Interestingly, I didn't realize modern slot machines were programmed to change their odds depending on previous outcomes. Are you sure? That doesn't even really sound legal. I don't actually have much experience with them and was basing my hypothetical scenario on old-school mechanical slot machines, assuming they worked like that at some point. In any case, I'll stick with hypothetical, perfectly-balanced dice for any further analogies.

Unless I've been misunderstanding how a computer solves a block/share, it's not a solution in the same way a human would sit down and solve a differential equation by methodically working through it. Rather the computer just spams thousands to millions of potential answers until one works. This is were it is like throwing dice.

If you throw an endless stream of dice over and over again into a box and you get one point for every 6 that comes up, you will get one point on average every six rolls. This is actually very different from saying that you should expect every sixth roll to be a six. The actual sequence of rolls is random, but due to the six equally probable outcomes of each roll you should expect that in a large set, 6 will account for 1/6 of the total number of rolls (as would every other individual number). If I decide to swap your box every few seconds, it shouldn't matter. Sometimes a box will go by without you rolling a six, other times you'll roll one, two or more sixes into a given box and it will still average out to 1/6. If I swap the boxes even faster, it still doesn't change your chances on each individual roll. Unless you roll a six as I'm switching the box and it hits the side instead of going in, which I suppose is a rejected share in this analogy.