -> 1 combo
- 7d6d-5d4d -> 7-5+1 = 3 combos
- 7d5d-5d3d -> 7-5+1 = 3 combos
- A9o -> 4*3 = 12 combos (9s not available)
- KQo -> 4*3 = 12 combos (Qd not available)
- KTo-K9o -> 4*3 + 4*3 = 24 combos (Td not available)
- QJo-JTo -> 3*4 + 4*3 = 24 combos (Qd and Td not available)
This is 123 hand combos or 123/1326 = 9% of all starting hands.
What are the different hand strengths possible on this board Qd Td 9s 2c 8c?
Board is not paired => quads, full houses, and one-card trips are not possible.
No 3-flush on board => straight flushes and flushes are not possible.
3-straights on board => straights are possible.
So the possible hand strengths are:
straights:
- KJ makes a K-high straight
- Jx not JK makes a Q-high straight
- 76 makes a T-high straight
sets:
two-pairs:
- QT, Q9, Q8, Q2, T9, T8, T2, 82
overpairs:
top pairs:
- Qx not QQ, QT, Q9, Q8, or Q2
worse than top pair hands:
Board: Qd Td 9s 2c 8c
Total number of combos in player's range and percentage of range:
straights:
- KJ, 0 combos
- Jx no KJ, 33 combos, 27%
- 76, 1 combo, 1%
sets:
- QQ, 0 combos
- TT, 0 combos
- 99, 0 combos
- 22, 0 combos
- 88, 3 combos, 2%
two-pairs:
- QT, 0 combos
- Q9, 0 combos
- Q8, 0 combos
- Q2, 0 combos
- T9, 0 combos
- T8, 0 combos
- T2, 0 combos
- 82, 0 combos
overpairs:
- AA, 0 combos
- KK, 0 combos
top pairs:
- Qx not QQ, QJ, QT, Q9, Q8, or Q2, 0 combos
less than top pair:
- everything else, 86 combos, 70%
So if you were in the BB with top pair or second pair good kicker, this would be a good spot to bluff catch.
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