The Basics of Modified Deal or No Deal:
There are ten boxes labeled 1 through 10.
The boxes have a check in them worth from .01 to 10,000,000 dollars as such $.01, $.10, $1.00, $10.00, $100.00, $1000.00, $10,000, $100,000, $1,000,000, and $10,000,000).
The amounts are randomly placed in the marked boxes.
The player first selects their chosen box.
The game proceeds as folllows:
Round 1:
The player select 2 boxes to be revealed
--An offer is made to the player, if the player agrees, the game is over.
Round 2:
if not- the player selects 2 boxes to be revealed
--An offer is made to the player, if the player agrees, the game is over.
Round 3:
if not- the player selects 2 boxes to be revealed
--An offer is made to the player, if the player selects, the game is over.
Round 4:
if not- the player selects 2 boxes to be revealed
--An offer is made to the player, if the player selects, the game is over.
Round 5:
if not- the player's chosen box is revealed and they take the prize.
The individual making the offer to the player is known as the banker. It is well-known, in this game, that the banker offers 85% below the median of the boxes for the first round and increases that percentage by 5% of the median of the remaining boxes each later round. A player was made the following offers
Round 1: 4,675.00
Round 2: 4,950.00
Round 3: 5,225.00
Round 4: 5,500.00
What boxes were chosen each round?
Should the player take the offer?