Portfolio Type II -- Modelling Probabilities in Games of Tennis

[elcrep]

Now, i'm finding this question difficult too, but let me share with you what I've worked out for myself.

If the game reaches deuce, both Adam and Ben will have had to have scored 3 points each (15, 30, 40).

This can be AAABBB, ABABAB, BBBAAA etc.

Therefore we must work out the probability that the game reaches deuce, which i think is 6C3 (2/3)^3 (1/3)^3

Once at deuce, one of the players must win by two points, if they are to win at all (advantage, win). This means that if adam wins, the last two points will have to be won by adam. In theory, the game could go on forever.

Lets take the probability that Adam wins the deuce:

The first scenario could be

AA (in which Adam wins the advantage, and then the final point, winning the game.) The probability of this happening is (2/3)*(2/3) = (2*3)^2

The next scenario could be

ABAA (2/3)*(1/3)*(2/3)*(2/3)

or

BAAA (1/3)*(2/3)*(2/3)*(2/3)

Therefore the probability of Adam winning is the sum to infinity of this geometric progression, where u1 is (2/3)^2 and r is (4/9)

basically i worked out that the probability of Adam winning the deuce is 4/5 (and consequently Ben winning the deuce is 1/5)

But i dont know where to go from there.

[moneyfaery]

There are a ton of other threads about this - check them first. I think you'll find them to be really helpful.

[LinuxBeta]

You're approaching the problem somewhat awkwardly.

Divide this question into three parts: probability that Adam wins without deuce being called (you calculated this in non-extended games), the probability that deuce is called and the probability that Adam wins when deuce is called.

The only thing that you don't have yet is the third possibility. What you are trying to calculate is not how often Adam wins if deuce is called, but the probability of him winning if deuce is called (I can't say any more, or I'll give it away. If you're on the right track, you'll get it).

[MP9]

Ok, so I'm stuck at #5 as well.. And i'm getting kind of desperate. Could someone help me? I'd just need to know if you get actually the 6/7 probability (the exact amount, I mean)? Because the indications say "prove that the prob. is almost 6:1". And I've gotten so many results, including the 4/5 someone mentioned before and I really don't know what I did right/wrong haha. I'd appreciate some help to get me on the right track, thanks!

Edited September 22, 2010 by MP9

[harshil12345]

can we start at the beginning of this IA... im just a bit confused to start

lol i just finished this last wednesday...good luck with it. I admit it's confusing at first, but if you review your probability you'll be fine later on. Don't think too complex, i realized that the solution was often easier than I perceived it to be...lol (wasted alot of brain cells for nothing T_T)

hey do u mind sending me a copy of ur portfolio to ********** (PM me)

Thanks appreciate it.

---

I just finished this at 3:00 a.m. Eastern US time. Very straightforward, and I thought rather easy for a Type II. Make sure to get the formula for deuce correct in the final stages, as that is where many of my friends messed up. I think it looks a lot better to the scorer when you put your n C r in terms of Y, instead of listing the exact numbers everytime or just putting n or r. Also, realize that to win a game, the person !must! win the last point, so you do not need to factor that into your calculations.

hey do u mind sending me a copy of ur portfolio to ********** (PM me)

Thanks appreciate it.

Edited March 27, 2011 by Desy ♫
do not publish your email address in the forum!