Monday, October 5, 2009

The Possible and the Impossible in Seven-Card Stud High-Low Poker

Every variation of poker has conditions on the kinds of hands possible, given the exposed cards (the board) and rules of the game. For example, in Hold'em full houses and quads are possible only if the board is paired. Knowledge of the possible is vital throughout the hand, when deciding to place or call bets. Here is a summary of what is possible and impossible in Seven-Card Stud High-Low.

High Hands


It is possible for a player to have a full house or quads without an exposed pair. The three hidden cards can combine with any one or two of the four exposed cards to make these kinds of hands.

If just two of the four exposed cards have matching suits, a flush is possible.

It is impossible for a player to have a flush when all four exposed cards are in different suits.

It is always possible for a player to have a straight, because the four exposed cards can never be arranged in such a way, that the three hidden cards couldn't fill a gap.

It is impossible for two players to have trips of the same rank. As a result, kickers never play when trips are compared. (The same is true for quads.)

It is possible for two players to have two-pair of identical ranks. In that case, the kickers decide the hand.

Exposed Hands

The following kinds of hands require all five cards and can never be completely exposed on the board:

Full houses
Flushes (including straight-flushes)
Straights
Qualified lows (low hands that meet the eight-or-better condition)

The following kinds of hands require less than five cards and can be exposed on the board:

Quads
Trips
Two-pair
One-pair

Low Hands

It is impossible for a player with three exposed high cards to have a qualified low.

It is impossible to have a qualified low and a full house or quads

It is impossible to have a qualified low with an exposed low-pair and two high cards. For example, a player with 5, 5, J, K, cannot make low.

For the same reason, it is impossible to have a qualified low with an exposed two-pair, when one of the pairs is high. For example, a player with J, J, 8, 8, cannot make low.

A player with an exposed high-pair and two low cards can have a qualified low-hand. However, the low-hand cannot be better than the highest exposed low card. For example, 9, 9, 7, 3 cannot be better than a 7-high low-hand.

A player with an exposed two-pair, with both pairs low, can have qualified low-hand, but it cannot be better than the rank of the highest pair. For example, 3, 3, 8, 8, cannot make a low-hand better than an 8-high.

It is always possible for a player with two exposed wheel cards to make a wheel. For example, a player with J, J, 2, 5, could have an A, 3, 4 hidden.

Similarly it is impossible to have a low hand better than the two lowest exposed low-cards. For example a player with 8, 7, 6, J exposed, can have at best a 7-6-high low.

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