@richy You're absolutely right that we can't calculate the winchance in any non-solved game. In fact, a "position evaluator", an algorithm that would compute the winchance given a gamestate, is impossible even in theory, because winchance depends not only on the gamestate, but also on the mindstates of the player(s).

However, the fact that we can't compute the exact value of winchance doesn't mean that it's useless as a concept ("depth" is another a value that can't be computed in a non-solved game but which is clearly not useless as a concept.) We can still develop hypotheses that provide guidelines about what types of winchance patterns are better or worse, and attempt to build games that conform to those guidelines (imperfectly, of course).

And even though winchance can't be

*computed*, we can have an intuitive sense, as designers and as players, of what the chance of winning is for a given situation. Feeling that you have an advantage over your opponent, for instance, is equivalent to feeling that you have a higher chance of winning they do (and the degree of the feeling of advantage correleates with the degree of the deviation from 50%). And feeling that the game is already decided even though it isn't technically over (i.e. feeling that you are in a foregone conclusion), is equivalent to thinking that the winrate is near 0% or 100%. So even though winchance can't be calculated, it can certainly be approximated (and in fact getting better at a game can be thought of as a process of learning to better approximate winchance, since "good decisions" are just the decisions which lead to higher winchances)

Hopenager, I’m not convinced by the idea that “as the chance of victory gets further from 50% (in either direction), the chance that new actions will change the outcome of the match gets lower”. I think that causal leap is one a bit too wide for me to make. However, I am convinced by my own argument to a similar conclusion, so let’s not dwell on the point.

We might have to dwell, actually, because my reasoning leads to the opposite conclusions on actual vs believed winchance: what matters is that the

*actual* winchance is at 50%, not merely that the player

*believes* that it's at 50%. But before I get to that, I want to say that I doubt that it's possible to hide the truth of winchance from the player, at least for experienced players, given what I said above about getting better at a game really being a process of better approximating winchance.

What I said earlier, "as the chance of victory gets further from 50% (in either direction), the chance that new actions will change the outcome of the match gets lower”, wasn't a great way of explaining my actual position. My bad. A better way of phrasing this is in terms of of feedback efficiency: 50% is the point at which entropy is maximized with respect to performance, or in other words 50% is the point at which a win or loss gives you the most information about your performance. See

this article for a deeper explanation. What this means, in practice, is that when the winchance is at 50%, you get feedback (from the game's end-state, at least) more efficiently than you do at any other winchance.

I am not sure exactly what you're reasoning is for thinking that 50% is ideal if it isn't this. You've said that 50% is the point at which there is "maximum ambiguity", but what exactly do you mean by ambiguity? And why is ambiguity, however you define it, a good property?