Imagine poker where, when all players end up all in, they win a percentage of the pot equivalent to their percent chance of winning the hand. "Running it twice" taken to the mathematical extreme. "Want to run it a billion times?"
I could see that being a strange mode in a computer or console game, but obviously not practical (and maybe not that interesting) in real life. A fun idea, though. There's no gambling on an all in, you get exactly the slice you deserve.
Could it be taken to a further extreme? You divide it up based on each street...If you bet $10 with AA preflop, and I call with 99, you get 80% of that $20 if we see a showdown. If the flop comes 972 rainbow and I move in for $50 and you call, I get 91% of the $100 and you get 9%.
Would people make bad calls just to see showdowns because they know they get *something* back if they call (barring drawing dead), and nothing back if they fold?
Just a random thought to share.