LCHIEN
The Monty Hall question made me think of this:
In the popular program deal or no deal, there are twenty or so boxes, each has a number inside ranging up to the top prize.
The values are usually usually roughly exponentially distributed
so there'll be like 1,2, 5, 10, 20, 50, 100... 100,000, 200,000, 500,000, 1,000,000 among them.
The play goes like this - you choose your box and set it aside, one of 20 to start with. The value inside is what you'll get at the end if you make no deal.
Then you eliminate boxes, point them out and they show you the value inside and tick them off the wall chart of values, showing only the values left (one of which is in your box).
Every few choices, the "banker" has the host make a buyout offer.
As long as you have a few 1, 2, 5 10 ... 100 values you stand the chance of being stiffed. But if there's 250,000, 500,000 or 1,000,000 left on the board you stand a chnce of really making out. The banker offers a value between the
bottom number and the top number left. The whole drama of the show is the contestant picking numbers and hoping to find only small values leaving the chance for a big value in is box. And, the banker making offers that get bigger or smaller as there are more or fewer big numbers left.
The contestant tries to decide whether the offer is good, or whether their luck will be good. At some point they may get offered $80,000 buyout, they turn it down, and on the next few picks they turn up the boxes containing 200,000 and 500,000 and suddenly the offer drops to $40,000
Few people make it to get what is in their box. When faced with 3 or four boxes, two with 100 and 500 and one with 5000, and one with 100,000, they usually "make a deal" and take an offer of, say $24,000.
There's a simple way of statistically valuing the offer. The statistical value of the players worth is the odds of winning each value times the value.
So of there are five numbers left, say 100, 500, 10,000 & 200,000, the statistical value is 1/5 of 100 + 1/5 of 200, etc. or 1/5 of the sum.
Therefore 1/5 of 210,600 or around 42,120.
You could just add the top values (say the ones in the right hand column, they show two colums on the TV, usually the right hand column has values of 10,000 or more) and divide by the total number of boxes remaining.
The banker's offers vary widely from what I've calculated to be a fair statistical value, but the players never seem to be able to figure out if they're offered a good deal or not.
In the popular program deal or no deal, there are twenty or so boxes, each has a number inside ranging up to the top prize.
The values are usually usually roughly exponentially distributed
so there'll be like 1,2, 5, 10, 20, 50, 100... 100,000, 200,000, 500,000, 1,000,000 among them.
The play goes like this - you choose your box and set it aside, one of 20 to start with. The value inside is what you'll get at the end if you make no deal.
Then you eliminate boxes, point them out and they show you the value inside and tick them off the wall chart of values, showing only the values left (one of which is in your box).
Every few choices, the "banker" has the host make a buyout offer.
As long as you have a few 1, 2, 5 10 ... 100 values you stand the chance of being stiffed. But if there's 250,000, 500,000 or 1,000,000 left on the board you stand a chnce of really making out. The banker offers a value between the
bottom number and the top number left. The whole drama of the show is the contestant picking numbers and hoping to find only small values leaving the chance for a big value in is box. And, the banker making offers that get bigger or smaller as there are more or fewer big numbers left.
The contestant tries to decide whether the offer is good, or whether their luck will be good. At some point they may get offered $80,000 buyout, they turn it down, and on the next few picks they turn up the boxes containing 200,000 and 500,000 and suddenly the offer drops to $40,000
Few people make it to get what is in their box. When faced with 3 or four boxes, two with 100 and 500 and one with 5000, and one with 100,000, they usually "make a deal" and take an offer of, say $24,000.
There's a simple way of statistically valuing the offer. The statistical value of the players worth is the odds of winning each value times the value.
So of there are five numbers left, say 100, 500, 10,000 & 200,000, the statistical value is 1/5 of 100 + 1/5 of 200, etc. or 1/5 of the sum.
Therefore 1/5 of 210,600 or around 42,120.
You could just add the top values (say the ones in the right hand column, they show two colums on the TV, usually the right hand column has values of 10,000 or more) and divide by the total number of boxes remaining.
The banker's offers vary widely from what I've calculated to be a fair statistical value, but the players never seem to be able to figure out if they're offered a good deal or not.
Loring in Katy, TX USA
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