Poker Tip: Rule of Four and Two

I was explaining this method for estimating odds to someone the other day, and thought it would be a great idea to write a short blog post explaining it to everyone.

The rule of four and two (also called ‘Solomon’s Rule’) is a very simple method for estimating odds in your head.  It’s especially useful for those who have a difficult time doing long division without a piece of paper or calculator.

To estimate the odds that you will hit a given hand after the flop, just count up the number of outs, multiply that number by 4 and the result is the approximate percentage chance that you will hit your hand on the turn or the river.  If none of your outs come on the turn, just multiply the number of outs by 2 to get the odds you’ll hit on the river.

Here’s an example:

You’ve got the ace and queen of hearts in your hand, the flop comes out six of hearts, ten of hearts and 3 of clubs, giving you four cards to a heart flush.  That means there are nine more hearts out there that will make your hand.  So to estimate the odds that you will hit your hand on the turn or the river just multiply 9×4 giving you a 36% chance that you’ll make your hand.  The actual odds that you’ll make your hand are 34.9%, so the answer is close enough and MUCH easier to calculate.

If that heart doesn’t come on the turn, simply multiply the number of outs by two (9×2=18) to estimate the odds that you will make your hand on the river.  The actual odds are 19.5%, again close enough.  Calculating accurate odds on the river is much simpler, but this method is still easier.

There is one exception to this rule, if you have more than 9 outs, you must make the following adjustment when estimating odds after the flop.  Multiply the number of outs by 4, then subtract 8 from the number of outs and subtract the result from your estimate.

If you had 12 outs, you would multiply 12×4=48, subtract 8 from 12 giving you 4, then subtract 4 from 48, so your approximate odds would be 44%.  The actual odds are 44.9%.

Incidentally, the formulas for caculating actual odds are as follows:

After the flop:

((outs/47) + (outs/46) – (outs/47) x (outs/46))x100 = Odds you’ll make your hand on the turn or river.

i.e. 9 outs to make your flush:

(9/47) + (9/46) – (9/47) x (9/46)

(19.14 + 19.56) – (19.14 x 19.56)

.387 – .0374 = .3496

.3496 x 100 = 34.96%

(47 is the number of unknown cards after the flop (The 5 known cards being the two in your hand and the three on the board) and 46 is the number of unknown cards after the turn.)

After the turn:

(outs/46)x100

9/46=.195

.195 x 100 = 19.5%

(I’m no mathematician, and I usually do these calculations in my head, so my notation may not be 100% accurate.)

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