So, how would you budget for a game show?
God help me, I'm gonna try this.
If you're a producer, your goal is to get as many of your shows greenlit as you can, because that maximizes the amount of money you can make. Speaking purely in prize budgets (a gross simplification, but the concepts that follow can be extrapolated to the entire production, so why not), there are two things that can kill you: a) underbudgeting and then getting canned prematurely when it's discovered that your show costs more than you represented that it does, and b) overbudgeting and therefore b1) your show doesn't get picked up due to whoever balking at the unnecessary extra cost or b2) you are unable to mount another, potentially more successful show because you have too much of your finite budget tied up unnecessary in this one.
You are assuming the maximum payout every single time, which, while safe, is stupid; as such you are doomed to failure; see b) above.
So the trick is in finding that sweet spot between a) and b), and the way you (should) do that is through LOTS and LOTS and LOTS of research and trials. With enough trials, you should be able to get a decent idea of a) the average payout-per-show and b) how that might fluctuate due to a run of good or bad luck. So if it's me, I then set the budget-per-show at (that average payout) + (a reasonable percentage representative of that fluctuation).
Is that 100% safe? No, but no investment is. But (assuming a constant return) minimizing your investment while maintaining a level of comfortable risk is how you maximize your own ROI. The best producers are the ones who can minimize that "comfortable risk" padding without getting bitten by it over the long run.