Texas Hold’em – A Beginner’s Guide to Outs and Odds

So you’ve played a few games of Texas Hold’em poker and you’ve probably seen some big hands played by the pros over a television table during the World Poker Tour or World Series of Poker and you’re wondering how these guys decide when to hold them and when to fold them in big money situations in a way that keeps them winning consistently. Well, there are a few hands where a well practiced and skilled “gut” reading a player will tip the ball, and for that you just have to play and gain experience, but most of the time the game is guided by the odds.

What are the odds in Texas Holdem?

Any game of chance (blackjack, backgammon, etc.) in which a player can gain an “advantage” is dependent on the players’ knowledge of the odds. If the odds are in your favor, put your money in it and if they aren’t, don’t bet your money. Sure, that’s easy enough, you think; but not all of us have a penchant for advanced math like poker superstar Chris Ferguson: with a mother with a PhD in mathematics, a father who is a professor of game theory and theoretical probability, and our very own PH.D. in computer science, but that’s okay. The truth is that during a hand of Hold’em poker, if you feel like you need to apply the level of math that charts the trajectory of the space shuttle, you should probably fold anyway,

Let’s lay the groundwork for the explanation with a simple hand example: you are the big blind with Ac & Ks, one player calls and everyone else folds. For simplicity, everyone has the same $100 stack and the blinds are $5/$10, so the pot now contains $25 (your blind+one caller+small blind). The flop comes down to Qd, Jh,3h. You check first to act again for simplicity and your opponent bets all in for his last $90, leaving the pot now $115 and $90 to call. Now we need to compare two kinds of odds to see if we should call or fold.

We can clearly see our straight opportunity if we can hit a 10, and again for simplicity we will decide that this is our only chance of winning the hand. So step one is counting your “outs”. Outs are the cards you could draw to give you the superior hand, and there are four 10s in a deck, so we are said to have four outs in this situation. Okay, we know our outs, now what?

Introducing the rules of two and four! The rule of two is this: “multiply your number of outs by two to get an estimated % of the times you draw one of your out cards with one card to go”. The rule of four is this. Multiply your number of outs by four to get an estimated % of the times you draw one of your out cards with two cards to go. Pretty simple huh? This is not an exact % (the exact % for one card with our four outs would be 8.51 and on and on in smaller decimals, but for practical purposes 8% is a good enough number to work with). So back to our example, we’re using the rule of four here because the opponent is all-in there, because if we call, we’re shown both cards with no further betting. Okay, we have a 16% chance (expressed as a ratio of 5.25:1 meaning for every 6.25 times we play this hand we win once) of hitting a 10 and winning the hand. These are our chances of winning the hand known as our “draw odds”.

However, knowing our draw probabilities is only half the information. Next, we need to know our pot odds. As we said, the pot is now $115 and it will cost us $90 to call. Expressed in a ratio is 115:90 or 1.28:1 (for our purposes in the heat of battle you could be working with a margin, so 90 goes about 1 time into 115 and a third time so margin = 1.3 :1) and that’s our pot of odds.

What are the odds of flopping quads in Texas Holdem?

Now we basically need to have a pot odds ratio greater than the draw odds ratio to make this a positive expectation call (positive/negative expectation means if you show a profit every time you make this call in this situation) or loss on average)? So let’s add it up: if we know we’re going to lose this hand about 5 times out of 6 (again, a useful margin to simplify instead of 5.25 out of 6.25) then that’s equal to losing 5 times $ 90 each for a total of -$450 compared to the 1 out of 6 we win the $115 pot for a total of $115. So at the end of the six hands we would show a loss of $335 or an average loss of $55.83 per hand, so in a nutshell, this is a call with a negative expectation, so it’s best to fold.

That got a little complicated towards the end to show you why you’d fold, but in reality all you needed to know was that the pot odds were significantly smaller than the draw odds, so your best play should be to fold. Let’s look at a slightly more complex example, but this time we omit the explanation of positive or negative expectation.

Again, you are the big blind, the stacks are all the same at $100, the blinds are $5/$10, one player makes a standard raise to $30, everyone folds to you and you decide to call the remaining $20 with 9c & 8c leaving the jar becomes $65 . The flop comes down to 7c, 10h, Ac. You check and your opponent moves all in for his remaining $70, now what? For many reasons like the raise preflop, the type of player they are, hands you’ve seen them play before, etc. you think he has a big ace like AK or AQ. So we’re pretty sure we know what to beat, let’s look at our hand.

We have an open ended straight draw meaning we have four cards to the straight and only need one of the cards on either side to make it, in this case a 6 or Jack will do. We also have a tie on any club to fill a flush that we don’t think will be beaten by a bigger flush because assuming we’re right about the opponent with a big ace means he won’t be beaten by a bigger flush. can have two clubs back because the Ac is on the board. Let’s count the outs, there are 9 more clubs in the deck and another three 6’s or three J’s to make our straight. (you only count the three sixes and J’s that are not clubs, because the 6c and Jc are all counted as flush outs) So that’s 15 outs. Now again because it’s an all-in call that we’ll face again, we can omit the rule of two and use the rule of four, as there is no further betting. So rule of four is 15 (our outs) times 4 = 60%, but wait a second before taking your chips. When dealing with high numbers of outs and two cards to come, one additional consideration needs to be made, which is “Solomon’s Rule”. Solomon’s rule is this, with two cards to come, apply the rule of four and then subtract the number of outs you have more than eight. In our example we have 15 outs which is 7 outs greater than 8 so take our rule of 60 and subtract the 7 extra outs and a more accurate number is 53% so we can see that we are holding our hand 53% of the time so that should be a call. So rule of four is 15 (our outs) times 4 = 60%, but wait a second before taking your chips. When dealing with high numbers of outs and two cards to come, one additional consideration needs to be made, which is “Solomon’s Rule”. Solomon’s rule is this, with two cards to come, apply the rule of four and then subtract the number of outs you have more than eight. In our example we have 15 outs which is 7 outs greater than 8 so take our rule of 60 and subtract the 7 extra outs and a more accurate number is 53% so we can see that we are holding our hand 53% of the time so that should be a call. So rule of four is 15 (our outs) times 4 = 60%, but wait a second before taking your chips. When dealing with high numbers of outs and two cards to come, an additional consideration needs to be made, namely “Solomon’s Rule”. Solomon’s rule is this, with two cards to come, apply the rule of four and then subtract the number of outs you have more than eight. In our example we have 15 outs which is 7 outs greater than 8 so take our rule of 60 and subtract the 7 extra outs and a more accurate number is 53% so we can see that we are holding our hand 53% of the time so that should be a call. with two cards to come, apply the rule of four and subtract from that number the number of outs you have more than eight. In our example we have 15 outs which is 7 outs greater than 8 so take our rule of 60 and subtract the 7 extra outs and a more accurate number is 53% so we can see that we are holding our hand 53% of the time so that should be a call. with two cards to come, apply the rule of four and subtract from that number the number of outs you have more than eight. In our example we have 15 outs which is 7 outs greater than 8 so take our rule of 60 and subtract the 7 extra outs and a more accurate number is 53% so we can see that we are holding our hand 53% of the time so that should be a call.

Some things to keep in mind when applying this are; one, you will have a better result as you develop the ability to read your opponent’s hand. In our second example, if we were wrong that the opponent had a big ace and instead had a KcQc, all our flushouts and our three jacks would give him the better hand, drawing one of the four sixes or a scenario where we pair the 9 or 8 and he misses everything, not situations where you want to be for all the marbles. Two, thin edges, like our second example, would always be a call in a cash game, as if you lose, you just go back to the dealer for another pile, lick your wounds and immediately look for a spot with an advantage that you have. could get, because cash games are all about your expected value in the long run and any positives will add up over the years. Where, like in a tournament, once you get rid of your stack it’s over, so you might decide to lay a hand with a very small advantage hoping to find bigger advantages to play for the whole pack, or be satisfied to slowly steal back the money you lost by picking up small undisputed pots. Also remember that in our two examples we bet all-in after the flop. To simplify the situation in most hands, you will use the rule of two much more often, because normally you have to calculate your odds after the flop the turn has to come and then you have to calculate them again (if you missed the turn) during the next betting round before the river with different amounts for the pot and bet. so you might decide to lay down a hand with a very small advantage hoping to find bigger advantages to play for the whole pack, or be content to slowly steal back the money you lost by picking up small undisputed pots . Also remember that in our two examples we bet all-in after the flop. To simplify the situation in most hands, you will use the rule of two much more often, because normally you have to calculate your odds after the flop the turn has to come and then you have to calculate them again (if you missed the turn) during the next betting round before the river with different amounts for the pot and bet. so you might decide to lay down a hand with a very small advantage hoping to find bigger advantages to play for the whole pack, or be content to slowly steal back the money you lost by picking up small undisputed pots . Also remember that in our two examples we bet all-in after the flop. To simplify the situation in most hands, you will use the rule of two much more often,

In closing, I’ll say this: this won’t turn into a poker superstar in time for next year’s World Series of Poker, but it’s an important weapon to have in your quiver, along with dozens of others you’ll have on your poker journey, and hopefully this has helped get you on your way to playing “correct poker” and that you don’t need as much luck as you do, just a little less bad luck.