Good post Evo. For the most part, I agree here. I can see the "flatness" in what you are saying but it's really a different definition than what I am saying. It's part of that muddy part.
For this purpose, I would say that flat betting implies risking the same amount each time, without equalizing the expected value of each bet.
What is at risk is the money out there, regardless of the perceived expected value and especially regardless of the odds offered. Once the bet is made, probability does not matter (unless you are adding to the position by live betting.) Once the bet is made, that is the amount at risk. A loss is a loss, you don't lose more, you don't lose less with different outcomes (Asian handicaps can be a bit of an exception.)
I frame it in the sense of a sports betting as a business because that's what I do. It can be very difficult to assess a given edge on a given game because of the long term nature of calculating EV.
For most bettors not seeing this, it will cost far too much in vigorish to adjust. Look at baseball, if a bettor bets $100 on an even money bet (+100) then likes the next games favorite at -125.
When the bettor determines the same edge in both offerings, adjusting to win the same $100 (similar to your $2 example) essentially means the bettor would risk $125.
This happens all the time and many bettors are essentially saying one game is worth 25% more risk than the other. The same example could work for higher moneylines.
If one is really finding games that are worth 25% (or higher) more risk than other games, it may be wise to just bet those games.
After all, those higher bets are the only ones that will matter in the end.
Like I said, I can understand what you are saying by equalizing the expected value of each bet, but it can cause a lot of problems for most bettors. I guess I view it more like teaching new bettors, especially with questions like this one.
Remember, I am recognizing a floating type of EV that changes on bettors as well as not finding the markets as efficient as you do evo. I've seen +EV results over many NFL games but have also seen the same methods yield less than 40% for some of those individual seasons (you can even break up the seasons into parts.)
Because a book lists a team at -200 does not automatically make that book twice as favored mathematically to win over a team at +100. It's just the bookmakers forced opinion based on marketplace and its environment.
Too much perception, even by sharper forecasters, causes inefficiencies all the time. The books lead everyone around by the nose, even the sharper groups.
Sharp money can tighten a line, but only if the books make the move. This doesn't always happen as books often aim to take positions from the open.
Cheers evo, I'm glad you posted.