2 Pokers in 10 hands - 3 players

[Ivan Basic]

What are the odds of witnessing two pokers in just ten hands ?

So, I've just played 1$ wish blast on 888poker.

I haven't won, but it was a very peculiar tournament...

 

[austral]

Seeing two of those hands in only 10 hands

We use a binomial approximation:

• p = 0.00024 per hand
• n = 10

Probability of exactly 2:

[
\binom{10}{2} p^2 (1 - p)^8
]

Since p is very small:

[
\approx 45 \times (0.00024)^2
]

[
\approx 2.6 \times 10^{-6}
]

0.00026%

Approximately: 1 in 380,000 sessions of 10 hands.