A common situation in Holdem

[Komodo]

We are in a holdem game and hold AKoff .

Flop comes K 2 and 2 rainbow.
The players are pretty loose, so we can assume they play random cards or almost random cards.
How big is the probability that another player is holding a 2?
Heads-up?
Against 2 other players
Against 3 other?
Against 4?
Against 5?
Against 6?
Agaisnt 7?
Against 8?
Against whole table?

[BruceZ]

[ QUOTE ]
We are in a holdem game and hold AKoff .

Flop comes K 2 and 2 rainbow.
The players are pretty loose, so we can assume they play random cards or almost random cards.
How big is the probability that another player is holding a 2?

[/ QUOTE ]

Heads-up?
1 - (45/47 * 44/46)

Against N other players
1 - C(45,2N)/C(47,2N)
= 1 - [(47-2N)/47 * (46-2N)/46]

<font class="small">Code:</font><hr /><pre>
#opponents P(2)

1 8.42%
2 16.47%
3 24.14%
4 31.45%
5 38.39%
6 44.96%
7 51.16%
8 56.98%
9 62.44%
10 67.53%
</pre><hr />

[Komodo]

Thx Bruce