# Calculating poker odds – Don’t misuse the rule of 2 and 4

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#### Cory | Poker Articles, Poker Mathematics

One of the first things we learn about the mathematics involved in poker is figuring out our chances of winning by using the rule of four and two.  For those of you who may not be sure exactly how that works, if you have an open ended straight draw for example, you count your outs, the unseen cards that make your straight, which is 8 and multiply your number of outs by 4 on the flop and 2 after the turn.  So on the flop you’re about 32% to make your straight with the turn and the river yet to come and on the turn you’re about 16% to make your straight with just the river to come.

Basically is what this means, is the odds of you completing your straight are just over 2:1 against it with 2 cards and just under 5:1 against it with 1 card.  This information is used to measure the likelihood of you hitting your draw against the price you’re getting on a call compared to how much is already in the pot.

If I’m playing a pot with \$80 and my opponent bets \$20, he creates a pot of \$100 and it costs me \$20 to potentially win that \$100, or I’m getting 5:1 on the call.  We’re all good so far right?

The problem is, I’ve recently run in to a lot of players who are completely misusing the rule of four and two to try and justify some pretty bad calls.  You really need to be thinking about what your chances are of hitting your draw on the next card because very often, you’re going to be faced with another bet.  The rule of four and two was designed for when you’re facing an all in bet on the flop or turn and you have a draw.  If you go all in, you’re guaranteed to see all five board cards, but if you and your opponent still have chips behind, it changes the math drastically.

Let’s say you’re in a \$1-\$2 game.  You and your opponent each have \$200 stacks to start the hand.  Your opponent opens from middle position to \$8 and you call with 8C7C from the button and take a flop heads up.  The blinds have probably been taken out for rake, so we have a pot of probably \$15.  The flop comes 9H, 6S, AD.  You have no clubs, but you have an open ended straight draw.  Your opponent bets \$10 creating a pot of \$25 and you’re getting 2.5:1.  Using your rule of four and two the odds are 2:1 against hitting your hand so this is a profitable call… if you can guarantee that you’ll see both remaining cards.

You can’t forget about how much you’re probably going to have to call on the turn.  If you call this flop bet there will be a pot of \$35, so if you miss the turn, you may have to call a bet somewhere between \$20 and \$30 to see the river card which you counted on with your rule of four.  So really, your flop decision has to be whether or not you’ll be willing to call somewhere between \$30 and \$40 to see both the turn and river.

This is where implied odds come in to play.  Since you and your opponent are both playing \$200 deep, it makes sense to call his bet on the flop and call a reasonable bet if you miss the turn.  Let’s say you call this \$10 on the flop creating a pot of \$35 and your opponent bets \$20 on the turn and you missed.  Now you’re getting \$55:\$20, or 2.75:1 pot odds, which is not a good price, but if you call, the pot will be \$75 and your opponent will have \$162 to pay you off with if you hit the river.

If your opponent should decide to bet the river when you hit, it’s going to be somewhere around \$50 in to a pot of \$75, in which case you’re going to be able to stack him enough of the time to make the call on the turn where you were getting slightly the worst of it profitable in the end.  Big bet poker games are more about implied odds than pot odds.  Limit games focus more on pot odds since implied odds in a limit game are reduced to maybe one or two extra bets.

Never forget when deciding whether or not to call on the flop to factor in how much that call is really going to cost you.  Always be aware of the effective stack size in the hand so you can calculate your implied odds.  Don’t make calls where you’re taking the worst of it if either you or your opponent has a shorter stack.  Stop using the rule of four and two to justify flop calls when you can’t call a bet on the turn and get that river card that you promised yourself on the flop.

### 1 Comment to Calculating poker odds – Don’t misuse the rule of 2 and 4

Mark
June 26, 2010

Good pointers Cory. If you remember that in order to calculate the probability of hitting your hand on the turn you multiply the number of outs with 2 and not 4 this will hopefully keep you from making bad decisions.
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