Counting outs is the easy half of a draw decision. The harder half is turning them into a percentage fast enough to compare with the price of a call. The rule of 2 and 4 does that with no division: count your outs, then multiply by 2 if one card is still to come, or by 4 if two are. This post checks how close those answers are to the exact figures, and what to do when they drift.
Where the rule comes from
Your hand is made on the next card with probability outs ÷ unseen cards. On the turn you can see six cards (your two plus four on the board), so 46 are unseen. On the flop you can see five, so 47 are unseen. Dividing by 46 is the same as multiplying by 2.17, and the rule rounds that down to 2, which is easy to carry in your head.
With two cards to come, the chance is one minus the chance of missing both. For a flush draw with 9 outs that is
1 − (38 ÷ 47 × 37 ÷ 46) = 35.0%
The rule of 4 says 9 × 4 = 36. For a first estimate that is a fair answer, and the same pattern holds for the other small draws.
| Draw | Outs | Rule of 2 | Exact turn | Rule of 4 | Exact flop to river |
|---|---|---|---|---|---|
| Gutshot straight | 4 | 8 | 8.7% | 16 | 16.5% |
| Open-ended straight | 8 | 16 | 17.4% | 32 | 31.5% |
| Flush | 9 | 18 | 19.6% | 36 | 35.0% |
| Flush plus gutshot | 12 | 24 | 26.1% | 48 | 45.0% |
| Flush plus open-ended | 15 | 30 | 32.6% | 60 | 54.1% |
The two rules fail in opposite directions
The rule of 2 always undershoots. It rounds 2.17 down to 2, so it is a little low at every size, and the gap grows with outs: 1.4 points at 8 outs, 2.1 at 12 and 2.6 at 15. That error is the safe kind. If the rule of 2 says you have enough to call, you do.
The rule of 4 is more awkward. At 4 outs it reads 16 against a true 16.5, and at 8 outs it is 32 against 31.5, both within a point. Past that, it overshoots. It treats two cards as if each were a separate full chance, but when your first card hits you do not need the second. The more outs you have, the more of the two-card total is that overlap, and the bigger the error.
A correction that works
For more than 8 outs, take 4 × outs and subtract the number of outs above 8. It is an approximation, not a law, but it lands close:
- 9 outs: 36 − 1 = 35, against an exact 35.0%.
- 12 outs: 48 − 4 = 44, against an exact 45.0%.
- 15 outs: 60 − 7 = 53, against an exact 54.1%.
Each answer is within about a point. The plain rule of 4 for 15 outs would have been off by nearly six.
Where the rule goes wrong in play
The arithmetic error is the smaller problem. Three others matter more.
- Using the rule of 4 when you will face another bet. The 35.0% for a flush draw on the flop pays for both cards only if you see them for one price. If your opponent bets again on the turn, you are buying one card at a time, and the figure for the flop call is the one-card chance: 9 ÷ 47 = 19.1%. The rule of 4 applies fully only when no further bet can come, usually because someone is all in.
- Counting outs that do not win. The rule only converts outs to a percentage. If one of your nine hearts also pairs the board and gives someone a full house, it is not an out, and the figure should come down to match.
- Comparing it with the wrong price. The number to beat is the call divided by the pot after you call. A half-pot bet needs 25% and a pot-sized bet 33.3%, as worked through in the post on pot odds. Dividing by the pot before the bet, or before your own call, gives a figure that is too high.
A worked example
You hold a flush draw and an open-ended straight draw on the flop: 15 outs. The pot is 60 and your opponent bets 60, so calling costs 60 and the pot would then be 180. The price is 60 ÷ 180 = 33.3%.
The plain rule of 4 says 60%, and the corrected version says 53%. The exact figure is 54.1%. All three say the same thing: if you see both cards, you are far ahead of the price. Now suppose the opponent will bet again on the turn. The one-card chance is 15 ÷ 47 = 31.9%, just under the 33.3% price, so the call is no longer comfortable. The rule did not change; what changed was which cards you are paying for.
The shortcut in full: outs × 2 for one card to come, outs × 4 for two. Above 8 outs, subtract the outs above 8 from the rule of 4. If another bet is likely, use only the one-card figure.
The "Is it worth calling?" lesson in Holdem Coach: Poker Trainer asks you to work out the price you are being offered and decide whether your hand is worth it, which is the comparison this post feeds.
Holdem Coach: Poker Trainer offers short lessons on one idea at a time, and nothing in them is timed. Practice works offline, and the app can read the cards, the question and the answer aloud using your phone's voice. It is a training app with no real-money wagering, not a poker solver or a promise of winnings.