Regrettably, I believe that our friend in the frozen tundra (Jogeephus) has given us the answer of "what is the odds of someone rolling the highest maximum roll" (i.e., 1/(1/49))... not "what are the odds of a tie high score, regardless of what that high score rolled" (which is the question the OP posed to the group).
Meaning, since the maximum score is 60 ... the odds are really pretty small (1/(1/49)) that this would occur. What, however, are the odds that there is a tie high score at (say) 51? However, just because you have two people tie at 51 doesn't mean that you won't have someone else score a 52 or higher.
One persons roll is not dependent upon someone else's roll. Meaning, everyone could roll the dice and get two numbers that add together to get a 6. It's not like once a score of 6 is rolled, nobody else can get that score.
So, the answer to your question is actually quite complex ... so ... I ran some numbers for you:
The odds of a 10 and a 60 are identical ... nearly 0%. The odds aren't much greater until you get to a combined score of 24 or 46, in which case, the odds of totaling either one is almost 1%.
To get a 25 or 45 would be 1.4% (approx)
To get a 26 or 44 would be 1.9%
To get a 27 or 43 would be 2.5%
To get a 28 or 42 would be 3.3%
To get a 29 or 41 would be 4.0%
To get a 30 or 40 would be 4.8%
To get a 31 or 39 would be 5.6%
To get a 32 or 38 would be 6.3%
To get a 33 or 37 would be 6.8%
To get a 34 or 36 would be 7.2%
To get a 35 would be 7.3%
So, restated, the odds that any given person would get a 35 for five rolls of two dice each roll is about 7.3%.
Figuring out the odds of a tie at any given number, where there was no higher combined roll is a whole other math problem.
The correct answer: Find an easy tie breaker and/or use the money to buy more beer.
