So you’ve played a few games of Texas Hold’em poker and you’ve probably watched a few big hands played by the pros via a televised table at the World Poker Tour or World Series of Poker and you wonder how these guys decide when to hold’em and when to fold’em in the big money situations in a way that keeps them consistently winning. Well there are a few hands where a well practiced and savvy “gut” read on a player does tip the decision, and for that you simply need to play and gain experience but most of the time the play is guided by the odds.
Every game of chance (blackjack, backgammon, etc.) in which a player can gain an “edge” is dependent on the players knowledge of the odds. When the odds are in your favor put your money in and when they’re not don’t put your money in. Sure that’s easy enough you think; but we don’t all have a head for advanced mathematics like poker superstar Chris Ferguson: with a mother who has a doctorate in math, a father who is a professor in game theory and theoretical probability and our own PH.D. in computer science, but that’s o.k.. The truth is that if during a hand of Hold’em poker you feel you need to apply the level of math that plots space shuttle trajectory you should probably fold anyway, and the good news is that all you need is a grade five or six level of math to make a solid decision on what play you should make.
Lets set the stage for the explanation with a basic hand example: you’re the big blind with Ac & Ks, one player calls everyone else folds. For the sake of simplicity everyone has the same stack of $100 and the blinds are $5/$10, so the pot now contains $25 (your blind+one caller+small blind) the flop comes down Qd, Jh,3h. You check as the first to act again for the sake of simplicity your opponent bets all-in for his last $90 making the pot now $115 and $90 to call. Now we have to compare two kinds of odds to see if we should call or fold.
We can clearly see our straight possibility if we can hit a 10, and again for simplicity we’ll decide that that’s our only chance to win 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 10’s in a deck so we are said to have four outs in this situation. Okay, we know our outs what next?
Introducing the rules of two and four! The rule of two is this: “multiply your number of outs by two to get an approximate % of times you will draw one of your out cards with one card left to come”. The rule of four is this. “multiply your number of outs by four to get an approximate % of times you’ll draw one of your out cards with two cards left to come”. Pretty simple hey? This is not an exact % (the exact % for one card to come with our four outs would be 8.51 and on and on into smaller decimal places but for practical application 8% is a good enough figure to work with). So back to our example we use the rule of four here because the opponent is all-in there for if we call we get to see both cards left to come without further betting. Okay we have a 16% chance (expressed as a ratio 5.25:1, which means for every 6.25 times we play this hand out we’ll win once ) of hitting a 10 and winning the hand. This is our odds to win the hand known as our “draw odds”.
Knowing our draw odds is only half the info though. Next we need to know our “pot odds”. The pot as we said is now $115 and will cost us $90 to make the call. Expressed in a ratio is 115:90 or 1.28:1 (for our purposes in the heat of the moment you could work with a ballpark figure so 90 goes into 115 about 1 and a third times so ballpark=1.3:1) and that’s our pot odds.
Now basically we need to have a pot odds ratio that’s bigger than the draw odds ratio to make this a positive expectation call (positive/negative expectation means that if you add up every time you ever make this call in this situation will you show a gain or loss on average)? So lets total it up: if we know we will lose this hand about 5 out of 6 times (again a usable ballpark to simplify instead of 5.25 out of 6.25) then that equals 5 loses times $90 each for a total of -$450 compared with the 1 time 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 negative expectation call so you’d be best to fold.
That got a little complex towards the end in order to show you why you would fold, but in reality all you needed to know was that the pot odds were considerably smaller than the draw odds so your best play should be to fold. Lets look at a slightly more complex example but this time we’ll leave out the explanation of positive or negative expectation.
Again you’re the big blind, stacks are all the same at $100, 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 making the pot $65. The flop comes down 7c, 10h, Ac. You check and your opponent moves all in for his remaining $70 now what? For a host of reasons such as the raise preflop, the type of player they are, hands you’ve seen them play before, etc. you figure he has a big ace such as AK or AQ. So we’re pretty sure we know what we need to beat, lets look at our hand.
We have an open ended straight draw, meaning that we have four cards to the straight and only need one of the cards at either end to make it, in this case a 6 or Jack will do it. We also have a draw to any club in order to fill out a flush which we figure won’t get beaten by a bigger flush because assuming we’re right about the opponent having a big ace means he can’t have two clubs back because the Ac is on the board. Lets count the outs there are 9 clubs remaining in the deck and an additional three 6’s or three J’s to make our straight. (you only count the three 6’s and J’s that aren’t clubs because the the 6c and Jc have been counted in all ready as flush outs) So that’s 15 outs. Now again because it’s an all-in call we’re faced with we can leave out the rule of two and use the rule of four because there will be no further betting. So rule of four is 15 (our outs) times 4 = 60% but wait one second before you grab your chips. When dealing with high numbers of outs and two cards left to come there is one extra consideration to be made which is “Solomon’s Rule”. Solomon’s rule is this, with two cards left to come apply the rule of four then subtract from that figure the number of outs you have over eight. In our example we have 15 outs which is 7 outs greater than 8 so take our rule of figure of 60 and subtract the 7 extra outs and a more accurate figure is 53%, so we can see that we will hit our hand 53% of the time so that should be a call.
Some things to be aware of when applying this are; one, you will have a better result as you develop an ability to read your opponents hand. In our second example If we were wrong about the opponent having a big ace and instead he had a KcQc then all our flush outs and our three Jacks would give him the better hand leaving us to draw one of the four sixes or a scenario where we pair the 9 or 8 and he misses everything, not situations you want to be in for all the marbles. Two, slim edges like our second example would always be a call in a cash game as if you loose you just go back to the dealer for a fresh stack, lick your wounds, and go right back to looking for a spot with any edge you can get because cash game play is all about your long run expected value and any positive edges will add up over the years. Where as in a tournament once you loose your stack it’s over, so you might decide to lay a hand with a very small advantage down in hopes to find bigger advantages to play for the whole wad, or be content to slowly steal back the money you lost by picking up small uncontested pots. Also remember that in our two examples we were facing all-in bets after the flop in order to simplify the situation in most hands you will use the rule of two far more often as you would normally have to figure your odds after the flop with only the turn to come and then you would have to re-figure them (if you missed the turn) during the following betting round before the river with different amounts for the pot and bet.
In close I’ll say this, This is not going to morph into a poker superstar in time for next years World Series of Poker, but it is an important weapon to have in your quiver, along with dozens of others you will acquire on your poker journey, and hopefully this has helped to start you down the path of playing “correct poker” and that with it you won’t need as much good luck, just a little less bad luck.