Basic Math Facts for Sixth Street in Seven-Card Stud High-Low Eight or Better

I've been busy doing some math calculations for my upcoming book on Seven-Card Stud High-Low. The tables that follow contain information on Sixth Street draws. Here is an executive summary of some basic math facts to remember:

• There can never be more than 42 unseen cards by Sixth Street because you must have at least one opponent with 4 cards showing, and you will know 6 of your cards. That means that you will always know the value and location of at least 10 cards by Sixth Street.

• If there were 7 players dealt into the hand at the beginning and 5 folded on Third Street leaving you with heads-up play against one opponent, there are 37 unseen cards.

• The percentages below are based on 42 unseen cards with totally live draws. For each missing out subtract 2.4% (1/42) from the calculated percentage.

• For every 4 additional seen cards (additional opponent) that do not include outs that you need, the numeric values of percentages shift upward by about 10%. For example the probability of hitting an open-ended straight draw (8 outs) shifts from 19.0% to 21.1%, an increase of 2.1 percentage points (the number 2.1 is a little more than 10% of 19.0).

High Hand Draws

Holding	Improve to:	Outs	Percentage
Trips	Quads	1	2.4 %
Open-ended Straight-Flush Draw	Straight-Flush	2	4.8 %
Pair	Trips	2	4.8 %
Inside straight-draw	Straight	4	9.5 %
Flush-draw with four-low	Low Flush	4	9.5 %
Two Pair	Full	4	9.5 %
Flush-draw with four-low	High Flush	5	11.9 %
Open-ended Straight-Draw	Straight	8	19.0 %
Flush-draw	Flush	9	21.4 %
Trips	Full	9	21.4 %
Pair	Two Pair	12	28.6 %
6 unmatched	Pair	18	42.9 %

Low Hand Draws

Holding	Improve to:	Outs	Percentage
8-high draw	8-high	16	38.1 %
7-high draw	8-high	4	9.5 %
7-high draw	7-high	12	28.6 %
6-high draw	8-high	4	9.5 %
6-high draw	7-high	4	9.5 %
6-high draw	6-high	8	19.0 %
5-high draw	8-high	4	9.5 %
5-high draw	7-high	4	9.5 %
5-high draw	6-high	4	9.5 %
5-high draw	5-high	4	9.5 %