Deal Or No Deal

Wikipedia:

”Deal or No Deal is the United Kingdom version of the Endemol game show, which began airing on Channel 4 on October 31, 2005. It is presented by Noel Edmonds and normally airs from 4.15pm to 5.00pm on weekdays and early on Saturday evenings in a varying time slot, usually lasting 45 minutes and very occasionally an hour.

Wikipedia:

At the start of each episode, one of the 22 contestants, each standing behind one of the red boxes is selected to be that episode's player. The selection appears to be random, though this is never stated and in fact selection is done by the production team (indeed, by 2007 it was being explicitly mentioned on the programme that contestant selection was non-random). In any case, the contestants themselves do not know who is to take the seat until it is revealed at the beginning of the show. They then take their box and walk to the centre of the set, taking their place at the main table, in what Noel often refers to as the "crazy chair". Once sat down the player introduces themselves, and after confirming that they selected their box at random, the game begins.

The player's box contains their (potential) prize. One at a time, the player chooses one of the 21 boxes remaining (other than their own) to be opened, eliminating the value inside it from the list of possible amounts in the player's box (displayed on a large screen opposite them). Clearly it is in the player's interest to uncover smaller amounts of money, hoping that their prize is a larger amount. Boxes are opened by the remaining 21 contestants; these contestants are also regularly spoken to by the host and offer support and advice to the player, though they play no active role in the game. These contestants, however, return for the following episode, along with a new contestant replacing the previous episode's player, so that all contestants eventually play the game, and the returning contestants build continuity between shows.

There are six rounds: in the opening round the player opens five boxes, then three in each subsequent round. After the required number of boxes have been opened in a round, the Banker (an unseen character who acts as the player's antagonist and whose money is notionally at stake in the game) offers to buy the player's box. The specific offer is made dependent on the remaining box values: if several larger amounts are gone, the offer is likely to be low, as the probability is higher that the player's box contains a small amount of money. Occasionally, the first offer (or on very rare occasions a later offer) has been replaced by an offer to the contestant to swap their box for one of the remaining unopened boxes. The Banker is never seen, relaying his offers to the presenter via telephone. The presenter tells the player the offer and asks the eponymous question. The player responds either "deal" or "no deal".

Responding "deal" means that the contestant agrees to sell the box for the amount of money offered, relinquishing the prize in their box. The game is now over, though play continues to show the hypothetical outcome had the player not dealt. Saying "no deal" means the player keeps their box, and proceeds to the next round, again hoping to reveal small amounts in the remaining boxes.

After six rounds, only two boxes remain. If the player rejects the final offer, they take the prize contained in their box (though often before the prize is revealed, the Banker offers the opportunity for the player to swap their box with the other remaining unopened box and take the prize contained in it instead).