If a person bets, the probability is1-5/6× 5/6× 5/6 = 91/216.

Two people bet, three people bet, four people bet, five people bet, and everyone's probability of winning is less than 1/2. Sure, you won.

I can explain this formula in detail.

If a person doesn't win, it means that none of the three dice has his pattern. For each dice, the probability of missing is 5/6, the probability of missing all three dice is 5/6×5/6×5/6, and the probability of missing is1-5/6× 5/6× 5/6.

This is from high school. If you are savvy, you should be able to understand.