The Rule of 4 and 2 multiplies the out count by four on the flop and by two on the turn. It is a linear approximation, and it always lands high: 9 outs gives 36% against an exact 34.97%, while 15 outs gives 60% against an exact 54.12%. The poker odds chart is where the exact numbers live.
What the shortcut is actually computing
The rule treats each out as one independent chance on each card still to be dealt. Two cards remain on the flop, so every out is counted across two streets; one card remains on the turn, so it is counted once. That is where the four and the two come from. It is a count of shares, not a probability calculation, and shares add cleanly while probabilities do not.
An odds calculator and the table below instead count the ways to miss on both streets and subtract them from the whole. For 9 outs, the Next Card column reads 19.15% and the By the River column reads 34.97%. The second figure is not the first one doubled, because the turn card changes the deck the river is drawn from.
Use the four-times figure as a mental ceiling; the By the River column is the number to carry into any comparison.
| Outs | Next Card | By the River |
|---|---|---|
| 1 | 2.13% | 4.26% |
| 2 | 4.26% | 8.42% |
| 3 | 6.38% | 12.49% |
| 4 | 8.51% | 16.47% |
| 5 | 10.64% | 20.35% |
| 6 | 12.77% | 24.14% |
| 7 | 14.89% | 27.84% |
| 8 | 17.02% | 31.45% |
| 9 | 19.15% | 34.97% |
| 10 | 21.28% | 38.39% |
| 11 | 23.40% | 41.72% |
| 12 | 25.53% | 44.96% |
| 13 | 27.66% | 48.10% |
| 14 | 29.79% | 51.16% |
| 15 | 31.91% | 54.12% |
Why the multiplier drops on the turn
On the flop the shortcut assumes a linear gain for each of two remaining cards. On the turn only one card is left, so the multiplier halves. The reasoning is about how many cards remain, not about a change in the deck; the same approximation is applied fewer times.
The table’s two columns show why that matters. For 4 outs the Next Card column reads 8.51% and the By the River column reads 16.47%; for 8 outs those are 17.02% and 31.45%. A single card scales almost linearly with the out count, while two cards do not. The shortcut extends single-card behaviour across two streets, which is where it starts to drift.
Read the Next Card column when only one card remains. That is the row the two-times figure approximates and the row a turn calculation needs.
Where the error grows
With 9 outs the shortcut gives 36% against the table’s 34.97%, about one percentage point high. With 15 outs it gives 60% against 54.12%, nearly six percentage points high. Both come from the same four-times multiplication, so the difference is the linear assumption failing more visibly as the out count rises.
The By the River column shows the shape of it: 16.47% for 4 outs, 31.45% for 8 outs, 34.97% for 9 outs, 44.96% for 12 outs and 54.12% for 15 outs. Equal steps in outs do not produce equal steps in probability, so the shortcut sits close to the truth at the low end and far from it at the high end.
Treat the multiplied figure as a bound rather than a value whenever the out count is large. The error always runs in the same direction, so the shortcut is a ceiling.
When the table replaces the shortcut
A 9-out draw is where the shortcut is closest to usable: 36% against 34.97%, about one percentage point apart. A 15-out draw is where it stops being usable: 60% against 54.12%, nearly six percentage points apart. Combination draws reach those higher counts, since a flush draw paired with a straight draw adds outs that the shortcut then multiplies.
A rough mental figure is fine when the gap is small. The By the River column is the number to use when the gap matters, such as any comparison against a pot-sized figure. Keep the Next Card column for the turn and the By the River column for the flop; the multiplied figure is only a bound on the latter.