Games where you repeat an action (or part of an action) until you decide to stop due to increased (or not) risk of losing points or your turn. Press Your Luck games include both Risk Management and Risk Valuation games, in which risk is driven by the game mechanisms and valuing how much other players value what you also want, respectively.
This mechanic is also called push your luck.
Here's a description of the category by Bruno Faidutti:
Double or Quits, Keep going or stop, cash your gains or bet them. The idea is not new. Many gambling games, such as Black Jack, make an intensive use of it, as well as some traditional dice game – and Pass the Pigs is only a modern version of those. This system is also used in many TV games, where the winner can either leave with his gains, either answer one more question at the risk of losing everything he won so far. Like in Luigi Comencini’s Scopone Scientifico, if you never stop, you always end losing. This system is also very efficient in board and cardgames, since it generates a high tension, and some anguish when rolling some more dice or drawing one more card. The best known “double or quits” game is probably Sid Sackson’s Can’t Stop, a clever dice game figuring, in the last edition, mountaineers so impatient to reach the summit that they usually end up falling down. It’s even trickier when all players are aboard the same ship, not knowing if, or when, it will sink. Time to leave or not ? That’s what happen in Aaron Weissblum’s Cloud Nine, as well as in Diamant, a game I designed together with Alan R. Moon.
Here's the introduction of the Jeopardy dice games from Reiner Knizia's Dice Games Properly Explained:
You focus on progessing and maximising your results. But the stakes are rising. If things go wrong, you lose it all. Great risks bring great rewards - or utter defeat!
Disaster strikes in many different ways. More than ever, you need to weigh up the potential gains and losses. Rolling specific numbers or reaching certain totals may catch you out. You see disaster looming - but can you escape? Other games allow you to continue throwing as long as you keep your options open. Know when to stop and secure your results. If you get greedy and your luck fails, you are out. You need to make the right decisions and be lucky, too.
Microbadge: - Fan of Press-Your-Luck Games