Leading mathematicians (I won't name names here) say that there is no formula for subjective probability (e.g. "I think, there is 20% of tomorrow rain", or "I think that Navier-Stokes conjecture is true with 90% probability"). There is a number and no formula? that's funny and untrue. The subjective probability certainly make no sense in (the usual) probability theory and math statistics, because the (objective) probability (or expected value) by definition are calculated from multiple cases of an event, not from a single event. (So 20% of tomorrow rain makes no sense in probability theory: either no rain (0%) or there is rain (100%). Well, we could define the rain probability tomorrow quantum-mechanically, but that makes no practical sense, because it is too hard to calculate. I created a mathematical framework, where subjective opinions of players are taken into account. So, we have a transition from game theory to players theory. Let’s fix a (probabilistic or not) game (in the sense of game theory) or more generally a probabilistic distribution of games (being in some way “averaged” to be considered as a single game), a hypothesis (a logical statement) a “doubtful” player (a function that makes probabilistic decisions for the game) dependent on boolean variable (called trueness of our hypothesis) for a “side” (e.g. for white or black in chess) of the game. Let’s “factor” the game by restricting the side to only these decisions that the doubtful player can make. The guessed probability is defined as the probability that given (fixed!) player (a probabilistic function that makes decisions for our side of the game) will choose the variant in which our hypothesis is true. A variation of this is when the doubtful player’s input is mediated by a function that takes on input logical statements instead of a boolean value. (The above is easy to rewrite in this case.) More generally guessed probability can be generalized to guessing real number (or any measure space)