Push-Your-Luck Stopping Calculator
Roll again and you add the face to this turn's pot; roll the busting face and the pot is gone. Everybody has a feel for when to stop, and the feel is usually wrong. With an ordinary six-sided die and the one busting, the answer is twenty: the average gain of a roll, divided by the chance of losing everything, is exactly where the two balance.
What this generator does
Works out, for every possible stopping point, how many points a turn is worth on average when played that way, and reports the point that does best.
How to use this tool
- Choose how many sides the die has.
- Choose which face wipes out the turn.
- Read the pot at which you should stop.
- Scan the table to see how flat it is near the top — being a couple out costs very little.
Understanding the controls
- Sides on the die
- Two to twenty. A bigger die gains more per roll and busts less often, so you should push further.
- The face that wipes the turn
- Usually the one. Choosing a higher face both removes a bigger gain and keeps the same risk, which pulls the answer down.
Common use cases
- Playing a push-your-luck dice game well
- Settling an argument about when to bank
- Designing a game and choosing a die that makes turns interesting
- Teaching expected value where the answer is counter-intuitive
- Comparing how the answer moves as the die changes
How this generator works
The value of a turn is worked out backwards from a full pot, so each figure is exact rather than sampled. It is then checked two ways: no other stopping point does better, and the answer agrees with the short argument — the average gain divided by the chance of busting — which it should, since that is the balance point.
Randomness and fairness
Nothing is random. The die is never actually rolled here; the whole answer comes from working the turn out backwards.
For how randomness is produced across the whole site, see how Generate Random works.
Limitations and good to know
- It maximises points per turn, not the chance of winning a race. Behind near the end, you should push much further than this says.
- One die at a time. Games that roll several and bust on particular combinations behave differently.
- Rules that lock in points, or bust only on a repeat, are not modelled.
- The calculation carries the pot one roll past the balance point and no further, which is enough for every die offered here; pots beyond that are not tabulated.
Privacy and your data
Everything is worked out in your browser and no figure is transmitted or stored; what is measured is that the tool was used.
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- Expected Value CalculatorThe long-run average of a set of weighted outcomes, with the variance beside it — and a note when the average is a result you can never get.