Inner Span

Two markers

Two cards are turned face up. The gap between them is the span, and it is visible before you decide anything.

The one decision

Stake on whether the third card falls inside the span. A wide span is likely and pays little; a narrow one is unlikely and pays more. Matching one of the two markers exactly settles against you.

Why the span is shown first

Because the whole game is judging a known gap. Hiding it would turn a decision into a guess, and there would be nothing left to learn.

Counting the span

With two markers showing, the cards that fall inside are simply the ranks between them, times four suits, out of the fifty remaining cards. The arithmetic is short enough to do in your head.

Why the margin is 3.55 percent

The rewards for each span width are set slightly below their true odds, and the exact-match rule takes a small extra slice. Together they come to 3.55 percent across the whole spread of spans.

Why cards are different

A grid draws afresh every round. A deck does not: every card that has already appeared changes what is left, so the odds move while the hand is in progress. That is the only family here where what you have seen tells you something.

Order of play is the whole game

In most card games the house acts last and knows more when it acts. The rules that look arbitrary — draw to sixteen, fold below a threshold, act before the fifth card — are all attempts to price that asymmetry.

Where the margin lives

A well-played card game has one of the narrowest margins anywhere: a fraction of a percent. Played carelessly, the same game can cost ten times that. The gap between the two numbers is the value of knowing the rule.

A caution about systems

Doubling after a loss does not change any game's margin. It changes the shape of the loss — many small wins and one very large loss — and the total expected result stays exactly where it was.