Ill try to keep it down so we don't wake the others, especially RJ, he gives me the feeling that he can get testy.
I keed, I keed. On a serious note: I have yet to read the above referenced post, which I will, but I felt it nessisary to post a quick reply before I do.
First, it isn't that my math "sucks" as you put it, it is that I don't complicate the issue with it. If I can't perform the simple multiplication required to come to the conclusions that you are arriving at, I deserve to be drawn and quartered. The simple mathematics of the issue at hand are absolutely not the problem. Multiplication, I can handle.
Second, while I concede that your analogy regarding the 9 ball in a billiards game is correct, I fail to see a correlation. I also stated in my previous post that using two points in time such as hand three and hand seven are not the correct way to view the problem. Maybe I didn't express myself eloquently enough, so I will try again.
The odds of being dealt pocket aces are 1/221 on each individual hand. Hand one: 1/221, hand two: 1/221, hand three: 1/221. Now lets take this example; you hit the jackpot and draw AA on hand one. Theoretically (by your estimation) you will have to beat 48,841/1 odds to draw the rockets again. While I completely understand where this logic is coming from, my rebuttal to this is that in order for this statistic to hold up, you have to draw variables for the equation from two completely independent occourances. One being the first hand, which is over and the deck has been randomized since playing it. This randomization of the deck takes the ability to carry the information over from hand one to subsequent hands and nullifies it.
Answer this question for me. You an I buy a new deck of cards and shuffle them until they are randomized, cut them, and play a hand. During this hand one of us gets pocket aces. Since this is my story, I got the aces and busted you down to the felt with them (ha ha). Anyway, after we finish the first hand, you're broke and I won't let you put your car title into the pot because I feel terrible about taking all your
bankroll on the first hand, so we decide to quit and leave the table. We agree that the same time next week, we reconvene and continue the game, same location, same deck, same everything. We return a week later to continue the game and begin just as before. Shuffle the deck, cut the cards, and deal. Lo and behold, again I get dealt the pocket aces. So in effect, for two consecutive hands dealt from the same deck, which hasn't been touched since the previous game, AA was dealt. Are you saying that the odds are 1/48k that this happened or is it 1/221, and why?