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Counting your Outs: the Rules of 4 and 2

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Are you Corey Zeidman unknowingly drawing (and hitting) to a 1-out straight flush against Jennifer Harman's queens full? Maybe not, but every poker player playing with the intention of making money needs to understand the basic concepts of outs and probability.

An "out" is any card that you assume will give you the winning hand. Be wary that an "out" that doesn't make you the nuts (the best hand possible) may, in fact, not be an out at all. That is best left for another article.

The Rule of 4 gives you the rough percent chance you will hit one of your outs on either the turn or river (essential if you want to know when to hold'em and when to fold'em). It's really simple to use. On the flop, take the number of outs you have and multiply it by 4. The product is the the probability that you'll hit your draw.

Example:
You have 2 hearts in the hole, and there are 2 hearts on the flop. You have a flush draw and want to figure out the chance of you hitting that flush by the river. There are 13 of any suit in a deck of 52 cards. You have seen 4 of them already. That leaves 9 (13-4) outs for you to hit. Therefore, the probability of you hitting your flush is about 36% (9x4).

The Rule of 2 is a slight modification on the Rule of 4. It gives you the probability of hitting when only the river card is left to come. To find the probability of hitting, simply multiply your outs by 2.

Example:
The turn card just arrived bringing you a gutshot straight draw (4 outs). The probability of hitting your draw on the river is 8% (4x2).

Note: Since these rules are rough (albeit more than good enough for poker purposes), when you have 12 outs the Rule of 4 estimates a 48% of hitting, where you are actually 45%. However, as your outs increase, the margin of error also grows. For example an open-ended straight draw + a flush draw gives you 15 outs. The Rule of 4 estimates 60%, where you are only actually 54%.

The next time you need to quickly calculate the approximate probability of hitting your draw, be it a 1-outer or 21, online or live, remember the Rules of 4 and 2.

Comments (5)

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nice explanation of how to figure out roughly where you are in a hand.

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by bsidensol on April 18, 2007 (login to reply)
This sounds a lot like what Phil Gordon uses and wrote in his little Green Book (and Little Blue). You should give credit to someone else if the idea isn't yours.

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by nwalden on May 14, 2007 (login to reply)
anyone else have a hard time running these quick calcs against the personalities they're playing against? focus on the numbers can compromise my gut feeling sometimes.

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by jasony on May 25, 2007 (login to reply)
cool shortcut - that hadn't occured to me but now that I think about it it should have been obvious 47 or 46 is pretty much half of 100 so it works nicely with percentages.

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by Quixotic on January 7, 2008 (login to reply)
This is very good article. Thank you very much.

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by Tiko_maf on October 25, 2009 (login to reply)
 
 

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