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House Edge Calculator

Enter the win probability and payout to see the house edge and RTP.

How it is calculated

The tool works per one unit staked. With win probability p (entered in percent and divided by 100) and a payout of X to 1 (the profit on a winning one-unit bet, stake not counted), the expected value is EV = p × X − (1 − p) × 1. The house edge is −EV × 100 in percent, the return to player is RTP = 100 − edge, and the player's EV per $100 staked is EV × 100.

Win probability must be greater than 0 and at most 100. A payout of 35 means "35 to 1", so a $1 bet returns $36 in total when it wins. A positive edge favours the operator, and a negative edge (a bet that favours the player) shows as a negative edge with an RTP above 100%. The tool describes a single independent bet. It does not model bonuses, commission, bet limits or strategies that change the odds from one bet to the next.

Worked example

Take a single-number bet on a wheel with 37 pockets. The win probability is 1 ÷ 37 = 2.7027%, and the payout is 35 to 1. EV per unit is 0.027027 × 35 − 0.972973 × 1 = 0.9459 − 0.9730 = −0.0270. The house edge is therefore 2.70% and the RTP is 97.30%. Per $100 staked, the player's expected value is −$2.70: over many such bets you lose about that on average, although any single bet either loses $1 or wins $35.

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Common mistakes

  • Entering the payout as "36" when the bet pays 35 to 1. The field is the profit per unit staked, not the total returned including the stake.
  • Entering the probability as 0.027 instead of 2.7027. The field is in percent.
  • Using the approximate probability and reading the second decimal as exact. A rounded 2.7 gives a slightly different edge than 1 in 37.
  • Reading the EV as what you will win or lose on one bet. It is the long-run average, and a single result is either a full loss or a full win.
  • Applying the result to games where you can change the bet size or your decisions during the hand. The tool assumes one fixed probability and payout.

About this calculator

The house edge is the built-in mathematical advantage a casino or bookmaker holds over a player on any given bet, expressed as a percentage of each wager the operator expects to keep over the long run. It's derived directly from the gap between the true odds of an outcome (based on its actual win probability) and the payout odds the house actually offers — the wider that gap, the larger the edge.

This calculator takes a bet's win probability and its payout (the net profit per unit staked, so 35 for a 35-to-1 bet, not counting your returned stake) and derives three related figures: the house edge, the return to player (RTP) — the inverse of the edge, showing how much of each wagered unit is returned on average — and the expected value (EV) of a 100-unit bet. These are standard statistical measures used in probability theory and game analysis to compare the relative cost of different bets or games, independent of any particular outcome.

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Comments (1)

  • Editorial team

    Comparing variants of one game is where this tool shows its value. A single-number bet at 35 to 1 with a 1 in 37 chance (2.7027 percent) has a 2.70 percent edge, while the same payout with a 1 in 38 chance (2.6316 percent) has a 5.26 percent edge, which is the difference between single-zero and double-zero wheels. A lower edge costs less over many bets, but it never predicts one session. Which bet or game are you comparing?

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