Probablility and The Fundamental Theorem of Poker

[lastcardcharlie]

I'd like to make the following observation on the FTOP.

Probability is to a large extent not a measure of reality as it is but of what one knows about reality. To see this, consider for example if you flip a coin and you can see the outcome and I can't. For me, the probability that the outcome is Heads is 0.5, whereas for you it is either 0 (you know the outcome is Tails) or 1 (you know the outcome is Heads). You and I are talking about the same reality (the outcome of the coin flip) but the respective probabilities of what that outcome is are very different (as you know more than I).

The FTOP seems to be a theorem based on reality as it is (i.e. on how one would act with perfect knowledge of what all the hole cards are) rather than on one's knowledge of reality. But one's knowledge of others' hole cards is usually limited, and the correctness of a decision is surely relative to this limited knowledge rather than to perfect knowledge?

To make a probably-very-unfair comparison, some people have great difficulty understanding that, say, the correctness of a turn bet has absolutely nothing to do with what card actually falls on the river. That e.g. I happen to make my gutshot in a small pot does not in any way mean that my call on the turn was the right thing to do. Thinking it was the right thing to do seems to be a reality-based view (the reality is that the river was favourable and I won the pot and am glad I called the turn) rather than a limited-knowledge-of-reality-based view (the contingency of what the river actually is has nothing to do with the correctness of the turn call).