Puzzle: Is your Golf Probability up to par?
 

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.

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.

Convoluted yet brief Answer
 

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