"18000" is just an estimate. It's probably a little conservative. I'd guess the actual number was between 15,000 and 30,000 but I didn't count.Did you actually count, or are you using 18,000 the way that some people (like me) use "bazillion" for a random large number? (This is not intended as a rudely skeptical question, I'm just trying to clarify things.)
When younger I sometimes played solitaire for hours and the longer I played the more likely I was to win. I did my best to shuffle the cards well, but somehow over a series of games (not as many as you played), the cards seemed to become sorted in ways more favorable to winning.
Being a mechanic gives a good understanding of tangible things, but I think we need a mathematician to explain this one!
In this case "mechanic" is a term for a person who performs parlour tricks with cards. Specifically I can shuffle the cards to make them come up in a desired order. I was not "stacking' these that I won. Even if I did it subconsciously it simply wouldn't have much effect on my chances of winning.
"Hospital solitaire is a simple game. You pull cards off the bottom of the deck and spread them in a fan on top one at a time. If the 4th card is the same number as the first all four cards are removed. If it's the same suit then the two cards in between are removed. Go through the entire deck comparing the last card from the bottom to the 4th card back in the fan removing cards the same way. A "win" is when you have no cards at all left.
It "seems" like an easy game to win but is very difficult. My math was never quite good enough to actually compute the odds but I'm guessing it's on the order of 1: 6,000 give or take.