No matter what your level of poker knowledge, you’re bound to realize sooner rather than later that poker is a game heavily determined by numbers. Of course, there’s a lot of truth to saying that poker is a “game of people” too—it certainly is—but the importance of numbers can’t be denied.
You’ve got odds and you’ve got probabilities. What’s the difference? Essentially, they’re different ways of saying the same thing. Odds describe the likelihood of an event occurring against the likelihood of that event not occurring; for example, you’ve got a 1 in 5 chance of passing your math test tomorrow. Probabilities express this information in terms of decimal points or percentages; in other words, you’ve got a .20, or 20%, chance of passing your math test tomorrow. Don’t get too confused by odds and probabilities. Whichever manner you prefer for looking at the game of poker, just be sure that you know where you stand, and how intelligent your next move is in a numeric context.
Let’s take a look at some common situations in poker that require an understanding of the numbers. It’s best to memorize as many of these as you can! Don’t worry, it gets easier the more you play…
Dealt Hands
First, what are the chances of being dealt five cards from a fresh, shuffled deck in a physical poker game and getting the following possible hands?
| Percentage | Odds | |
|---|---|---|
| Royal flush | 0.0002 % | 1 in 649,740.00 |
| Straight flush | 0.0012 % | 1 in 72,193.33 |
| Four of a kind | 0.0240 % | 1 in 4,165.00 |
| Full house | 0.1441 % | 1 in 694.16 |
| Flush | 0.1967 % | 1 in 508.80 |
| Straight | 0.3532 % | 1 in 254.80 |
| Three of a kind | 2.1128 % | 1 in 47.32 |
| Two pair | 4.7539 % | 1 in 21.03 |
| One pair | 42.2569 % | 1 in 2.36 |
| Nothing | 50.1570 % | 1 in 1.99 |
Making a Texas Hold’Em Hand
In the game of Texas Hold’em, when players are initially dealt two face-down cards, what are the chances of making a hand, before and after the flop? Let’s take a look at the odds:
| The probability that before fhe Flop… | Percentage | Odds Against It |
|---|---|---|
| You will hold a Pair | 5.88 % | 16 to 1 |
| You will hold suited cards | 23.53 % | 3.25 to 1 |
| You will hold 2 Kings or 2 Aces | 0.90 % | 110 to 1 |
| You will hold Ace-Kings | 1.21 % | 81.9 to 1 |
| You will hold at least 1 Ace | 14.93 % | 7.70 to 1 |
| If you hold… | Percentage | Odds Against It |
|---|---|---|
| A Pair, probability that at least one more of that kind will Flop | 11.76 % | 7.51 to 1 |
| If you hold no Pair, probability that you will pair at least one of your cards on the Flop | 32.43 % | 2.08 to 1 |
| If you hold two suted cards, probability that two or more of that suit will Flop | 11.79 % | 7.48 to 1 |
| If after the Flop you have… | Percentage | Odds Against It |
|---|---|---|
| Four parts of a Flush, probability that you will make it | 33.97 % | 1.86 to 1 |
| Four parts of an Open-end Straigt-Flush, probability that you will make a Straight-Flush | 8.42 % | 10.9 to 1 |
| Four parts of an Open-end Straight Flush, probability that you will make at least aStraight | 54.12 % | 0.85 to 1 |
| Three-of-a-kind, prabability that you will make a Full House or better | 33.40 % | 1.99 to 1 |
| Pair, probability that at least one more of that kind will turn up (on the last two cards) | 8.42 % | 10.9 to 1 |
| If you begin… | Percentage | Odds Against It |
|---|---|---|
| Suited nad stay through seven cards, tree more (But not four or five more!) of your suit will turn up | 5.77 % | 16.3 to 1 |
| Paired and stay through seven cards, at least one more of your kinde will turn up | 19.18 % | 4.21 to 1 |
Essential Numbers
While the above numbers are useful to know as you play poker more often, there are some numbers that are “crash-course” figures. That is, they’re numbers that can help you quickly improve your game and allow you to start thinking about what kind of hand the other players are holding. Look at the following percentages very closely, because these are the ones that can get you quick success at the poker table:
Probability of hitting a flush draw (both turn and river, needing one card to hit): 35%
Probability of hitting an open-ended straight draw (i.e. four straight cards; need one on either end to hit on turn or river): 31.5%
Probability of hitting a gutshot draw (inside straight draw) on turn or river: 16.5%
Probability of being dealt a pocket pair: 5.88%
Probability of being dealt suited cards: 23.5%
Probability of hitting three of a kind or quads at the flop, when you hold a pocket pair: 11.8%
Probability you’ll make a pair at the flop, holding two unpaired cards in the hole: 32.4%
Probability of being dealt A-A: 0.45%
Probability of no one holding an ace, by number of players, assuming you don’t have an ace, by number of total players. Note: this can be used for any card (because the chances of you being dealt an ace or a king is exactly the same):
2: 84.5%
3: 70.9%
4: 59%
5: 48.6%
6: 39.7%
7: 32.1%
8: 25.6%
9: 20.1%
10: 15.6%
Probability someone else does not have an ace, assuming you do have an ace, by total number of players:
2: 88.2%
3: 77.5%
4: 67.6%
5: 58.6%
6: 50.4%
7: 43%
8: 36.4%
9: 30.5%
10: 25.3%