Do you bet more if you're a big winner? I do, but not because
the money is 'free' - it's just that I have a bigger stash to
make additional bets that I think are warranted.
But many will bet recklessly at such times, thinking that it's 'free' money, mattering less if they lose. When you bet recklessly (without careful planning) your chances actually go down. The casinos love it when you do, of course.
Moral: Once those winnings are in your pocket, they're YOURS. If you then choose to bet them, thet's fine, but you're betting YOUR money. Don't forget that, and don't let emotion overpower your money management.
And now, how about the flip-side, 'Throwing good money after bad'?
Look at that poker pot. There's $100 in there, and $80 of it came from your bets. Do you now bet recklessly to 'protect' it. Just as in the first example, your chances will go down. It's just a $100 pot - no matter how it got that way.
Moral: Once it's in the pot, the money is NOT YOURS. Your subsequent bets need to be based on your probabilities and your bankroll, regardless of who built the pot.
Any thoughts, Chalkies?