House edge and RTP: what the numbers really mean

Every casino game is built so that the casino keeps a small share of the money bet on it. Two numbers describe that share: RTP and house edge. They are one fact seen from two sides.

This guide explains what the two numbers mean, how to turn them into an amount, and what they cannot tell you. Neither number shows you a way to come out ahead. Both describe what a game costs you on average.

What are RTP and house edge?

RTP stands for return to player. It is the share of all the money bet on a game that the game pays back as winnings, counted over a very large number of bets. It is written as a percentage.

The house edge is the share the game keeps.

The two always add up to 100%, so house edge = 100% − RTP.

• An RTP of 96% is a house edge of 4%.
• An RTP of 99% is a house edge of 1%.
• An RTP of 97.3% is a house edge of 2.7%.

Both numbers are worked out from the rules and payouts of the game. They do not come from what happened to any one player.

Where does the edge come from?

A game pays a little less than the true odds. Roulette shows this clearly. A wheel with one zero has 37 pockets, and a bet on a single number pays 35 to 1.

• Put 1 on every number. You have staked 37.
• One number wins. You get 35 in winnings and your stake of 1 back, which is 36.
• You are down 1 for every 37 you staked. 1 ÷ 37 = 2.70%.

That 2.70% is the house edge. No pocket is rigged. The shortfall sits in the payout.

How do you work out your expected loss?

Your expected loss is the average cost of a stretch of play. It is an expected value: what you would average out at if you played the same session a great many times.

1. Total wagered = average bet × number of bets
2. Expected loss = total wagered × house edge

Here is the example that the house edge calculator opens with. A slot has an RTP of 96%, so its house edge is 4%. You place 500 bets of 2 each.

• Total wagered: 2.00 × 500 = 1,000.00
• Expected loss: 1,000.00 × 4% = 40.00

The amounts have no currency. Use any unit you like, as long as it is the same one throughout.

The same 1,000 wagered costs a different amount at each house edge.

Total wagered is not your deposit

This is the part people miss. Say you sit down with 100 and bet 2 at a time. If your money lasts for 500 bets, you have wagered 1,000. That is ten times what you brought. It is possible because you bet your winnings again, and each of those bets carries the edge too.

So the expected loss in the example is 40 out of the 100 you brought, if your money lasts for all 500 bets, on a game that "pays back 96%".

Why is "RTP 99%" not "I get 99% back tonight"?

There are two reasons.

The percentage applies to each bet, not to your deposit. Start with 100 and bet 1 at a time on a game with an RTP of 99%. After 1,000 bets you have wagered 1,000, and the expected loss is 1,000 × 1% = 10. That is 10% of what you brought, not 1%. After 5,000 bets it is 5,000 × 1% = 50.

The percentage is an average over a huge number of bets. The UK Gambling Commission says this about gaming machines, and the same holds for online games:

The %RTP is an average achieved over a significant number of game plays and not each time the gaming machine is played.

RTP also does not make a game "due". In a game run by a random number generator, each bet stands alone. A run of losses does not make a win more likely. Believing that it does is called the gambler's fallacy.

Why do short sessions vary so much?

RTP tells you the average. It does not tell you how far one session can land from that average. That spread is called variance. For slots, the usual word is volatility.

Take two made-up games. Both have an RTP of 96%.

• Game A wins half the time and pays 1.92 times your bet. 50% × 1.92 = 0.96.
• Game B wins 1 time in 100 and pays 96 times your bet. 1% × 96 = 0.96.

Place 500 bets of 2 on each. The expected loss is 40 on both. The sessions look nothing alike.

On Game A you win about 250 times, and each win returns 3.84. With 250 wins you get 960 back and lose 40. With 235 wins you lose 97.60. With 265 wins you finish 17.60 ahead. Most sessions end somewhere between those two.

On Game B you win 5 times on average, and each win returns 192. With 5 wins you get 960 back and lose 40. With 3 wins you lose 424. With 7 wins you finish 344 ahead. Neither is unusual. Three wins or fewer turns up in about one session in four.

A high-volatility game is like Game B: long runs of losses and a few large wins. Some game providers publish a volatility rating next to the RTP.

Two things follow.

• Volatility does not change the edge. It changes how bumpy the session is, not what it costs on average.
• More play does not win it back. Over more and more bets, the share you have got back moves closer to the RTP. The amount you have lost tends to grow, because the edge is taken from every bet.

Changing your stake from bet to bet does not change the edge either. A system such as the Martingale moves the risk around. It does not remove the cost. See bankroll basics and betting systems.

What is a typical house edge for each game?

These figures are for common versions of each game. The last column says what moves them.

Slots do not have one RTP. A slot can be built with several RTP settings. One provider's own page for a single slot lists four: 96.38%, 94.55%, 92.33% and 88.42%. That is a house edge of 3.62% at the top and 11.58% at the bottom. On 1,000 wagered, the expected loss is 36.20 at the top setting and 115.80 at the bottom one, which is more than three times as much. The casino picks the setting.

Some regulators set a floor. Malta's regulator asks for an RTP of at least 85% from the casinos it licenses, which still allows a house edge of 15%. A casino licensed elsewhere is not bound by that floor.

Blackjack depends on the rules and on you. With generous rules the edge can be as low as about 0.3%. A table that pays 6 to 5 on a blackjack, not 3 to 2, adds about 1.4 percentage points. These figures only hold if you play every hand by basic strategy, which is the worked-out best play for each hand. If you play by feel, the edge is higher.

Baccarat depends on the bet. The figures are for the standard game with eight decks. The tie bet costs more than ten times as much as the banker bet.

A casino's own games have no standard figure. The casino sets the edge on its dice, crash and similar games. Look for it on the game's information page. A provably fair check does not remove it, as how provably fair works explains.

Where do you find a game's RTP?

• Inside the game. Open the information, help or paytable screen. For a slot with several settings, this is where the figure for your casino should be shown.
• On the provider's website. The provider may list the RTP, or all the settings. It cannot tell you which setting your casino chose.
• On the casino's website. For a casino's own games, look for a rules or fairness page.

The UK Gambling Commission requires that information on your chance of winning, such as the RTP or the house edge, is "easily available before the customer commits to gamble". A casino licensed elsewhere may not be under that rule. If you cannot find a figure for a game, you do not know its edge.

How does the edge add up when you clear a bonus?

A bonus usually comes with a wagering requirement: an amount you must bet before you can withdraw. That is a large total wagered by design, and the edge is taken from all of it.

Here is the example that the wagering calculator opens with. You deposit 100 and get a bonus of 100. The terms ask for 35x wagering on the bonus. You play a slot with a house edge of 4%.

• Total to wager: 35 × 100.00 = 3,500.00
• Expected loss: 3,500.00 × 4% = 140.00
• Expected value: 100.00 − 140.00 = −40.00

If you complete all the wagering, this bonus costs you about 40 more on average than it gives you.

It costs more if the game only counts in part. With a game weighting of 50%, each 1 you bet clears only 0.50. You then have to wager 7,000.00, and the expected loss is 7,000.00 × 4% = 280.00.

Wagering requirements explained goes through the terms one by one.

Questions people ask about house edge and RTP