Poker Math Trainer
Every formula you need at the table: outs, pot odds, MDF and EV, on one page, plus a quick drill to build the muscle memory.
Outs and the rule of 2 and 4
- Flop → river (2 cards)
- outs × 4 ≈ equity%
- Turn → river (1 card)
- outs × 2 ≈ equity%
- Flush draw
- 9 outs ≈ 36% / 19%
- Open-ended straight draw
- 8 outs ≈ 32% / 17%
- Gutshot
- 4 outs ≈ 16% / 9%
The rule overstates equity as outs climb past about 8: for a big combo draw, subtract roughly 1 percentage point from the estimate for every out over 8.
Pot odds
- Required equity
- bet / (pot + 2 × bet)
- 3:1 pot odds
- need 25%
- 2:1 pot odds
- need 33.3%
- 1:1 pot odds
- need 50%
Here 'pot' is what's already in the middle before this bet: add the bet twice (villain's, then your call) to get the pot you're playing for. Call if your real equity is above the required number; fold if it's below.
Minimum defence frequency (MDF)
- MDF
- pot / (pot + bet)
- Half-pot bet
- MDF ≈ 66.7%
- Pot-sized bet
- MDF ≈ 50%
- 2× pot bet
- MDF ≈ 33.3%
MDF is the whole-range share you must continue with so a bettor can't profit by bluffing any two cards. It answers a different question to pot odds, which is about one hand.
EV of a decision
- EV
- (win% × amount won) − (lose% × amount lost)
- Break-even equity
- EV = 0
A call, bet, or bluff is profitable in the long run whenever its EV is positive, whatever it feels like in the moment.
Why these four formulas
Almost every in-game maths decision in poker comes down to one of four calculations: how likely you are to improve, what equity a call needs, how often you must defend against a bet, and whether a decision is profitable overall. Learn these four and you can work out the right answer at the table without memorising a single hand.
Related pages
Frequently asked questions
- What is the rule of 2 and 4 in poker?
- A quick way to turn an outs count into an equity estimate without running a full equity calculation. With two cards to come, multiply your outs by 4; with one card to come, multiply by 2. Nine outs (a flush draw) is roughly 36% on the flop and 19% on the turn.
- Why does the rule of 4 overstate equity with a lot of outs?
- It is a linear approximation of a curve that flattens out as outs increase, so it gets less accurate the more outs you have. A 15-out combo draw is closer to 54% by the river than the 60% the rule of 4 suggests. Past about 8 outs, subtract 1% for every out over 8 to correct for this.
- What is the formula for pot odds?
- Required equity = bet / (pot + bet). If your real chance of winning is above that number, calling is profitable in the long run; if it is below, folding is.
- What is minimum defence frequency (MDF)?
- The smallest share of your range you must continue with against a bet so the bettor cannot show an automatic profit by bluffing any two cards. It is calculated as pot / (pot + bet), the mirror image of the pot odds formula.
- Is MDF the same as pot odds?
- No. Pot odds tell you the equity one specific hand needs to call profitably; MDF tells you how much of your whole range must continue. They share the same formula shape, bet vs pot, but answer different questions.
- How do you calculate the EV of a poker decision?
- EV = (probability of winning × amount won) − (probability of losing × amount lost). A decision is profitable in the long run whenever its EV is positive, whatever the outcome of any single hand.
- Do I need to memorise these formulas at the table?
- Not exactly, but the shortcuts on this page (rule of 4, common pot odds ratios, standard MDF percentages) are worth memorising, since deriving them from scratch mid-hand is too slow. The drill on this page is built to help that stick.
- What is a combo draw and why does it change the maths?
- A combo draw is two draws at once, most often a flush draw plus a straight draw, so its outs add together (a flush draw plus an open-ended straight draw is often 15 outs). Because the rule of 4 overstates equity for large out counts, combo draws are exactly where the correction matters most.
- Is this different from the Equity Calculator or Pot Odds Calculator?
- Those two tools solve one specific hand exactly, given real cards or ranges. This page is a reference and drill for the underlying formulas, including MDF and EV, which neither calculator covers on its own.
- Is this free to use?
- Yes, the cheat sheet and drill are free with no sign-in and no limit. The ranked Trainer, which grades full hand decisions and adapts to your rating, is a separate subscription with a 14-day free trial.
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