Methodology

How the probabilities, payouts and house-edge figures on this site are derived, and which assumptions each one carries.

House edge, defined

The house edge is the expected loss per unit wagered, expressed as a percentage:

edge = −(expected value of the bet) / (amount wagered)

A pass line bet in craps wins 244 times out of 495 resolutions. Expected value per $1:

(244/495 × +1) + (251/495 × −1) = −7/495 = −0.01414

So the house edge is 1.41%. Every figure on this site is built the same way — enumerate the outcomes, weight by probability, sum.

Edge per bet vs edge per resolution

These differ, and the difference is routinely abused in marketing.

A craps place bet on 6 is resolved on average every 3.27 rolls. A pass line bet with odds behind it ties up more money than the flat bet alone. Quoting “edge per roll” instead of “edge per resolved bet” makes a bad bet look better. Unless a page says otherwise, every figure here is per unit wagered on that bet, per resolution. Where the distinction matters we give both.

What “element of risk” means

For bets where you may be required to wager more after the initial bet — Three Card Poker, Caribbean Stud, Let It Ride — two figures exist:

• House edge: expected loss ÷ the original ante.
• Element of risk: expected loss ÷ the average total amount actually at risk.

Three Card Poker’s ante-play is 3.37% by house edge and 2.01% by element of risk. Neither is wrong; they answer different questions. We label which one we are quoting.

Blackjack figures

Blackjack cannot be solved in closed form because the composition of the remaining deck changes as cards are dealt. Published basic-strategy edges come from combinatorial analysis or large simulations. Unless stated otherwise, blackjack numbers here assume:

• 6 decks, dealt from a shoe, reshuffled at the cut card
• Dealer stands on soft 17 (S17)
• Doubling permitted on any two cards
• Double after split permitted (DAS)
• Split to four hands; aces split once, one card each
• No surrender
• Blackjack pays 3:2
• Player uses correct basic strategy, no card counting

That game is about 0.43%. The rule-variation table gives the adjustment for every common deviation.

Video poker figures

Video poker is fully solvable: 2,598,960 possible deals, 32 discard choices each, one optimal play per hand. Published return figures assume optimal play of that specific pay table. Expert human play typically gives up 0.1–0.5% against the theoretical optimum.

Slot figures

We publish slot RTP only where a manufacturer or regulator has published it. Individual slot titles are frequently shipped in multiple RTP configurations, and the operator chooses which one to run. A number found on a review site is not evidence of the setting on the machine in front of you.

Rounding

Percentages are given to two decimal places where the underlying figure is exact, and to one where it depends on rule assumptions. Payout odds are given as they appear on the felt (“35:1”, “7:6”) rather than converted, since that is what you will read at the table.

Sources

Primary derivations are our own, done from first principles and checked against published combinatorial analyses. Where a figure originates in a standard reference — Griffin’s Theory of Blackjack, published regulatory return reports, manufacturer pay tables — it is cited on the page that uses it.