The Rule of 2 and 4

Basic Poker Math Skills

"The majority of players are looking for reasons to fold. I am looking for reasons to play."
~ Daniel Negreanu

The Rule of 2 and 4

The Rule of 2 and 4 are quick shortcuts to help us work out the percentage needed to get a draw in Texas No-Limit Hold'em. These shortcuts aren’t exact. However, they are good enough for doing quick probabilities in our head at the tables.

The Rule of 2
The Rule of 2 states: Multiply your number of outs by 2 to get the approximate percentage of a draw you have on the turn or the river.

For example, let's say you have a flush draw after the flop.

There are 2 cards of the same suit in your hand and 2 cards of the same suit on the board.
That makes 4 cards to a flush.
There are 13 cards to a suit, and 9 cards (outs) that can help you make a flush (13 - 4 = 9).
Use the Rule 2 to approximate your percentage of hitting a flush on the next card.
2 x 9 = 18% probability of getting your flush.

The exact calculation is:

There are 13 cards to a suit, and 9 cards (outs) that can help you make a flush (13 - 4 = 9).
There are 52 cards in the deck minus 2 cards in your hand and 3 cards on the board.
This leaves 47 cards remaining (52 - 5 = 47).
(9/47) = 19% probability of getting your flush.

The Rule of 2 works because there are 52 cards in the deck
and 52 goes into one hundred approximately twice.

The Rule of 4
The Rule of 4 is used when you are considering an all-in move after the flop and will see both the turn and river cards. Multiply your number of outs by 4 to get the approximate percentage of a draw.

Like the Rule of 2 example, you have a flush draw after the flop.

There are 2 cards of the same suit in your hand and 2 cards of the same suit on the board.
That makes 4 cards to a flush.
There are 13 cards to a suit, you have 9 cards (outs) remaining that can help you make your flush (13 - 4 = 9).
Use the Rule 4 to approximate your percentage of hitting a flush on the next two cards.
4 x 9 = 36% probability of making your flush.

The exact calculation is as follows:

There are 52 cards in the deck minus 2 cards in your hand and 3 cards on the board.
Consequently, there are 47 cards remaining (52 – 2 – 3 = 47).
There are 9 cards that will help you make your flush.
Thus, there are 47 - 9 = 38 cards that will not make your flush on the turn.
The probability of not making your flush on the turn is 38/47.
Subtract one from the numerator and denominator for the river card which is 37/46.
Multiply both numbers together and subtract from 1 to determine your probability of making a flush.
1- 38/47 x 37/46 = 35% probability of making your flush.

Once again, that’s close and useful for quick estimate at the tables.

Note: The Core Math Chapter of Mastering Poker Math provides more detail on how this equation is derived.