Sphinx Pairs

How to play

1. Set your entry and start the round.
2. On a higher or lower board you see one card and call the next. A correct call moves you a step forward and raises the running multiple; a wrong call ends the round. You may collect at any point, and collecting early is a real option rather than a lack of nerve.
3. On a memory board you turn two cards per move. A matching pair stays face up. Clear every pair inside the move limit and the round scores; run out of moves and it does not.
4. Cards carry numbers in four colour families. There are no face cards and no suits on these boards.

The rules

Cards here carry numbers only, in four colour families, with no faces and no suits. On a higher-or-lower board you see one card and call the next; a correct call advances you a step and grows the running multiplier, a wrong call ends the round. You may collect at any point. On a memory board, turn two cards per move; a matching pair stays face up, and clearing the board within the move limit scores.

If this is your first board

Take the four-by-two memory board first. Eight cards, four pairs, five moves, and every mistake is visible immediately. On higher-or-lower, remember that collecting early is a real choice and usually the mathematically better one: the multiplier grows more slowly than the chance of the chain breaking.

Pay table

Every figure below is computed from this board's own settings, not typed in by hand.

Best play

1. Open a cell you have never seen before as your first card of a move, because a cell you have already seen tells you nothing new.
2. If the first card matches something you have already seen, go straight to that cell as your second card.
3. If it does not, open another cell you have never seen, so that one move buys you two new pieces of information instead of one.
4. Never re-open a pair you have already cleared, and never spend a move confirming something you already know.

The maths behind it

On higher-or-lower with a top card of H, seeing a card of value v makes "higher" correct for (H − v) of the H values and "lower" correct for (v − 1). The best call is whichever side holds more, and against a low card that edge is large. Chaining calls multiplies the probabilities, which is why a five-step chain is far less likely than it feels: five calls at 70% each land together only about one time in six.

Where it comes from

Numbered cards are among the oldest portable randomisers, and the two mechanics here are the two oldest questions you can ask of them. Is the next one bigger or smaller than this one, and can you remember where you saw its twin. Both questions predate any formal theory of probability, and both were used as teaching devices long before they became pastimes.

If this is your first board

Take the four-by-two memory board first. Eight cards, four pairs, five moves, and every mistake is visible immediately. On higher-or-lower, remember that collecting early is a real choice and usually the mathematically better one: the multiplier grows more slowly than the chance of the chain breaking.

Other boards in this family

Open the board Scribe’s Cards