Saturday, March 31, 2012

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

In keeping with last month's theme on math facts for Sixth Street draws, here are tables with information on Fifth Street draws. Here is an executive summary of some basic math facts to remember on Fifth Street with two cards still to come:

• There can never be more than 44 unseen cards by Sixth Street because you must have at least one opponent with 3 cards showing, and you will know 5 of your cards. That means that you will always know the value and location of at least 8 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 39 unseen cards.

• The percentages below are based on 44 unseen cards with totally live draws. For each missing out subtract 2.3% (1/44) from the calculated percentage.

• For every 4 additional seen cards 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) by the end increases from 33.4% to 36.4% which is an increase of 3 percentage points (the number 3 is a little less than 10% of 33.4).

High Hand Draws (probability of improvement by drawing two cards)


Holding Improve to: Outs Percentage
Trips Quads 1 4.5 %
Open-ended Straight-Flush Draw Straight-Flush 2 9.0 %
Pair Trips 2 9.0 %
Inside straight-draw Straight 4 17.5 %
Flush-draw with four-low Low Flush 4 17.5 %
Two Pair Full 4 17.5 %
Flush-draw with four-low High Flush 5 21.7 %
Open-ended Straight-Draw Straight 8 33.4%
Flush-draw Flush 9 37.1 %


Low Hand Draws (probability of improvement by drawing two cards)

Holding Improve to: Outs Percentage
8-high draw 8-high 16 60 %
7-high draw 8-high 4 17.5 %
7-high draw 7-high 12 47.6 %
6-high draw 8-high 4 17.5 %
6-high draw 7-high 4 17.5 %
6-high draw 6-high 8 33.4 %
5-high draw 8-high 4 17.5 %
5-high draw 7-high 4 17.5 %
5-high draw 6-high 4 17.5 %
5-high draw 5-high 4 17.5 %

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