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 %

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 %

Stealing Antes

Of the Stud variants of poker, Seven-Card Stud High/Low is the hardest game in which to steal antes. For example in Razz, the bring-in is usually a face card, and very rarely will the bring-in defend against a complete bet from an exposed low card. In Razz you can have wired kings with an exposed 2 and steal the antes. It is more difficult to steal antes in high-only Seven-Card Stud because bring-ins can have many possible card combinations worth defending. In fact, in high-only Seven-Card Stud a bring-in with a pair or high-cards in the hole, will usually defend against someone she believes is trying to steal the antes. However, a bring-in in high-only Stud will usually not defend complete garbage.

However, in Seven-Card Stud High/Low, the bring-in will often defend against a player that she believes is stealing the antes. If the bring-in has an exposed low-card and picks up a second exposed low-card, she can become very aggressive. An opponent trying to steal antes with garbage might find himself in an uncomfortable situation, because the bring-in’s low-cards could allow her to freeroll on later streets. In Seven-Card Stud High/Low, low-cards because of the their dual roles in both high and low hands, have greater value than mid-range cards, which can only contribute to high-hands. A bring-in with an exposed 2 and 6, 7, in the hole has a better starting hand than an opponent with an exposed K and Q, 8, in the hole, even though the bring-in has no over cards. Attempting to steal antes with uncoordinated high-cards will not work in Stud-High/Low as often as it will in Stud-high. A significant fraction of the time, the bring-in will have a hand worth defending, or even raising with in response to a completed bet.