Wednesday, July 14, 2010

Drawing Hands in Seven-Card Stud High-Low

In high only poker the concept of drawing to improve the rank of your hand is simple. The hand can only increase in rank; cards drawn either raise the rank of your hand or they do not. But, in high-low forms of poker, defining improvement is more complicated because there are three kinds of improvement—increasing the rank of your high-hand, qualifying for a low-hand, and improving your low-hand. All hands, no matter how low, have the potential to win the high-pot, but not all hands qualify for the low-pot. To complicate matters further, some drawn cards can simultaneously improve your high and low hands, while some drawn cards can improve your high hand at the expense of disqualifying you from holding a low-hand. To account for these complexities we will define two categories of hands—half-made hands and drawing hands, and within each of these categories define three kinds of hands.

Half-made hands are holdings that can win half the pot, but need improvement to win the other half. The three kinds of half-made hands in order of desirability are:

Coordinated highs are hands that still need to qualify for the low-pot, but have outs for a low-hand that will improve the rank of the high hand. For example consider the best possible coordinated high that you could hold on Sixth Street—2-clubs, 3-clubs, 4-clubs, 5-clubs, 5-diamonds, 5-spades. This hand is already trip 5s, but it has four sequential suited low-cards. It can improve its high ranking to quads, a full house, or a 9-high flush or better without qualifying for the low-pot. But, it can also improve it high ranking to a 5-high or 6-high straight flush, 7-high or 8-high flush, 5-high or 6-high straight and at the same time qualify for a low-hand. It can also qualify for low without improving its high ranking. For example it can become a 7-high or 8-high low-hand, and remain trip 5s.

Uncoordinated highs still need to qualify for the low-pot, but in doing so cannot improve their high ranking. While coordinated highs might have some outs to qualify for the low-pot that do not improve the high ranking, for uncoordinated highs none of the outs for low improve the high hand. Consider the best uncoordinated high-hand that you can hold—A-spades, 2-spades, 3-spades, 5d, Q-spades, K-spades. This hand is an A-K-Q-high flush with four low-cards. There are 16 outs to qualify this hand for the low-pot—any of the 4s, 6s, 7s, or 8s—but none of these outs will change the fact that the high hand is a flush.

Lows are hands that qualify for the low-pot, but rank poorly as high hand. For these hands you are drawing for the high half of the pot. For example the holding—2-hearts, 3-hearts, 4-hearts, 5-hearts, 7-diamonds, 8-spades is a qualified 7-high low-hand, but only an 8-high high hand. However, it has many outs available to improve its high ranking. An A-hearts or 6-hearts would result in a straight flush, a K-hearts, Q-hearts, J-hearts, 10-hearts, 9-hearts, 8-hearts, or 7-hearts, would make it a flush, while an A-clubs, A-diamonds, A-spades, 6-clubs, 6-diamonds, or 6-spades, would make it a straight. Any of the remaining 2s, 3s, 4s, 5s, or unsuited 8s or 7s would make it one pair.

Drawing hands are holdings that need improvement to win any part of the pot. In order of desirability the kinds or drawing hands are:

Scoop draws have outs available that can simultaneously win the high and low pots. Consider a Sixth Street holding of 2-clubs, 3-clubs, 4-clubs, 5-clubs, 9-hearts, 10-spades. This open-ended straight flush-draw has outs that will improve to a high-only flush (K-clubs, Q-clubs, J-clubs, 9-clubs, 10-clubs), outs that will qualify for the low-pot (7-hearts, 7-spades, 7-diamonds, 8-hearts, 8-spades, 8-diamonds) along with outs that qualify for the low-pot and improve the high hand. The 7-clubs or 8-clubs completes a flush and qualifies for low; the A-clubs or 6-clubs completes a straight flush and qualifies for low; the A-diamonds, A-hearts, A-spades, 6-diamonds, 6-hearts, 6-spades, would all complete a straight and qualify for low.

One-way high-draws can never qualify for the low-pot. The only outs available improve the high-ranking. Consider K-spades, K-diamonds, K-hearts, Q-hearts, J-hearts, 10-hearts, played against a 3-hearts, 4-diamonds, 5-spades 6-clubs, 7-diamonds, 8-hearts, 8-spades. The trips Kings will lose to the 8-high straight, but the hand has many outs for a better high hand. It can improve to a straight flush, quads, full house, flush, or straight, and all of these hands would beat a low straight for the high-pot. However, the 8-high straight has a lock on the low-pot because a hand with trip Kings can never qualify.

One-way low-draws are drawing dead for the high-pot, but can still qualify for the low-pot. For example the hand A-clubs, 2-spades, 4-diamonds, 7-hearts, J-clubs, K-spades can never make a high hand better than one pair. If it plays against an opponent showing two pair—10s and 9s—on the board the hand is drawing dead for the high-pot, but drawing any of the remaining 3s, 5s, 6s, or 8s will win the low-pot.