odds of this

This really happened to me last night, we were playing about 5 handed, for about 5 hours, throught 4 hours of play I got dealt


Q J of Hearts 5 times.......what are the odds of this happening???


5 times yesterday in about 5 hours of play....

Ill let others ellaborate.

The probability of being dealt any specific two card hand is



<PRE>

p = 1/(52*51)



</PRE>

Assume your are dealt 25 hands/hour. That's 125 hands in 5 hours.

The probablilty of seeing the exact same 2 card starting hand exactly 5 times is



<PRE>

P = (125 choose 5)*(p^5)*((1-p)^120))

P = 1.7e-9

= 0.00000017%



</PRE>



It's a wacky world, huh?

certain meaning it already happened, so it is 100% likely that it happened.

The probability of being dealt any specific two card hand is


p = 1/(52*51)


Twice this. There are 52*51/2 different hands since we don't care about the order we got the 2 cards. Also, this assumes we require a particular suit. For any QJ suited there are 4 ways to make it. For a pair of partcular rank there are 6 ways, and for two unsuited cards of particular rank there are 16 ways.

Ambiguous question. Perhaps you mean to ask:


"[A] What's the chances that during my next 150 hands I'll get QhJh at least 5 times?"


"[b] What's the chances that during my next 150 hands I'll get the exact same hand at least 5 times?"


"[C] During my lifetime, what's the chances that I'll EVER get the same hand at least 5 times during a session?"


"[D] During the lifetimes of all 2+2 readers who like to post very noteworthy coincedences, that ANY of them during the 5 years of the web site will EVER get at least the same hand 5 times during the same session?"


- Louie