[MrGrob]

By this logic, if you have MADE 19 flushes in a row, and start with a 4 flush now, you should fold, as the odds of making this one (the 20th in a row) is going to be much less.

This is just wrong. You mistake comes from take into account information THAT HAS HAPPENED and applying it to a situation that is not relying on this same information.

Let me explain. If you were to say that it is going to be highly unlikely that I will miss 20 flushes in a row, I would say you are correct. The chances of me starting to draw to flushes NOW and missing 20 in a row is small. HOWEVER, once I already missed 19 flushes, the odds of missing 19 flushes in a row has already been reached. YOU ARE ALREADY at the freakish point for the odds. HOWEVER, these odds don't somehow add or influence the next flush draw, as that is going to be the same as the 1st. Since you have already reached the freak-of-the-odds point in missing 19, missing 20 is now the SAME AS MISSING 1, as there is ONLY 1 flush draw to go.

So, yes, missing 20 flushes IS HIGHLY UNLIKELY...FROM THE START...but once you have ALREADY MISSED 19 etc, the NEXT is not more likely to hit or miss then if you looked at missing only 1 flush draw...as this is only 1 flush draw. The freak of the odds has passed ALREADY, so the odds are not long NOW...they were already long and have already gotten there.

Make sense? The HISTORY of missed flushes, the long odds, have already been covered...it is not likely that it will, but once it happens, it has happened...the next flush doesn't know or does it care that 19 have missed...it is just the odds of making or missing 1.

I see how you are looking at it, but it is not right...I hope the above make sense....