So in this instance I have a standard deck of 52 cards and am playing a high/low game with it (ie turn over the top card, guess if the next card is higher or lower) and maintain a record of all the cards used.
Each guess has an easily calculable chance of being either higher or lower. IE if you draw an 8 for a first cards it's 50% chance that it's higher, and 50% chance that it's lower and a ~5% chance it's another 8 which counts as a "win" regardless of your choice of high or low.
What I don't know how to calculate:
The odds that you will successfully win this game getting all 51 guesses correct strictly guessing the most probable choice.
Any solution I come up with would be different for every game and relies on the cards already drawn. I want to know this probability before even starting a game.
Edit: Additional info:
- Suits don't matter
- Ties are wins.
- Aces are high