Texas Holdem Odds
Poker Odds, Outs, Rule of 4, Rule of 2

When beginners first start to play poker they usually make the classic mistake of 'chasing.' They play too loose and are overly optimistic about the quality of their hand. They might be playing with three cards to a flush after the flop hoping for two more diamonds on the turn and river to make a winning flush hand. Of course they may not have noticed the pair on the board and someone betting into them hard with a full house.

Poker has been described as a game of people that just happens to be played with cards. This is very true in a real life game. Body language and 'tells' should color our decision to fold or play. However, in the online game there are fewer tells and it is certainly important to understand the basic underlying math surrounding the game.

Expert poker players always consider how many 'outs' they have before they make a decision. There are many other factors they consider, but a fundamental understanding of poker odds will certainly make you a better player.

When you are playing a hand of Texas Holdem there are four essential points when a serious decision needs to be made. Before the flop, after the flop, and after the turn (one card to come) and on the river (all cards are displayed and the final hand is known). On this page we will discuss two of those four points. How you bet before the flop is determined by the strength of your two hole cards relative to the cost of entering the pot. However, once you have made it to the flop you have now seen five cards and it is necessary to evaluate the potential of your hand now and the chances of betterment.

After the flop there are three possible situations:

1. You have made a great hand which can range from a good hand such as top pair (e.g. one of your cards pairs with the highest card on the board) to an almost unbeatable hand such as four of a kind or a straight (or royal) flush.
2. Your hand is junk or obviously beaten and needs to be folded as soon as it is your turn.
3. You have a drawing hand.

Drawing Hands

Poker odds come into play when you have a drawing hand. You have three or four cards which have the potential to become a winner. There are two more cards to come (turn and river) which offer the opportunity to create the hand you believe will win the pot. You need to play your hand with knowledge of the chances of making your dream hand.

The table at the bottom of this page shows the mathematical probability of making your hand based on the number of outs.

What is an 'out'?

Most people who have seen poker on TV will have heard talk of outs. An out is a card that will improve your hand. Let's say you are playing a hand and have A K Q J. There are no pairs on the board and no possibility of a flush either. Therefore the chances are if you get your 10 to make an Ace high straight you will have the best possible hand. So if this example is right after the flop you have two cards in your hand (let's say A K) and the flop is Q J 2. So we can deduce that if the deck contains 52 cards and we have seen five of them there are 47 cards that we have not seen, and two to come (turn and river).

In this example we have a number of outs. The most obvious is a 10. There are four 10s in a deck of cards and we have not seen any so far. So this gives us four outs. Four chances out of the 47 cards remaining unseen. So we could say there is a 47/4 chance of getting our ten. Now this math is not entirely the complete picture because there are two cards going to be drawn and there are other outs that would give a good hand.

Another common example of a drawing hand might be a flush draw. You hold A 9 of clubs and the flop is 5 8 4 with two clubs you now have four to an Ace high flush. So how many outs do we have? Well there are 47 cards we have not seen and we know that in a deck of cards there are 13 cards of each suit. So if we've seen 4 clubs there are 9 clubs remaining unseen. So we have a 47/9 chance of getting our final club.

An out is a card that helps your hand so you might also consider that another ace would help your hand. So if you were counting your outs in this example you might throw in 3 more for the three unseen aces. So now you could think that you have 12 chances in 47 to get a winning hand.

Clearly the more 'outs' you can think of that would win the pot the more sensible it would be to stay in the pot.

Calculating Poker Odds (Rule of 2 and Rule of 4)

So one of the essential ingredients to calculating odds is to know how many outs you have. But since many people find difficulty dividing numbers into 47 in their head before taking into account two remaining cards (the turn and river) there is a good cheat to get an approximate idea of how good your hand is.

The Rule of 4

The rule of 4 is a neat way of figuring your odds after the flop and before the turn. First you count your outs. How many cards are in the deck that you have not seen and how many of those would win you the pot. If you have four cards to a flush this leaves us nine remaining cards that might win you the pot with a flush. So in this example you take your number of outs and multiply by four. So 9 multiplied by 4 is 36. The rule of 4 tells us that on a flush draw after the flop you have a 36% chance of making your flush by the river. Now mathematically the actual odds are 35%, the rule of 4 is only an approximation to be used while playing, but knowing your odds to within a few percent should be accurate enough. According to the odds you will make your flush one in every three times you attempt this play.

The Rule of 2

After the turn and before the river the Rule of 2 applies. You now have only one card left to make your hand. Continuing the flush draw example from above you now have 46 cards remaining in the deck that you have not seen, and assuming you missed your card on the turn, you still have 9 cards that would make your flush i.e. 9 chances in 46. Using the Rule of 2 saves you from dividing 9 by 46. Simply multiply 9 by 2 to get 18. You have an 18% chance of making your flush on the river. Mathematically the true odds are 19.6% but again 18% is a pretty good approximation for game play. You can basically surmise that you will make your flush on the river about 1 in 5 times.

Professional or Expert players may decide that rather than use these approximations they will simply memorize the table below. The table shows the mathematical odds of making your chosen hand on the turn and the river. The table is again based on the number of outs you have to improve your hand.

Never forget that as with anything involving odds, there are no guarantees. You might have four cards to a full house twenty times in a playing session and never make your hand. In the absence of all other information this table and the rule of 4 and rule of 2 will give you a very good indication what you need to be doing. But these odds are a mathematical certainty only when playing a large number of hands (perhaps millions of hands). So don't become a slave to the odds, but be aware of them.