Counting Cards in Poker to Determine Odds and Outs

Most losers I know suck at math. Not that poor math automatically makes you a loser (there are plenty of other things that make you a loser), but it can definitely work to your advantage in poker. One way it can help is by doing quick math in your head to determine your outs, in comparison to the pot odds. Both those pages I link to offer detailed advice on each subject, so I’ll only be using the basics here. If you’re too lazy to read it all, tough luck. Have fun losing all your money, loser.

Counting Outs

If you can, you should always know what your outs are. Here’s an example:

Your opening hand is 6♥ 5♥

The flop comes down as: Q♥ 3♠ 7♥

In this case, your hand has almost no chance of winning, unless it improves. But if it does improve, you have a very good chance of winning. There are a number of ways it can improve:

• A♥ 2♥ 3♥ 4♥ 8♥ 9♥ 10♥ J♥ K♥ will all give you a flush.
• 4♣ 4♦ 4♥ 4♠ will all give you a straight.
• Since 4♥ gives you a straight flush, it shows up twice. Only count it once.

Go ahead, count those cards. In the current situation, you have 12 outs. In the next round, 12 cards can come that will improve your hand enough to make it a potentially winning hand.

The Rule of 4 & 2

A well-known mathematics based rule that many people base their strategies on is The Rule of 4 & 2.

Use the Rule of 4 after the flop. To determine the rule of 4, take your outs, and multiply them by 4. This will give you a percentage of chance to make your hand in the game. In this example:

12 x 4 = 48

You have a 48% chance to make your hand by the river, according to the rule of 4.

After the turn card, you should then use the rule of 2. Let’s go back to our example hand:

Opening hand: 6♥ 5♥

After Turn: Q♥ 3♠ 7♥ 8♣

Looking at our outs again:

• A♥ 2♥ 3♥ 4♥ 8♥ 9♥ 10♥ J♥ K♥ will still give you a flush.
• 4♣ 4♦ 4♥ 4♠ will still give you a straight.
• And now 9♣ 9♦ 9♥ 9♠ will give you a straight as well.

You now have 15 outs after the turn. Multiply that by 2:

15 x 2 = 30

The Rule of 2 determines that you have a 30% chance of catching the winning card on the river.

Calculating Pot Odds

I have posted an extremely thorough discussion of pot odds already, so be sure to read up on that.

Luckily the math is pretty simple here, so even an idiot like you can figure it out. Let’s use a really easy example:

• The pot has $300 in it
• Your opponent bets $100, bringing the pot total to $400
• So to win $400, you will have to bet $100
• Your pot odds are 400:100, or 4:1.
• If you do call, your $100 represents 20% of the pot ($100 of the now $500 pot)

Putting it all Together

So using the rules of 4 and 2 above, you can then compare it to your pot odds. This will give you a rough idea on your odds of winning. In our scenario, we have a 30% of winning at the river, and are being asked to call 20% of the pot. Since your 30% chance outweighs the pot odds, then you should most definitely make that call! Obviously that was a very good scenario, so let’s put something else together:

• Let’s say you have 5 outs at the flop
• Rule of 4 means 5 x 4 = 20%. So you have a 20% chance of making a winning hand by the river.
• After the bet, there is $200 in the pot. You’re being asked to call $100. 2 to 1 pot odds.
• Therefore, you need a 1:3 or 33% chance to win to justify calling that bet.
• Since The Rule of 4 states you only have a 20% chance of winning, you should fold this time.

This should be used as a basic guide to determine if you should call or fold, and mathematically speaking you should come out on top in the end. However, since you are playing with other people (most of them being idiots) you shouldn’t adhere to this ruleset 100%. It is a guideline though, and has helped many players start out on the right track. You just have to be quick with those math skills. Eventually, you’ll know your outs just by glancing at the draws.

Poker Outs

In a poker game with more than one betting round, an out is any unseen card that, if drawn, will improve a player’s hand to one that is likely to win. Knowing the number of outs a player has is an important part of poker strategy. For example in draw poker, a hand with four diamonds has nine outs to make a flush: there are 13 diamonds in the deck, and four of them have been seen. If a player has two small pairs, and he believes that it will be necessary for him to make a full house to win, then he has four outs: the two remaining cards of each rank that he holds.

One’s number of outs is often used to describe a drawing hand: “I had a two-outer” meaning you had a hand that only two cards in the deck could improve to a winner, for example. In Draw poker, one also hears the terms “12-way” or “16-way” straight draw for hands such as 6? 7? 8? (Joker), in which any of sixteen cards (4 fours, 4 fives, 4 nines, 4 tens) can fill a straight.

The number of outs can be converted to the probability of making the hand on the next card by dividing the number of outs by the number of unseen cards. For example, say a Texas Holdem player holds two spades, and two more appear in the flop. He has seen five cards (regardless of the number of players, as there are no upcards in Holdem except the board), of which four are spades. He thus has 9 outs for a flush out of 47 cards yet to be drawn, giving him a 9/47 chance to fill his flush on the turn. If he fails on the turn, he then has a 9/46 chance to fill on the river. Calculating the combined odds of filling on either the turn or river is more complicated: it is (1 – ((38/47) * (37/46))), or about 35%. A common approximation used is to double the number of outs and add one for the percentage to hit on the next card, or to multiply outs by four for the either-of-two case. This approximation is reasonably close only for small numbers of outs.

Note that the hidden cards of a player’s opponents may affect the calculation of outs. For example, assume that a Texas hold ‘em board looks like this after the third round: 5? K? 7? J?, and that a player is holding A? 10?. The player’s current hand is just a high ace, which is not likely to win unimproved, so the player has a drawing hand. He has a minimum of seven outs for certain, called nut outs, because they will make his hand the best possible: those are the 2?, 3?, 4?, 6?, 8?, 9?, and Q? (which will give him an ace-flush with no possible better hand on the board) and the Q? and Q?, which will give him an ace-high straight with no higher hand possible. The 5? and J? will also make him an ace-high flush, so those are possible outs since they give him a hand that is likely to win, but they also make it possible for an opponent to have a full house (if the opponent has something like K? K?, for example). Likewise, the Q? will fill his ace-high straight, but will also make it possible for an opponent to have a spade flush. It is possible that an opponent could have as little as something like 7? 9? (making a pair of sevens); in this case even catching any of the three remaining aces or tens will give the player a pair to beat the opponent’s, so those are even more potential outs. In sum, the player has seven guaranteed outs, and possibly as many as 18, depending on what cards he expects his opponents to have.