Mark, you may have missed the point. You are so convinced that previous results have no bearing on future results. try this on for size.

Three identical boxes with lids, with a ten dollar note placed in one of the boxes. Odds of picking the box with the ten dollar note? 3/1? I know which box contains the note. You choose which box you think has the note. After you have chosen, I open the lid of another box, one of the remaining two boxes .... that box will always be empty (remember I know which box has the ten dollar note). I now offer you the chance to stay with your first choice (3/1?) or to switch your choice. What do you do and why would you do it?

This may demonstrate the rigidity of your thoughts.