Mike,

Congrats to your nephew, that's an impressive resume and set of choices to make.

I don't think #10 is 50/50 at all. But only based on changing variables. If strategy begins at the green and goes back, then I think it's even more determinant what may be the best strategy on any given day. I just don't believe there is ever a situation in golf where there isn't a best way and slightly worse way, and so on and so forth.

Let's go nerd for a minute....( his words)

In general one calculates the number of possible combinations by using the binomial coefficient. (

http://en.wikipedia.org/wiki/Binomial_coefficient). Here n represents the number of "objects" to choose from, and k represents the number of "objects" chosen.

To make par on a par 4 hole, you have to use 4 strokes. Therefore there should be only 1 choice (using 4 strokes).

If one means: How many possibilities of making par or under when starting at the tee, then there are 4 possible outcomes (at least theoretically). You can make the 1st, 2nd, 3rd, or 4th shot. Once you have hit the ball once and do not make it in the hole, you now have 3 possible outcomes: Sinking the ball on the 2nd, 3rd, or 4th shots. This should be pretty intuitive though.

In general it would be interesting to model golf play as a stochastic process. This could be done by sectioning the course into finite elements, each of which has a probability of being reached on the 1st, 2nd, 3rd, etc. shots. Of course the model can become quite complex because the location of the ball after the nth shot is dependent on the previous location of the ball, and so on. Additional complexity can be added if hazards, such as lakes and trees are added. Of course all of this would require observed data to calculate the mean and variance of the shot distance and direction.