Poker Hand Odds
Poker is all about probabilities, or odds as we like to call them. It is a game of both skill and luck. The skill lies in knowing when the hand odds are on your side. In this chapter you will learn to calculate poker hand odds under relatively simple circumstances. This in turn will help you understand the strategy presented in subsequent parts of the school.
Probability: The probability of an event occurring is the number of times the event occurs divided by the total number of events.
Chance: This is the probability expressed in % (the probability multiplied by 100).
Odds: This is the ratio of the probability of an event occurring to the probability of it not occuring. Odds are always presented on the format x:1 where 1 denotes the smaller of the odds, whether it is for or against the event occuring. |
Probability/Chance/Odds Example
If a certain event occurs 13 times out of 52, then the probability is 13/52=0.25. The chance of that event occurring is 0.25x100=25%. If an event has a probability of 0.25 to occur and consequently a probability of 0.75 to not occur, then the odds are 0.75:0.25 against which is the same as 3:1 against (0.75/0.25=3).
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Poker Hand Odds Scenario 1
►By drawing one card from a deck of 52 your probability of getting a K i 4/52 which equals 1/13 or 7.7%. This means that if you attempt this, you will succeed 1 time out of 13. That makes the hand odds 12:1 against.
►By drawing one card from a deck of 52 your probability of getting a Hearts is 13/52 which equals 1/4 or 25%. This means that if you attempt this, you will succeed 1 time out of 4. That makes the hand odds 3:1 against.
►By drawing one card from a deck of 52 your probability of getting a K of Hearts is 1/52 or 1.9%. The hand odds are 51:1 against. This is easily calculated seeing as you have only one such card in the whole deck of 52. You can also arrive at this figure but multiplying the probability to draw Hearts with the probability to draw K (1/13 multiplied by 1/4).
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Poker Hand Odds Scenario 2
►You have four cards in your hand 2-3-4-5 and there are 48 cards left in the deck. By drawing one card from this deck the probability of getting an A is 4/48 which equals 1/12 or 8.3%. The hand odds are 11:1 against.
►You have four cards in your hand 2-3-4-5 and there are 48 cards left in the deck. By drawing one card from this deck the probability of getting a 5 is 3/48 which equals 1/16 or 6.25%. The hand odds are 15:1 against. With one 5 in your hand, it means only three 5 are left in the deck, hence 3/48.
►You have four cards in your hand 2-3-4-5 and there are 48 cards left in the deck. By drawing one card from this deck the probability of getting a straight is 8/48 which equals 1/6 or 16.7%. The hand odds are 5:1 against. Both A and 6 can complete the straight and there are four of each card left in the deck, hence 8/48. The chance of getting a straight is exactly twice as big as that of only getting A or 6.
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Poker Hand Odds Scenario 3
You have four cards of the suit Clubs in your hand. There are 48 cards left in the deck. By drawing one card from the deck the probability of getting a flush is 9/48 which equals a chance of 18.75%. The hand odds are 4.3:1 against. There is a total of 13 cards of the suit Clubs. You have 4 of them. That leaves 9 cards of the suit Clubs in the deck. By dividing 9 by the remaining 48 cards you get the probability.
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Poker Hand Odds Scenario 4
By drawing five cards from a deck of 52 your probability of getting a flush is 12/51 x 11/50 x 10/49 x 9/48 which equals 0.00198 or 0.198%. It translates to roughly 2 times out 1000. The hand odds are roughly 499:1 against. The suit of the first card does not matter. It is only the remaining 4 cards that have to turn out right. Multiplying their probability in sequence yields their combined probability.
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Poker Hand Odds Scenario 5
You have four cards in your hand Td-Jh-Qc-Kc. There are 48 cards remaining in the deck. By drawing two cards from the deck, your probability of getting a straight is 1-(40/48 x 39/47) which equals 0.34 or 34%. The hand odds are 1.9:1 against. When you are drawing several cards but only need one of them to turn out right, then you must first calculate the probability of not getting the card. You subtract that probability from 1 to get the probability of getting the card. There are 8 cards (9c; 9d; 9h; 9s; Ac; Ad; Ah; As) among the 48 cards in the deck that will form a straight with the 4 cards already in your hand. There are 40 cards among those 48 that you don't want. If the first card you draw is one of those 40, then there will only be 39 cards that you don't want among the 47 remaining ones. Multiplying these probabilities (40/48 x 39/47) yields the probability of not getting the card.
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