DeletedUser31308
Using your example, if I knew that I'd have a 75% chance of winning again if I won the prize I wanted and a 75% chance to lose again if I failed to get the prize I wanted, I would only open the chest more than once if I manage to win the first time and I'd stop at my first loss. This is because I'm paying the same amount for each attempt, and some attempts will give me the EV of 0.75 of what I want while the other attempts only give me an EV of 0.25 of what I want. I know your example isn't one you'd actually suggest to be implemented, but my point is as I said: as soon as you make successive trials dependent on one another, it opens the door to abuse.The conditional probabilities in the example are changed by design but the unconditional probabilities don't change. I don't know what you're argument is.
Phrased another way: As soon as the absolute probabilities of individual trials differs, as in your example of sometimes having a 75% to win and other times having a 25% chance to win, there is room for abuse. If a pattern exists, and players figure out what it is based on data analysis, the players will abuse the pattern to avoid the trials with the worse probabilities.