Guides Math You Can Do at the Table
The Rule of 2 and 4, and Where It Lies to You
Multiply your outs by four with two cards to come, by two with one card to come. It is the most useful approximation in poker and it is wrong in two specific places, both of which cost money if you do not know about them.
The Rule
Count the cards that improve you to a winner. Multiply by 4 on the flop when both the turn and the river are coming, by 2 when only one card is left. The result is a percentage.
Nine outs for a flush draw on the flop: 36 percent. The true number is 35 percent. Eight outs for an open-ended straight draw: 32 percent against a true 31.5. Four outs for a gutshot: 16 percent against a true 16.5. For the draws you will actually face, the rule is accurate to about a point, which is far inside the margin of your read.
The Numbers Worth Memorizing
| Draw | Outs | Two cards | One card |
|---|---|---|---|
| Gutshot | 4 | 16% | 9% |
| Two overcards | 6 | 24% | 13% |
| Open-ended straight | 8 | 31% | 17% |
| Flush draw | 9 | 35% | 19% |
| Flush draw plus an overcard | 12 | 45% | 26% |
| Open-ender plus flush draw | 15 | 54% | 33% |
The First Lie: The Rule of 4 Overshoots Big Draws
The multiplier drifts upward as the out count climbs. At 15 outs the rule says 60 percent and the truth is about 54. The correction is easy: for anything above 8 outs, subtract the difference between your outs and 8 from the multiplied result. Twelve outs gives 48 minus 4, which is 44, against a true 45. Fifteen outs gives 60 minus 7, which is 53, against a true 54.
The Second Lie, and This One Costs Real Money
The rule of 4 only applies when you are seeing both cards for the price you are paying now. That means all-in on the flop, or a spot where no further betting is realistically coming.
Call a flop bet with a flush draw in a hand with money behind and you are not buying two cards. You are buying one, and then facing another bet on the turn. Pricing that call at 35 percent instead of 19 is how a losing flop call gets talked into being a good one. On the flop with money behind, use the rule of 2 for the turn card, and put the rest of the value in implied odds where it belongs.
The Equity at a Glance drill runs the all-in family numbers and the rule of 2 and 4 at straddled-pot sizes, with no solver and no chips in hand. It generates fresh questions rather than cycling a fixed set.
Dirty Outs
An out that improves you to a second-best hand is not an out. Discount them before you multiply, not after.
- A flush out that pairs the board can fill a full house for someone else. It is a fraction of an out.
- A straight out that puts three to a flush on the board gives you a hand you cannot bet and cannot call with.
- Overcards against a range that is mostly pairs are worth far less than six outs. Against a raiser who has AK often, your queen is not clean.
- A non-nut flush draw against a bigger one is the expensive version. Q-high flush draws stack people.
Nut draws need no discount, which is exactly why they are worth more than their raw count. Ace-high suited on a two-flush board and a queen-high suited hand on the same board are the same nine outs and different hands.
Putting It Together in One Spot
Flop is Q-7-2 with two hearts. You have the ace and jack of hearts. Villain bets $40 into $60 and has $300 behind.
Price: two-thirds pot, so you need 28.6 percent. Equity for one card: 9 outs times 2, so 18 percent, and the three ace outs are live against much of his range, call it 12 outs by the turn on one card, roughly 24 percent. That is short of the price on raw equity alone, which means the call needs money to arrive later. He has $300 behind, you have the nut draw, and a heart river gets paid by a queen. That is the call, and the reason for it is the $300, not the 24 percent.
Questions People Ask About This
How accurate is the rule of 2 and 4?
Within about one percentage point for draws up to eight outs. Above eight outs the rule of 4 overstates, and you should subtract the amount your out count exceeds eight.
When should I not use the rule of 4?
Whenever there is meaningful money left to bet. You only get both cards free when you are all in, so on the flop with stacks behind, use the rule of 2 for the turn.
What is a dirty out?
A card that completes your hand but plausibly gives someone a better one, such as a flush card that pairs the board. Discount it before you multiply.