You have a standard pack of 52 playing cards. You then shuffle them and begin to draw out cards until you have three of a kind. What is the most likely number of cards drawn when this happens?

You then shuffle another pack of 52 playing cards into the pile. What happens to the expected number of cards now? (i.e. does it double / halve / stay the same?)

(In reply to re: simulation by SilverKnight)

BTW,

Here is the cumulative probability (based on Charlie's simulation results)

And this shows that not only is the mode 14, but that it is not until the 14th card that we can expect (cumulative probability > 50%) to have a three-of-a-kind.

I look forward to seeing if my prediction is true.
_______________________________

01 0.000000
02 0.000000
03 0.002386
04 0.009395
05 0.022948
06 0.044750
07 0.076799
08 0.119865
09 0.174715
10 0.240610
11 0.316328
12 0.400820
13 0.489729
14 0.580381
15 0.668071
16 0.749315
17 0.820684
18 0.879594
19 0.924547
20 0.956844
21 0.977930
22 0.990159
23 0.996353
24 0.998885
25 0.999752
26 0.999968
27 1.000000
Edited on November 19, 2003, 5:03 pm

Posted by SilverKnight on 2003-11-19 17:00:34