ODDS and PROBABILITIES

written by BeatTheFish.com

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There are some simple odds and probabilities that you should be aware of (especially in No-Limit play) when you’re drawing to a hand or want to prevent your opponents from doing so. If you figure that your draw will be the best hand if you hit it, just compare the odds below to the odds the pot is giving you to decide if you’re making a mathematically sound play.

The odds below are separated into preflop and postflop sections and while some are essential, some were just thrown in for fun. You will run into this situation often at the table, so get into the habit of comparing the actual odds of making your hand against the pot odds. Of course, in No-Limit games you should often also consider the implied odds (the amount of money that you expect to make from your opponent after you make your hand), but that is the subject of another article.

If I recommend that you memorize a vital statistic, it will be bolded and you will run into it frequently playing hold’em. In parenthesis, the probability will be expressed in percentages to the nearest tenth.

Preflop Odds
These odds won’t really affect your game strategy, but it’s interesting to see how rare certain premium cars are. It’s also important to realize that many players overvalue random suited cards or a single, which are dealt relatively frequently. However, the odds that these hands will improve are much less frequent.

Probability of being dealt:
• Any pocket pair: 16 to 1 (5.9%)
• Two suited cards: 3.25 to 1 (23.5%)
• A-K (Big slick – suited or offsuit): 81.9 to 1 (0.9%)
• Any single ace: 5.7 to 1 (15%)
• Pocket Aces: 220 to 1 (0.5%)
• Pocket Aces or Kings: 110 to 1 (1%)

Odds of Hitting on the Flop:
• Hitting another kind of your pocket pair on the flop: 7.5 to 1 (11.8%)
• You will pair at least one of your unpaired hole cards on the flop: 2.1 to 1 (32.4%)
• You will hit two pair on the flop with unpaired hole cards: 49 to 1 (2%)
• Hitting two or more of your suit on the flop when you hold suited cards: 7.5 to 1 (11.8%)
• Hitting a flush on the flop with suited hole cards: 118 to 1 (0.8%)

On the Flop, when you have:
• Four cards to a flush on the flop, you will complete it by the river: 1.9 to 1 (35%)
• Four cards to an open-ended straight on the flop, you will complete it by the river: 2.2 to 1 (32%)
• A gutshot straight draw on the flop, you will complete it by the river: 5.1 to 1 (17%)
• Two pair, you will complete at least a Full House: 5 to 1 (16.7%)
• Three of a kind, you will complete at least a Full House: 2 to 1 (33.4%)
• One pair, you will complete at least three of a kind: 10.9 to 1 (8.4%)
• An open-ended straight flush draw, you will complete at least a straight: 0.9 to 1 (54.1%)
• An open-ended straight flush draw, you will complete it: 10.9 to 1 (8.4%)

All-in One-on-One
This comes up most often in tournaments when only two players are involved and one of them is all-in. When all of one’s money goes in preflop against one opponent, no further decisions need to be made and the cards will be dealt to the river to determine a winner.

• Larger pocket pair vs. smaller pocket pair (AA vs. KK): Larger pair is at least an 80% favorite
• Pocket Aces vs. unpaired cards (AA vs. KQ): Pocket Aces are at least an 80% favorite
• Pocket Pair vs. Overcards (QQ vs. AK): Pocket pair is at least a 52% favorite
• Pocket Pair vs. one overcard (JJ vs. A10): Pocket pair is at least a 66% favorite
• Overcards vs. Undercards (AK vs. Q10): Overcards are at least a 57% favorite
• One overcard (A3 vs. J10): Overcard is at least a 50% favorite
• Better kicker (AK vs. AJ): Better kicker is at least a 70% favorite

Just for Fun
These statistics probably won't affect your game in the slightest, but it's interesting to know what some of the extreme odds are in Hold'em.

• If you're holding a pair, the flop will bring you four of a kind about 1 in 119 tries, or 0.84% of the time.
• The odds are 70.5 to 1 (1.4%) against no one having an Ace or a King at a 10-handed table.
• The odds are 87,897 to 1 (0.01%) against you not being dealt an Ace or a pair for 50 hands.
• You will be dealt pocket Aces four consecutive times 1 in 2,385,443,281 times. Expressed as a percentage, it will happen 0.00000004% of the time.