For the math folks give me the odds

[spxChrome]

I have to know cause it has happened a few rare times now but what are the odds of going through 4,000 hands with no quads?  I wrote it off the first time but after breaking my record yesterday I have to know the math behind it.  Playing DDB 9/6 I went through about 4,000 hands with no quads

[New2vp]

The probability of the next hand being a non-quad in 9/6 DDB using machine-perfect strategy is 19,885,531,417,860/19,933,230,517,200 = 0.9976070563.  The probability of the next 4000 hands being non-quads is  0.9976070563^4000 = 0.0000688730.To turn any probability p into "odds to 1", use the formula odds = (1 - p) / p.  If you do that here, you get odds of 14518.46807 to 1.It's probably not too much fun to experience this run because this turns the game from an 98.981% game to an 80.415% game (an expected loss of 3917 coins over 4000 plays assuming max coin), or a 78.451% game (loss of 4310 coins) if one was to presume a royal drought at the same time.

[spxChrome]

So if I read this right this should happend only 1 out of 14k visits.  I go about 60/70 times a year and I have been through this cycle now 3 times in the past 4 years.  Do the math on that and lets just see how impossilbe the possible.
 
 

[shadowman]

No, that's not quite right. A new cycle starts after every quad, not every visit.

[New2vp]

I agree with shadowman.  In order to do this calculation, we would need to know how many quads you played.  If you play 4000 hands per visit and had 280 visits in 4 years, we could figure that typical luck would get you 2680 quads.  The odds of having 3 or more strings of 4000 hands with no quads such as you stated with 2680 starting points are about 1095 to 1 against.If you play more hands per visit, then the odds move down; less hands would make the odds move up.

[spxChrome]

Went last night still no change, hit 1 quad (and it was dealt) played around 2,200 hands.  So now Im cold as ice, place that in with my last two sessions.  I have cycled through 16,800 hands only 5 quads two of which were dealt.  Normal numbers should have put me around hitting 36 quads.  I won't even mention how many hands I have played since my last Royal.  I quickly going from  to  and almost at 

[MissElMonte]

Egads! Go someplace else to play!