Puzzle: Is your Golf Probability up to par?

[jfc]

After the overwhelming Smartgambler response to my AFL Top 8 quiz, here's an encore. Again original, as far I know.

Golfer A only pars, birdies or bogeys holes. With equal likelihood.

His identical twin B is 1 stroke behind A, with H holes to play.

No playoff if they finish equal.

What is the chance of B overtaking A for H = 1, 2 or 3?

Answer only for the highest H you are confident about. That way others unfamiliar with the techniques can still tackle whatever level they find challenging.

[AssumeTheCrown]

1711/6561 for H=4

[jfc]

1711/6561 for H=4

Agreed.

I'm impressed. Because I couldn't find any accepted formula or calculator to ~directly produce the result.

I'll wait to see if there are any takers for other H's before swapping notes.

[jfc]

Time to hit the 19th hole.

Very briefly, the problem is an example of Trinomial Convolution.

It can be easily be solved with a spreadsheet by building a Trinomial Triangle.

Here is such a triangle produced by a pervert who couldn't be bothered making it isosceles.

http://mathworld.wolfram.com/TrinomialTriangle.html