Deck SimplificationDeck simplification is the process of identifying the unique hands in a video poker game which can be used to completely and accurately represent all possible starting hands. Only these unique hands need to be analyzed, which greatly reduces the time needed to analyze a game. A simplification is possible for every video poker game, although some games are less simple than others. The first thing you have to do is separate ranks from suits, and begin identifying the unique rank patterns. In order to determine these, it is necessary to figure out the possible combinations for each of the following core hand types:
Each core hand type has its own set of rank patterns, each of which makes use of a specific number of ranks. Five of a Kind hands have only one rank, repeated five times. Four of a Kind hands make use of two ranks, one for the Quads and one for the Kicker. Full House is similar - one rank for the Three of a Kind and one rank for the Pair. Three of a Kind hands have three ranks, one for the Trips and two for each of the Kicker cards. Two Pair hands have three ranks, one for each Pair and one for the Kicker. One Pair hands have four ranks, the Pair and three Kickers. No Pair hands have five ranks, each of which must be different (otherwise it would be a different core hand type). Looking at each core hand type individually, it is now possible to identify the unique suit patterns which can exist for every rank pattern within that core hand type. I indicate suit patterns using an ABCD notation as follows: "A" refers to whichever of the four suits appears first; "B" refers to whichever of the three remaining suits appears second; "C" refers to whichever of the two remaining suits appears next in the hand, and "D" therefore refers to the last suit. For example, consider a hand which has five distinct ranks, such as 23456. The suit pattern AAABB can represent all of the following permutations:
The type of suit patterns available for each rank pattern changes if wild cards are present in the game. For example, you don't treat the four Deuces in Deuces Wild as having the same suits as the rest of the cards. Instead, they need to be treated as four cards which all have the same suit, and that this suit is different from the regular four suits. This actually results in fewer unique patterns, but this savings is virtually cancelled out by the increased time required to score a hand. In the Programming tab of each video poker game analyzer you can find the formulas to calculate the number of rank combinations for each core hand type, as well as the actual suit patterns for each rank combination (they all use the ABCD notation, unless otherwise specified). The following table shows how many unique and total hands there are for each type of game, and how much processing time is saved by eliminating redundant hands:
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