PERCENTAGE TABLES
The calculations in this section were made by poker hand. The only accurate way to do this is to list all the possible cards that could come on fourth street, and then see how many winning combinations for the drawing hand are formed with the possible fifth street cards. The number of winning combinations are added, and this sum is then divided by the total number of possible combinations (1980) to give the percentage of times the drawing hand will win. Obviously, the deducting the winning percentage of the drawing hand from 100 percent.
The total number of possible combinations (1980) is formed by multiplying the number of possible fourth street cards (45) by the number of possible fifth street cards (44). The number 45 is derived by taking the total number of cards in the deck (52) and subtracting the number of cards we know (7).
The cards we know are the three boardcards and the four cards that are held by the players contending the pot. It is irrelevant whether the unknown cards are in the remaining stock of the deck or in the discard pile.
596 divided by 1980 equals 30.1 percent for the drawing hand, leaving 69.9 for the two pair. There are nine hearts left in the deck, but the 8♥ fill the two pair, so it is counted as a lockout card (along with the 8♠, 9♣, and 9♠). “Other” is of course any card not previously mentioned, and is derived by adding the sum of the cards previously mentioned and subtracting this figure from 45, which is the number of unknown cards on fourth street. The number of fifth street wins for each card or card grouping is based on the 44 different cards that could come on fifth street. For example, the eight hearts that could come on fourth street will win unless an 8 or 9 comes on fifth street to make the opponent, so the remaining 40 cards will win for the draw. If a 4 or 3 hits the board on fourth street, the draw can win with eight hearts plus two cards that make trips, for a total of ten cards. Obviously, if an 8 or 9 comes on fourth poker street to fill two pair hand, the draw has no wins on the last card. By adding all the cards for which we have calculated the odds, we find there are 18 in total. We subtract 18 from 45 to give us 27 cards that can come on fourth street which are neutral in character.
For these 27 cards, the flush-draw will have eight cards that can come on the end that complete a flush without making the opponent a full hous. In other words, every heart except the 8♥ will give the flush-draw a winning hand.
This same basic method was used for all the other calculations in this section. The number of times a drawing hand of a certain type will win can vary slightly from the figures provided in this section, which are based only on the specific hands given. For example, with a flush-draw and overcard against top pair, it would make a slight difference if the overcard were bigger or smaller than the pair’s side card. A frequent occurrence is for the draw to have a three-flush or some sort of three-card straight working along with the main drawing combination. Naturally, a back-door possibility improves things a little bit for the draw.