This is the push-your-luck family. You roll six dice, set aside the ones that score and face the same question every turn: bank the points, or roll again and risk losing them all. Farkle is the best known name, Ten Thousand the classic target-score version.
Same thrill, smaller doses
The same tension powers simpler games. In Pig one die and one bad roll can wipe your turn, and Drop Dead kills your dice one by one. They make good warm-ups before a full evening of Farkle.
House rules are the rule
No two families play these games quite the same way. The pages here describe the common core and mark the popular variants, so you can agree on a table before the first roll instead of arguing after it.