How the Remaining Cases Shape the Offer
After each case is opened, its amount is removed from the board. The banker’s calculation starts with the values still hidden: add them together and divide by the number of unopened cases. That average is the expected value—the average payout the contestant would receive over many repetitions of the same situation, if every remaining case were equally likely.
For example, a board with a few large prizes and many small ones can have a high expected value even though landing on a large prize is unlikely. The average captures both possibilities; it does not predict which case the contestant actually holds.
Why the Offer Creates a Dilemma
The offer turns that average into a concrete choice: take a guaranteed amount now, or reject it and keep playing. In the game’s standard calculation, the amount on the board—not a banker’s personal impression of the contestant—is the basis for the offer. The offer can be lower than the expected value, so accepting it may mean giving up some mathematical upside in exchange for certainty.
That difference is what makes the choice tense. A contestant who continues is not simply betting on a particular case; they are accepting the chance that the remaining outcomes will produce less than the guaranteed offer. As cases disappear, both the expected value and the spread between the best and worst possible outcomes can change sharply.
The Board, Not the Personality
Because the calculation responds to the amounts still in play, opening a case can alter the next offer even if nothing about the contestant has changed. Reveal a major prize, and the board’s average may fall. Remove a small amount, and the average may rise. The same person can therefore face very different choices from one round to the next.
The banker’s formula gives the drama a measurable hinge: each opened case changes the numbers behind the decision, while the contestant must decide how much certainty is worth.
