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 while the risk stays the same, 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 pot is capped at eighty for the calculation, which is above any sensible stopping point but does clip extreme settings.
Privacy and your data
Everything is worked out in your browser and nothing is transmitted or stored.
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