Poker Math · 7

Exact Drawing Odds

Beyond the Rule of 4 and 2: the exact math for common drawing situations.

Formula

Single street odds = Outs / Unseen Cards
Flop → River = 1 − ((47 − Outs) / 47 × (46 − Outs) / 46)

Explanation

After the flop, 47 cards are unseen (52 minus 2 hole cards and 3 board cards). The Rule of 4 estimates equity by river but slightly overshoots with many outs. The exact formula matters when you're on the bubble of a close decision.

Example

Setup

Flush draw on flop: 9 outs. Compare Rule of 4 vs exact.

Calculation

Rule of 4: 9 × 4 = 36%
Exact: 1 − (38/47 × 37/46) = 1 − 0.650 = 35.0%
Rule is 1% off — close enough for in-game

Conclusion

Rule of 4 is good enough for most situations.

Setup

Combo draw (flush + open-ended straight) on flop: 15 outs.

Calculation

Rule of 4: 15 × 4 = 60%
Exact: 1 − (32/47 × 31/46) = 1 − 0.459 = 54.1%
Rule overshoots by ~6% with many outs

Conclusion

For 12+ outs, mentally adjust: Outs × 4 minus a few percent.

Practice

Open-ended straight flush draw on the flop: 15 outs (9 flush + 8 straight − 2 double-counted). Roughly what equity do you have by the river?