probability

[ferrygirl]

I hope some one can help. Two friends Jack & Tom were gambling with coins.The bet was to keep flipping coins...the bet was a total of 20 dollars (10 from jack and 10 from Tom) with winner take all...now if the coin turns out to be heads then Jack get a point and and if the coin turns out to be tails Tom gets a point...the bet was that the first person who gets to 10 points wins the game....

now in the middle of the game Tom had to leave and the score was 8 points for Jack & 7 for tom.Now that we cannot go for the full game, how can we fairly decide on who won the game???

I really hope some one can help.I have been struggling with this

 

[pka]

Many mathematicians cite this type of problem, known as the PROBLEM of POINTS, as the beginning of probability. We know that it dates back to at least the tenth century. It appears in a textbook in 1494. However, no correct solution was found until seventeenth century! It was worked in correspondence between Pascal and Fermat. Both men realized that the solution is in the games that remain to be played.
In your problem, if four more coins were tossed there would definitely be a winner. If all four tosses were made there would 16 possible outcomes. Tom wins in 11 of the 16 and Jack wins in 5. The calculations are done in the following graphic.
So divide the money 11:5 in Tom’s favor.