Expected return & house edge

There are 2,598,960 distinct unordered five-card deals in a 52-card deck. For any one of those deals, a computer can enumerate all 32 holds and every legal draw from each hold. The game’s theoretical return combines those possibilities, assuming the highest-expected-value hold is chosen every time.

For 9/6 Jacks or Better, that configured perfect-play return is 99.54%. In long-run accounting terms, every $100 wagered returns $99.54 on average. It does not mean a player keeps 99.54% of a starting bankroll, wins 99.54% of hands, or loses exactly $0.46 in the next $100 of play.

A return percentage weights outcomes by their sizes. A pair of jacks at five credits returns the five-credit wager and nets zero. A royal returns 4,000 credits. Those two results cannot be treated as two equal “wins,” and neither tells you the game’s average without knowing how often every other result occurs.

This also explains how games with similar returns can feel completely different. One can deliver more of its return through frequent small awards; another can place more of it behind rare premium hands. Expected return describes the center of the distribution, while variance describes its spread.

On a quarter-denomination game, five credits cost $1.25 per hand. After 100 hands, total wagers add up to $125 even though the same balance may have been recycled through many hands. At a 0.46% edge, the theoretical average cost of that action is about $0.58.

Two cautions matter. First, this assumes perfect holds; mistakes add strategy cost. Second, $0.58 is an average across repeated play, not a likely result for one 100-hand session. A royal, a run of full houses, or a long stretch of misses will overwhelm that small expected loss in the short run.

Sharper Edge’s supported returns range from 98.01% for 7/5 Bonus Poker to 99.73% for NSUD Deuces Wild. Every figure is tied to its complete pay table, five-credit royal schedule, and perfect strategy. Progressives, player rewards, unusual feature bets, and non-max wagering are not included.

A player who follows a different strategy has a lower personal expected return. That is the part training can improve. It cannot control the deals, remove the remaining house edge, or turn a long-run average into a promise.