Common Fallacy in Odds Calculation

I FLOPPED back to back quads starting with a pocket pair eain a money game on Planet Poker a few weeks ago.


I calculated the odds of this happening as follows:


Being dealt 1 pocket pair: 16:1

Flopping quads with that pocket pair: 407:1

Total odds of 1st hand being dealt pocket pair AND flopping quads: 6512:1 (YES, that high!)

2 hands in a row like this: 42,406,144:1


WOW! The event of a LIFETIME!


BUT WAIT! THERE IS A FLAW IN MY ODDS CALCULATIONS! I actually knew what it was before I figured this out, but can you find it? It is a similar flaw used in many calculations and people are always falling victim to it. In fact, I have never heard this flaw mentioned (that I can remember).


Here it is...42,406,144:1 IS NOT the odds for any 2 hands in a row flopping quads in the manner described. It is the odds of the NEXT TWO HANDS flopping quads in this manner. If you have already flopped quads once, the odds of the next hand doing the same in the manner indicated are but 6512:1, since the first event is already in the past.


I am correct in my thinking, but I have never tried expressing my thoughts on this. I know some people will disagree with me, BUT I AM CORRECT. If someone who understands what I am saying would please clarify my explanation, I would appreciate it greatly!