While your description of Gambler's Fallacy is accurate and apt to the statistics described for share calculation, your choice of slot machines as the example is probably the worst possible choice.  Gambling laws around the world regulate the RTP (Theoretical Payout Percentage) for slots and that is controlled by firmware/software. Las Vegas has a minimum payout of 75% and Atlantic City 83%. The slots are individually tweaked upon setup and are audited.  If they pay too much to the House over thousands of pulls, then the casino is fined.   Also, there is a record kept of each pull, winnings paid, pulls per session (if a casino card is used), etc. These all factor in to the calculations/controls. So yes, slot machines have a memory if you pulled 500 times.

So... There is a "progress" of sorts, because over the course of hours, if there isn't at least one payout at that particular machine up to the threshold established by law, the firmware "forces" a win of a certain amount to meet the ratio of winnings needed. Not pure chance then.

What does this have to do with Middlecoin, Hashrates/shares and difficulty? Nada