A range is not a probability
The remaining Heat range tells you the smallest and largest ordinary Heat still in your crew. It helps show what could fit on the alarm. It does not tell you how often each value appears.
A remaining range of Heat 1–5 could mean one quiet card and many loud ones, or many quiet cards and one loud one. Those decks share endpoints and have different overflow risks.
Start with the room: 18 minus the current alarm. An ordinary card with more Heat than that room busts. A card that brings the alarm to exactly 18 does not.
Count the remaining ordinary cards
For a teaching example, suppose the alarm is 15 and eight ordinary cards remain with Heat values 1, 1, 2, 2, 3, 3, 4 and 5. Three bars fit. The Heat 4 and Heat 5 cards overflow, so two of eight ordinary cards are dangerous: 25%.
That number applies to ordinary-card overflow only. It is not yet the complete next-flip risk, because the Tripwire can appear instead of an ordinary card.
Draws also change the remaining set. As the OpenStax probability discussion explains, taking cards without replacing them changes later probabilities. In a vault, use the cards still unseen, not the original twelve-card percentages.
Add the Tripwire once
Eight ordinary cards remaining means four crew cards have appeared. Under the current normal ramp, the next Tripwire chance at that point is about 7.4%. The complete calculation is:
Tripwire chance + chance of no Tripwire × ordinary-card overflow chance.
For this example, that is about 7.4% + 92.6% × 25%, giving about 30.6% overall. The current interface rounds the total to 31% and the separate Tripwire figure to 7%.
The separate Tripwire number explains part of the total. Adding 31 and 7 to get 38% would count that danger twice. Neither number says that the actual next card has been revealed to you.
Know what one successful flip leaves unresolved
The main next-flip risk concerns your next reveal. It does not automatically describe surviving every later action until you choose to leave. If the rival remains inside, they normally receive the next turn after your successful flip.
The current rival-risk hint estimates Heat overflow after your successful ordinary flip. It averages the ordinary cards that fit; it does not include the rival's Tripwire. Treat it as a partial warning, not their complete bust probability. The rival must also choose to flip for that warning to become relevant. Do not add it to your own percentage and call the result your chance of losing the vault.
Your revealed card changes the alarm the rival faces. A Heat 1 result and a Heat 4 result can both survive your turn while leaving different dangers afterward. A complete future calculation must keep those branches separate.
Use percentages as evidence, not commands
| Number | Useful interpretation | What it does not say |
|---|---|---|
| Heat range | Smallest and largest ordinary Heat left | The frequency of each outcome |
| Total next-flip risk | Tripwire or overflow on your next reveal | Whether taking the risk helps your score |
| Tripwire percentage | The Tripwire's contribution | An extra risk to add again |
A 31% risk can be unnecessary if banking already wins a finished final-vault comparison. It can also be the best remaining chance if leaving guarantees a loss. Read the available bank and the target score before letting a percentage choose for you.
When learning, practice explaining one turn aloud: “Three Heat fits, two ordinary cards overflow, the total already includes the wire, and the rival is still in.” That sentence is worth more than memorizing a table of odds you cannot connect to the current vault.