We're going to start up with some very basic poker probabilities - you can find these just about anywhere. It's definitely good to be aware of these probabilities since you'll get a much better idea of what kind of hands you make and how often. poker hand rankings & nicknames will help you to get to know poker hands better. Hands that are more unlikely for you to get position better in poker hand rankings.
Counting Outs
It's necessary for you to know how to count outs. Fortunately, this part of poker mathematics is quite easy. So, let's see how we can work out one of the most basic poker probability calculations:
"I got 4 outs" means there are 4 cards left that you can win the pot with. An out means a winning card for you. So really, it's quite simple to calculate how many outs you've got. It's just how many cards make you a winner. The probability of "hitting" one of those outs is quite easy to calculate, too.
You just divide the amount of outs by unknown cards. Scenario in which you've got JT, board is 2389 and your opponent's got AA leaves you with 8 outs (four sevens and four queens). There are 52 cards in a normal card deck, and you've got 2 of them, your opponent's got 2 of them and 4 of them are on the board. This means there are 44 unknown cards. 8/44 = 0.18 = the probability for you to hit your 8 outs is 18%.
5 Card Poker Probabilities
Royal Flush - There are 4 combinations of royal flushes. Spades, Diamonds, Hearts and Clubs. The probability of getting a royal flush is 0.000154%, so it's safe to say this hand is quite rare. In other words, odds for you to get a royal flush are 649,350 to 1.
Straight Flush - 36 combinations of a straight flushes, and this doesn't include a royal flush. This hand is a rare one, too, since the probability of getting this hand is 0.00154% and odds are 71,941 : 1.
Four of a Kind - This hand isn't that rare anymore and there are 624 different kinds of Four of a Kind (example: 55552). Probability for this poker hand is 0.0240% and odds are 4,166 : 1. Meaning if you average 100 hands/hour per table and you play 4 tables simultaneously, you'll have to play a bit over 10 hours on average to get a four of a kind.
Full House - A Full house (example: 44555) can be made in 3,744 ways, and you'll get to see this hand already quite often. Probability is 0.144% and odds 694 : 1.
Flush - All cards must be the same suit, and there are 5,108 different kinds of flushes. Probability: 0.197% and odds 507 : 1.
Straight - 10,200 possible ways to make a straight (example: 45678), probability is 0.392% and odds are 254 to 1.
Three of a Kind - Three of a kind (example: QJ999) can be formed in 54,912 ways, the probability is 2.11% and odds are 46.4 : 1.
Two Pair - As an example, two pair is 88773, there are 123,552 ways to make two pair, the probability is 4.75% and odds are 20.1 : 1.
One Pair - 1,098,240 possibilities to make one pair, the probability is 42,3% and odds are 1.37 : 1.
If you want to count the probability and odds for getting at least certain hand, you'll have to sum the particular hand up with the ones above it.
Starting Hand Probability
Being Dealt Pocket Aces: Probability is 0.45% and odds are 220 : 1.
Any Pocket Pair: 5.9% - 16 : 1.
Ace-King: 1.2% - 82 : 1.
Suited Cards 24% - 3.3 : 1.
Flop Odds
Flop a Pair: 29% - 2.5 : 1.
Flop Two Pair: 2% - 49 : 1.
Flop a Set: (with a pocket pair) 10.8% - 8.3 : 1.
Flop a Full House: 0.74% - 136 : 1.
Rainbow Flop: (all cards on the flop are different suit) 40% -1.5 : 1.
Two Sequential Cards: 40% - 1.5 : 1.
Poker Mathematics:
Poker Probability,
Pot Odds
(Continue: Implied Odds),
Expected Value,
Winnings in the Long Run |
|
