Odds Question?

[FloridaPhil]

Is there any way to calculate the odds of not getting a DDB 4-of-a-kind in a particular number of hands?    Most sources say a 4-of-kind happens every 400 hands or so.  That's an average of about 2 1/2 4-of-kinds in 1000 hands.   I play at about 800 hands an hour.  1000 coins normally lasts me about 2 hours counting bathroom breaks.  If I start with a 1000 coins, play max 5 coins each hand and cash out and keep every 4-of-kind, what's the odds of going home totally broke with nothing? 

[New2vp]

Is there any way to calculate the odds of not getting a DDB 4-of-a-kind in a particular number of hands?    Most sources say a 4-of-kind happens every 400 hands or so.Fairly easy formula (if you have a calculator or spreadsheet that takes numbers to a power).  For 8/5 DDB with computer-perfect strategy, average occurrence of 4 of a kind is 417.55 hands.  Probability of NOT getting quads in "n" hands is (1 - 1/417.55)^n.Hands  Pr(no quads)  Odds to 1 (no quads)  100         78.68%                 0.3 to 1  200         61.91%                 0.6 to 1  289         50.01%                 1.0 to 1  500         30.15%                 2.3 to 11000           9.09%               10.0 to 12000           0.83%             120.0 to 1These are the odds starting out at hand zero.  Of course with independence, you can't say that if you have missed quads on the first thousand hands that you are more due to hit in the next 1000.  At that point you would have another 9% chance to miss quads by the time you play the 2000th hand.   If I start with a 1000 coins, play max 5 coins each
hand and cash out and keep every 4-of-kind, what's the odds of going
home totally broke with nothing? 
Much harder calculation to do and explain.  With 8/5 DDB, you have about an 82.1% chance of hitting quads before going bust, so only 6.5 to 1 odds of going home totally busted; an 86.7% chance of getting quads or better at least once (Here, I assumed that you would also cash and keep straight flushes and royals or leave in the unlikely event of improving your bankroll to 1250 coins withOUT any quads or better--which will happen less than 1 time in 100,000.)With 9/6 DDB, your chance of hitting quads before bust under the same circumstances is 84.1%, 88.8% chance of quads or better, and the odds of going home totally busted would be higher, nearly 8 to 1.

[FloridaPhil]

Thanks for the numbers.  It's rare that I don't get a quad starting with 1,000 coins.   It does happen, but thank God not too often.  My money mangement strategy relies on cashing and and keeping quads, SFs and Royals and I hate going home totally broke.