Okay, I think I managed to make at least the case C1-C2 intuitive with a Venn-type drawing:
(edit: originally did not use spades for C1)
The left half is C1, the right one is C2. In C1 we actually exclude both some winning ‘worlds’ and some losing worlds, while C2 only excludes losing worlds. However due to symmetry reasons that I find hard to describe in words, but which are obvious in the diagrams, C1 is clearly advantageous and has a much better winning/loosing ratio.
(note that the ‘true’ Venn diagram would need to be higher dimensional so that one can have e.g. aces of hearts and clubs without also having the other two. But thanks to the symmetry, the drawing should still lead to the right conclusions.)
I think your left diagram is correct but the one for C2 is off somewhat. In both, we’re conditioning on the statement that “you have an ace of spades”, so we’re exclusively looking in that top circle. Both C1 and C2 have the same exact grey shaded area. But in C2, some of the green shaded region inside that circle is also missing: the cases where you have an ace of spades but I happened to tell you about one of the other aces instead. So C2 is a subset of C1 (condition on being told you have the ace of spades) where only a randomly selected subset of the winning hands are chosen (1/2 of the ones with two aces, 1⁄3 of the ones with three, etc).
But that correction doesn’t really change much since your diagram is just the combination of four disjoint diagrams, one for each of the suits. So the ratio of grey to green is right, but I find it harder to compare to C1.
Either way, my main point was that C2 might have been driving our intuition that C=B, and in fact, C2=B, so our intuitions isn‘t doing too bad.
Okay, I think I managed to make at least the case C1-C2 intuitive with a Venn-type drawing:
(edit: originally did not use spades for C1)
The left half is C1, the right one is C2. In C1 we actually exclude both some winning ‘worlds’ and some losing worlds, while C2 only excludes losing worlds.
However due to symmetry reasons that I find hard to describe in words, but which are obvious in the diagrams, C1 is clearly advantageous and has a much better winning/loosing ratio.
(note that the ‘true’ Venn diagram would need to be higher dimensional so that one can have e.g. aces of hearts and clubs without also having the other two. But thanks to the symmetry, the drawing should still lead to the right conclusions.)
I think your left diagram is correct but the one for C2 is off somewhat. In both, we’re conditioning on the statement that “you have an ace of spades”, so we’re exclusively looking in that top circle. Both C1 and C2 have the same exact grey shaded area. But in C2, some of the green shaded region inside that circle is also missing: the cases where you have an ace of spades but I happened to tell you about one of the other aces instead. So C2 is a subset of C1 (condition on being told you have the ace of spades) where only a randomly selected subset of the winning hands are chosen (1/2 of the ones with two aces, 1⁄3 of the ones with three, etc).
But that correction doesn’t really change much since your diagram is just the combination of four disjoint diagrams, one for each of the suits. So the ratio of grey to green is right, but I find it harder to compare to C1.
Either way, my main point was that C2 might have been driving our intuition that C=B, and in fact, C2=B, so our intuitions isn‘t doing too bad.
oh.., right—it seems I actually drew B instead of C2. Here is the corrected C2 diagram:
Beautiful! That’s also a nice demonstration of B=C2.