Betting Probabilities in Poker
The relative values of Poker hands were not just conjured up by some rule maker or arbitrarily assigned by the first Poker players. They were discovered through the use of permutation and combination formulas. The exact number of possible five-card Poker hands in a 52-card deck is 2,598,960.
These hands were divided into group (ranks) of : no pair, pair, three of a kind, straight, flush, full house, four of a kind, straight flush and royal flush. The ranks were then arranged in relative value according to the frequency of their occurrence. The hands which can be expected to appear most often have the lower rank; those which appear least often the highest rank.
A good poker player must have a fair idea of Poker odds and probabilities. Without such knowledge, he has no good way of deciding on his course of action in the various situations which arise. That is, he has no way of making a mathematical analysis on which to base a decision. The tables that follow provide the information that will help a poker player make an analysis.
These same tables can also be used to prove the relative value of Poker hands and to settle disputes that arise regarding the chances of drawing certain valuable hands in Five-Card Draw Poker or in the first five cards dealt in any other form of Poker.
It would be simple if all one had to do to become a winning player was to memorize the following Poker tables. Knowing the exact strength of your hand or the exact chances of bettering your hand on the draw will not always help you. Thats because the playing habits of your opponents will often throw a monkey wrench into your best-laid mathematical plans. Example: A big raise from a habitually tight player means quite a different thing from the same big raise from a drunk who has already been caught trying to steal (bluff) the last half-dozen pots.
Although Poker is a game of skill, the judgments and decisions to be made by even the average Poker player involve a general knowledge of the game’s probabilities.
The chances of being dealt any certain pat hand are the same, regardless of the number of players in the game. The same hold true in drawing cards to try to improve a hand. There are 2,598,960 different possible poker hands in a 52-card deck.
The following table lists the name of each different possible hand in order of their rank. It also lists the possible number of ways each can be made and the chances of being dealt such a hand in the first five cards dealt. An example would be the original five cards dealt in Five-Card Draw Poker before you draw.
|Rank of Hands||Number of Possible Ways Hand can be Made||Chance of Being Dealt in Original 5 Cards|
|Royal Flush||4||1 in 649,740.00|
|Straight Flush||36||1 in 72,193.33|
|Four of a Kind||624||1 in 4,165.00|
|Full House||3,744||1 in 694.16|
|Flush||5,108||1 in 508.80|
|Straight||10,200||1 in 254.80|
|Three of a Kind||54,912||1 in 47.32|
|Two Pairs||123,552||1 in 21.03|
|One Pair||1,098,240||1 in 2.36|
|No Pair Hand||1,302,504||1 in 1.99|
In the chance column above, fractional figures have been carried out to only two decimal places, since further extension would mean little.
The probability of being dealt a pair or better in the first five cards dealt is almost even—to be exact, 0.499— and the probability of being dealt a no pair hand is practically the same — 0.501. So it’s almost a 3 to 1 chance, when playing against two opponents, that one of them will hold a pair or better in the first five dealt cards. The probabilities vary slightly depending upon what you hold.
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