How the Banker’s offer is calculated
The exact Banker formula used on dond.win: offer = discount factor × average of the remaining prizes × buy-in. The factor rises linearly from the first open to the 23rd. Worked examples and the live parameters.
The formula
On the TV show the Banker is a character and the offers are a mix of maths and drama. On dond.win the Banker is a published function:
offer = k(opened) × mean(remaining prizes) × buy-in
- mean(remaining prizes) is the plain average of the multipliers still on the board, including the one in your sealed case.
- k(opened) is a discount factor that depends only on how many cases you have opened. It starts at a base value on the first open and rises in a straight line to a cap on the 23rd open, which is the last open that produces an offer. At the time of writing the base is 0.5 and the cap is 0.9. The live values are at /api/rules as offerKBase and offerKCap.
In symbols, with 25 cases: k(n) = base + (cap − base) × (n − 1) / 22, for n from 1 to 23.
Worked examples
| Opened | k (base 0.5, cap 0.9) | Mean of remaining | Offer (buy-in 10) |
|---|---|---|---|
| 1 | 0.50 | 1.50× | 7.50 |
| 6 | 0.59 | 1.30× | 7.67 |
| 12 | 0.70 | 1.80× | 12.60 |
| 18 | 0.81 | 2.20× | 17.82 |
| 23 | 0.90 | 5.50× (two cases: 1× and 10×) | 49.50 |
The means in the table are illustrative; yours depend on which prizes you have opened.
Why the offer goes up even when the board gets worse
Two things move the offer: the mean of what is left, and k. Opening a small prize raises the mean; opening a big prize lowers it. Meanwhile k rises with every open no matter what. In the early game k dominates, so offers tend to climb. In the late game the board dominates, and one bad open can knock the offer down hard.
No hidden inputs
The offer does not look at your balance, your history, your deposit size or how often you deal. It uses only the public ladder, the set of opened cases and the two parameters above. You can recompute every offer you were shown from the information on the screen.
Where the house edge lives
The gap between k and 1 is one of the two sources of house edge; the per-open fees are the other. Both are published and both are the same for every player. See Deal or No Deal odds and expected value.
Frequently asked questions
Does the Banker know what is in my case?
No. The offer uses only the average of all prizes still on the board, which includes your case, and the number of cases opened. The layout is committed before you pick and revealed after the round, so it cannot be used by anyone mid-round.
Why is the first Banker offer so low?
Because the discount factor starts at its base value (currently about 0.5) on the first open. You are being offered roughly half of what your case is worth on average. The factor rises with every open.
What is the highest the Banker will ever offer?
At the 23rd open the factor reaches its cap, currently 0.9. The offer is then 90% of the average of the last two cases. The factor never reaches 1, so an offer is never above the fair value of your case.
Can the Banker’s offer change without me opening a case?
No. An offer only changes when you open another case. It stays on the phone until you deal or open.