Calculating Odds and Outs; Part IV, Using Percentages

by ~ May 15th, 2008. Filed under: Instructional posts.

* Modified June 15th, 2010 *

Rather than considering odds in terms of 3 to 1, you can look at them in terms of percentages.

First, determine your outs as we did previously. 9 outs to a flush on the turn, with 47 cards possible. Simply get the percentage of 9 to 47 which equals 19%. So, you have a 19% chance of hitting the flush on the turn.

Phil Gordon claims to have named the “rule of two and four”. This is a method for approximating the percentages of hitting your outs on either the river alone or the turn and river combined. With 9 flush outs, you multiply by two to get the river percentage; 18%. To get the odds for the turn and river combined, you multiply the outs by 4; 36%. This is not exact, but is a pretty fast and fairly close approximation of the likelihood of hitting your outs.

This method tends to get more inaccurate the more outs you have. If you want your results to be more accurate, adjust the rule of four by subtracting one percent for each out greater than 8. For 15 outs, 15 times 4 = 60. 15 – 8 = 7, so 60 – 7 = 53%.

Please note that the rule of four applies to both the turn and river combined. And as we saw earlier, this does not take into account the possibility that you will have to call another bet on the turn. Where this does apply is where one of you will be all in. This means that there will be no bet on the turn and no bet on the river. Say you are playing a tournament and you raise your A8 from late position to 3 big blinds. Other players fold, but the big blind, who only has 7 big blinds left, just calls you. The flop is as before, K65 and the big blind pushes in his last 4 big blinds. Now the pot is your 3 BBs, the small blind’s 1/2 BB that he folded, the big blind’s 3 BBs to call plus his 4 BBs shove for a total of 10.5 BBs. You have 9 outs = 35% chance of hitting. You are being asked to call 4 BBs into a 10.5 BB pot, so 10.5 + 4 =14.5. Your call of 4 as a percentage of the total future pot of 14.5 = 28%. Your percentage of hitting is better than the percentage that you have to put into the pot, so call.


Comparing Odds with Percentages

We’ve now come to the point of another confusing aspect for beginners.

When you use percentages to determine whether or not to call as we just did, you must add your bet to the pot to get the pot percentage. Then, if your percentage is greater than the call bet to total pot percentage, you call. When you use odds, you don’t include your bet in the pot size, and you call if your card odds are smaller than the odds the pot to bet ratio is giving you.

This is because

  • percentages are calculated as a wins compared to the total of all wins and loses, whereas odds are ratios comparing wins against losses, and
  • better winning percentages are bigger numbers, whereas in ratios the wins are always 1, so the smaller the number of loses, the better your ratio is.

So to calculate the flush example above, you have to call 4 BBs, so you’re getting 10.5 to 4 odds, or 2.6 to 1 pot odds. You have a 1.9 to 1 chance of hitting your flush on either the turn or the river, and there will be no turn bet to call. Pot odds are better than your card odds, so call.


One last thing to keep in mind that the number of outs can increase on the turn. In particular a runner-runner draw that you valued at 1 out may become a full value group of outs if one of your runners come in on the turn. Say you have two of a flush in your hand, and one appears on the flop. Because you need a two more of your suit which is a longshot, you value it for perhaps only one out. But if one of your suit comes on the turn, now your chances have improved and you can count the full 9 remaining flush outs.

But a really interesting one is flopping a set, especially if there is three to a flush in the flop. Say you call with 88 and the flop comes K82. If someone has a made flush, you have 1 out to make quad 8s, 3 outs to pair the K and 3 outs to pair the 2 to make a full house so a total of 1+3+3=7. Say the turn misses you with a 6. Now your outs actually increase. Your 7 outs on the flop are still good but now you have gained 3 more outs if a 6, 6, or 6 comes on the river for a total of 10 outs.


The rest of the series:


Compendium of instructional posts:

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