Sunday, February 26, 2012

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 %