This is an open-ended question about how Texas Hold'em would be affected by a rule change.
Suppose we have the following scenario:
- Short-stack A goes all-in.
- There are two callers B and C.
- On a later street, possibly after further bets into a side-pot, B folds.
In typical gameplay, B will win nothing, C will win the sidepot, and the strongest hand between A and C will win the main pot.
How would strategy change if B's fold relinquished his claim only to the side-pot, and he was still eligible to win the main pot, say because he has put as much money into the main pot as all other players?
I am interested both in how this would change strategies (for example, I think short stacks lose some power because their all-ins are more likely to be called by players who needn't fear getting blown off the hand in later streets) and in whether there are fundamental principles of poker that this rule change would violate.