3rd street question

[7stud]

whipsaw,

I'm getting slightly different numbers, but the pattern is the same:

1 king up: 13.3%
2 kings up: 17.5%
3 kings up: 13.6%

My methodology:

1)What are the chances that a King up will get another King when two cards are dealt to him from a deck of 44 cards(52 - 8 seen cards):

The chances of getting a King are 1 minus the chances of not getting a King. When the King is dealt two cards in succession from the 44 cards left, what are the chances the King does not catch a King on the first card AND the second card dealt? There are 41 cards out of 44 cards that aren't Kings to start. The chance of the player not getting a King when he is dealt two cards is:

41/44 x 40/43 = .867

So, the chances of getting a King are:

1 - .867 = .133 ==> 13.3%

2) When two players each have a King, what are the chances of at least one of the players getting one or more Kings?

The same as 1 minus the chances of player1 AND player2 not getting a King dealt to them. There are 42 out of 44 cards that aren't Kings to start, and if you deal player1 two cards, and then deal player2 two cards, the chances of both not getting a King is:
<font class="small">Code:</font><hr /><pre>
player1 player2
(42/44 x 41/43) x (40/42 x 39/41) = .825</pre><hr />
So, the chances they get a King are:

1 - .825 = .175 ==&gt; 17.5%

3) More of the same with 3 Kings up. There are 43 cards out of 44 that aren't Kings to start. If each player is dealt two cards in succession, then the chances none of them gets a King are:

<font class="small">Code:</font><hr /><pre>
player1 player2 player3
(43/44 x 42/43) x (41/42 x 40/41) x (39/40 x 38/39) = .864
</pre><hr />
1 - .864 = .136 ==&gt; 13.6%