THE WORLD'S #1 POKER MANUAL - Card Games

Poker Book, Poker Odds
Four-card flush 1 Flush 5
Four-card straight flush, open both ends 1 Straight or better 3
--- 1 Straight flush 24
Four-card straight flush, inside or one end 1 Straight or better 4
--- 1 Straight flush 48
* Approximate values rather than precise values must be reported for the following reason: Consider an extreme
example--the odds on a four-card draw to an ace. Does one assume a blind draw into a forty-seven-card deck that
would give a precise value of 12.8 draws per catch of two pair or better? Or does one assume a draw into a fiftyone-card
deck (a deck with one ace missing) that would give a precise value of 15.6 draws per catch of two pair
or better? Now a 20 percent difference exists between those two precise values with no basis for selecting one
assumption over the other (forty-seven-card deck versus fifty-one-card deck). Furthermore, neither assumption
represents the actual situation: The draw is not blind from a forty-seven-card deck, and the draw is not from a
fifty-one-card deck. An accurate and precise value is obtained only by defining each of the four discarded cards
and then drawing from a forty-seven-card deck. But that would not be practical because a complete table of draw
odds to the ace alone would consist of hundreds of thousands of values. All those values do, however, lie
somewhere between the values for a blind draw into the forty-seven-card deck and a draw into the fifty-one-card
deck. So where necessary, draw odds are calculated at the midway value between the two extreme precise values
and then rounded off to a whole number. That is the most practical way to report such draw odds in a consistent
and accurately defined manner.
Hand
3. PAT-HAND ODDS
A. Various Hands
Hands
Possible
Pat Hands
per
200,000
Deals
Deals
per Pat
Hand
Deals per
Pat Hand
or Better
Royal straight flush 4 .15 649,740 649,740
Straight flush 36 1.4 72,193 64,974
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