Monkier, all is forgiven regarding your calculations. Lack of sleep has definitely contributed to many bad calculations for myself. However, I still stick to the impossible story. Let's assume that I lost 15 in a row then won, then 15 more losses and then won and then 17 more losses. At 3-1 odds for me to win each hand even losing 15 in a row is on par with winning 6/49 lottery. I would then have to win the 6/49 two more times in a row.

Take 3 cards (say Q K A) and mix them up. Try to pick the Ace every time. You may get it two or three times in a row. Perhaps even 5 or 6 times in a row and if you are extremely lucky maybe 7 or 8 times but that is it.

And as for each draw being mutually exclusive that's true but it doesn't change the odds overall as every mutually exclusive event has to be achieved to make up the whole and these events have to be done in an exact order. Not even one of the events can be changed or the whole is lost.

In 6/49, after the first ball is drawn, and you have that number it makes sense that you now have a better chance of winning as you only need 5 more numbers but that doesn't change your overall odds. Its still approx 1 in 14 million. 1 in 14 million is not impossible but doing it 3 times in a row is.

Or look at it as you having to walk a mile. After you have walked 400 meters, you only have 1600 meters to go. That's less than a mile. But in the end you have still walked a mile.