DART Poster Magenta
DART Poster
Question:
Solution
The Unfinished Game - There are many ways of discussing this.
- Shouldn't they just split the money as the game isnt completed?
- Isn't the leading hand likely to win, so shouldnt he get the money?
- Shouldn't they split it 5 : 2?
The problem is set out as originally expressed. But how about looking at it another way. Suppose the game was to continue and you were to offer to buy one of the hands? How much each they be worth?
That depends on the probability of either hand winning if the game continued.
Imagine the person on "heads" is on 5
and the person on "tails" is on 2
The next throw can be either heads or tails
The person on tails needs to win the next 4 throws in a row. Four tails is only one combination possible out of all the combinations possible over 4 throws.
There are two possible results for each toss (H or T) and for each of these on the following toss there are 2 more possibilities.
So after 4 tosses there should be 2* 2* 2*2 = 16
As only one of these possibilities will give Tails a win the probability for tails is 1/16 and for Heads to win it is 15/16.
So the money should be split in that order!!
The combinations are
HHHH
HHHT
HHTT
HHTH
HTHH
HTHT
HTTH
HTTT
THHH
THHT
THTH
THTT
TTHH
TTHT
TTTH
TTTT Tails Wins!
See
The Monty Hall Conjecture
You should change. When you make your first choice, you have a 1/3 chance. Therefore there's a 2/3 chance that the car is behind one of the other doors. Therefore by changing you move from a 1/3 chance to a 2/3 chance. You wont necessarily win, but you double your chances.
