Odds for hand sequence

[kennyplayer]

I was at Harrahs last week, and had a wierd
win streak. I want to know the "odds" of this happening

I was playing $1 Double Double bonus poker $5 per hand, after 15 minutes, I hit 4A with kicker (2 card draw) for $2000. 5 minutes later I hit another Natural 4A with kicker for $2000. 15 minutes later I hit another 4A with kicker (2 card draw).

I estimate I played for 1 hour for this session. I am an experienced VP player, and play pretty fast. Other
sites say a reasonable fast player plays 600 hands per hour. I estimate I played 500 hands in this session.

Note that these were hand pay, so I was not playing while waiting for attendant.

So my question is: What are the odds of hitting 4A/k three times in 500 hands?

I have done some reading and found that 4A/k occures approximatly once every 16,000 hands, so I am
calling this 16,000 to 1 odds to get 4A/k on one play.

Since I played 500 hands, I say the odds of hitting one 4A/K in this session is 16,000/500 = 32 to 1

Since I hit three of them, I say the odds are 3*32 = 96 to 1

Does this make sense to anyone? It seems low to me.

[Gronbog]

I haven't checked your 1 in 16,000 number, but assuming it's accurate, then the odds of exactly three 4A/K in 500 hands are(1/16000)^3 x ((1 - 1/16000) ^ 497) x (500 x 499 x 498) = 0.0000294 or one in ~34,006

[Eduardo]

The odds are in in "never" for me. Congrats on an incredible run!

[New2vp]

I haven't checked your 1 in 16,000 number, but assuming it's accurate, then the odds of exactly three 4A/K in 500 hands are(1/16000)^3 x ((1 - 1/16000) ^ 497) x (500 x 499 x 498) = 0.0000294 or one in ~34,006
Hey, G-bog, I give you props for working out the calculation formula longhand rather than just using an Excel spreadsheet binomial distribution formula.You need to check the binomial coefficient, though.  500!/(497! 3!) = (500 x 499 x 498)/(3 x 2 x 1), so the calculation of the probability is off by a factor of 6, making the probability 0.000004901150, odds of 204033 to 1, or 1 chance in 204034, using integers.Whatever the odds, there is more fun in the winning than the "ciphering."

[billryan]

You fellows certainly know your gozintas.

[Tedlark]

Mmm, gozintas.....con queso of course.

Congrats kennyplayer on a very nice little 35 minute run up.

[billryan]

Four gozinta eight twice.

[tech58]

Fine run KP. I often hit one of those in a 2-dayer. Of course my game being JOB,i get to avoid the hand pay "problem".                                                        
                                                     
                                                                                                                           

[sza]

Keep doing it and lose all money back then you will not feel the surprise.