Definition of a zero sum game

I had a debate with my friend over what the term zero sum game meant. Quite simply, zero sum games means that for someone to win, someone else has to lose. If I gain 100 dollars, someone has to lose 100 dollars.

My friend seems to believe this is about probability, as in zero sum has to be 50/50 odds.

Let's say player A and player B both had $100, meaning there was $200 total in the system. Let's say player A gives player B 2 to 1 odds on their money on a coin flip. so a $20 bet pays $40 for player B. It is still a zero sum game because the gain of $40 to player B means that player A is losing $40 - it has nothing to do with odds. The overall wealth is not increasing, we are only transferring the wealth that is already existing. A non-zero sum game would be a fishing contest, where we could both gain from our starting position of 0, but I could gain more than them, meaning I gain 5, they gain 3, but my gain of 5 didn't take away from their gains at all.

SO my friend is saying I'm wrong, i'm an idiot blah blah blah but then he sobers up and says "You’re using the binary definition, but I’m using a dynamic definition. In the scenario that you lay +200 on a coin flip, value is created through probability. Even though the win and loss is +1/-1 making it 0 sum, my position has created more value than its true probability."

This still does not mean anything - no value is being created. It doesn't matter if you lay +200 on a coin flip because the only value that exists is the value that is being transferred from one person to an other. The net value is unchanged. This is what makes it zero sum.

Is there some kind of "dynamic definition" of zero sum game where my friend is right or is he just wrong or am I wrong?