Twin Rivers

How to play

1. Set your entry and start the round. You are given a grid of numbers taken from the pool.
2. Numbers are drawn one at a time. Nothing is marked for you.
3. When a drawn number is on your grid, tap it. A number stays claimable only while it is still on the recent strip; once it scrolls off, that number is missed for good and the counter records it.
4. Complete the named pattern before the draw limit runs out and the round pays the published multiple. Reach the limit without completing it and the round ends.
5. Pause stops the draw if you need a moment. The pattern, the pool, the limit and the multiple are all printed on the board before you start.

The rules

You hold a grid of numbers taken from the pool. Numbers are drawn one at a time and marked automatically. Complete the named pattern before the draw limit is reached and the round scores; reach the limit without completing it and the round ends. Every board publishes its pool size, its grid, its pattern and its limit before you start.

If this is your first board

Take a single-line board first, with a generous limit. Watch the "left" counter rather than the grid: it tells you whether the pattern is still reachable long before the grid does, and reading it correctly is most of the skill this family offers.

Pay table

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

The formula

The maths behind it

This is sampling without replacement, so the probabilities shift with every draw: after k numbers are gone from a pool of P, the next one comes from P − k. A board that needs one full line of five from a pool of 75 within 30 draws is a very different question from one that needs all twenty-five. The draw limit is what makes the format a game rather than a wait, and it is the number to check first on any board.

Where it comes from

Drawing numbered tokens from a container against a grid held by each participant is one of the oldest group formats there is, and it survived because the rules fit on a postcard. Its use as a teaching tool is nearly as old: a room full of grids being marked at the same time is a live demonstration of sampling without replacement, and everyone in the room can see the pool shrinking.

If this is your first board

Take a single-line board first, with a generous limit. Watch the "left" counter rather than the grid: it tells you whether the pattern is still reachable long before the grid does, and reading it correctly is most of the skill this family offers.