Is it really risking anything to bet money already won from the house?

The “house money” concept boils down to saying, “All the money I still have invested in X is pure profit I got from investing in X. Thus even if X goes to zero, I'll still be better off than if I never invested in X at all, thus I won't feel too bad about it.”

One could also say:

  1. “All the money I still have invested in X is pure profit I got from investing in Y. Thus even if X goes to zero, I'll still be better off than if I never invested in X or Y at all, thus I won't feel too bad about it.”

  2. “All the money I still have invested in X is money I inherited from my parents. Thus even if X goes to zero, I'll still be better off than if I never inherited anything from my parents at all, thus I won't feel too bad about it.”

  3. “All the money I still have invested in X is money I got from working at my job. Thus even if X goes to zero, I'll still be better off than if I never had a job, thus I won't feel too bad about it.”

It's natural to feel that some money is precious because it was earned through sweat and sacrifice, while other money is not as precious: easy-come-easy-go. But those feelings are irrational in the sense that a dollar buys the same amount of goods and services no matter how you came by it.