If you greed then total income is the sum of E[ (A - B) * Inc ] Where A is your current wave and B is the total waves until this game ends (which is always an unknown entity), and inc is how much you increase on that round, and E is every instance where you increase income. How much gold you get by pushing can only be known when the game is over. Every time you leak you lose money, a fraction of that can be picked up by your allies or the enemy team. Money not gained by leaking is a subtraction either from future income increase or defense, defense representing a loss of future kill gold and income representing a sum. Leaking has a cascading effect. Where A is the wave you get the income at, B is how long the game last, Inc is how much income you increase by that level. But it's more complicated than that, and gold is only a means to an end. The goal is to kill the enemy king, not earn the most gold. Gold merely helps you defend if you spend it on defenses, and greed helps you kill. Pushing wisps might cost you the game, or win it. IMO that's what makes Legion TD so great, because of this complicated strategy.

Not possible. Greed can pay off in some contexts, destroy the team in others. And it matters the degree. To illustrate this, in LTD Mega and Hellhalt, LOD can allow you to push to 7/3 or even 7/5 by wave 5. You will likely leak 5 and 10, maybe 7. But, overall, you will have double inc of others. This will usually pay off so long as the game goes past R5 and past R10. But, if no one on the team holds 5 and 10, you may lose. So, in a sense, it is simultaneously 100% pay-off and 100% loss, just depending.

well the problem is they dont really know what theyre doing. they're building to try and hold even when it wont make a difference. and when they greed to push lumber then they dont really use it. its like the worst of both sides.

His roof belongs to his mom's house

Because it's just a game, mistakes don't matter in the long run as long as they all had fun.