There is no such thing as house money.
I see the 'house money' fallacy all the time (most commonly in the context of 'take out your initial investment').
Can you explain further, because it sounds weird to me?
The idea is that you shouldn't think "I already have some bitcoins, may as well let them ride" but instead think "Would it be better to have bitcoins or dollars?" And then, whatever your answer and current assets are, reposition yourself so you're consistent with your beliefs.
If you have a bitcoin that you bought for 10 dollars and you hold on to it even though you believe the price will likely fall because you think you'll still be able to sell above 10 dollars, that's a fallacy in the sense that you'd probably make the most money basing your decisions only on what you think is likely to happen and not what the original cost of your assets was.
Saying that the history of your investing shouldn't impact your choices is saying that your total wealth shouldn't affect your choices.
But if I borrowed $100K against my home and it gets foreclosed and I'm homeless, that's very different from if I gambled $100 and got $100K whose loss will be no worse for me than losing the original $100.
A = Bob has $1M in bitcoin.
B = Bob can afford to lose $1M.
It appears to me you think P(B) = P(B|A). I think obviously P(B) < P(B|A).How about:
A = Bob has $1M in bitcoin which he paid $100 for.
B = Bob has $1M in bitcoin which he paid $1M for.
C = Bob can afford to lose $1M.
It appears to me you believe P(C|A) = P(C|B) = P(C). I'd expect P(C|A) > P(C|B).