Okay, this has been bothering my quite some time now, it might be difficult for me to explain it but please bear with me:
I will be using Martingale negative progression betting system for this example. For those of you who don't know what that is, you don't have to know the specifics but it's a betting system where you keep making steady profit until you encounter a very unlikely event (let's say 1% chance) and you lose all your money. The method is said to be a good "short-term" strategy as the chances of you encountering that event are very slim, but the longer you play the higher the chances of you encountering one. So just for the sake of it, let's say your chances of making profit is 80%, 19% chance of losing some money and 1% chance of losing ALL money per 100 games (thus "a good short term betting strategy"). As the number of games increases, your chances of profiting go down, eventually converging to 0% after infinite amount of games.
Now this is the part that I can't wrap my head around. If you take a LARGE number of games and split them into multiple "short term" sessions with 100 games per session, WHY doesn't that reset your chances back to 80%?
I know the chances are decreasing and odds of you losing are accumulating within each extra game played, but in what manner? Does the decrease follow some kind of pattern or a function (e.g linear decrease)? How does one predict or at least get the idea of when the "short term profitable strategy" starts to become a "long term non-profitable strategy"? Is there such thing as an optimal "mid term" solution, or is it just a concept of my imagination?
My current theory is that each individual betting system follows a specific pattern of your chances decreasing within number of games played, even though it might look like a gold mine in short term. That pattern can be simulated mathematically but given the nature of probability itself, it would be very hard to predict WHEN that strategy is starting to bring you net profits of less than 0. What do you guys think?
I would really appreciate any insights or suggestions you have regarding this topic as it's been bugging me for a while now!