Oh, fun thread. Thanks for bumping. I have way too much time on my hands.
I love the casino analogy. Dahs mentioned the 1s and 0s example as a counter to flipping a coin. To simplify, if you had a bag full of 1s that represented favorable outcomes for team 1, and 0s that favored team 2, if more 1s happened to be drawn in the first half and were not put back in the bag, then there would be a natural correction and probability that more 0s would be drawn in the second half for team 2. This was written off as a red herring.
Before that example, it was previously asked: "Would you play poker or blackjack at a casino that engineered “expected” results like this?"
Blackjack is exactly the 1s and 0s example in real world practice. Once a card is dealt, you do not put it back in the shoe. Your winning percentage as a player is dependent on the cards previously drawn and discarded. When more face cards or aces have been discarded, the deck favors the dealer and the expected result is lower. More of them? You have a hot deck and better chance of winning. Identifying that by counting cards is how those MIT students won millions. Without being able to see the cards in a blackjack shoe, you could easily sit at a table with a cold deck and lower odds of winning. At this point, the deck is stacked against you. Does this mean you started playing a casino game with perverse probability? No. It’s still statistics. When the decks are exhausted, the house’s winnings will be close to the mean.
FTs keep getting brought up since it is easy to understand. At least in a sim game, free throw shooting is the roulette of the casino. Each spin is an independent action, just like flipping a coin. You have the same exact probability of the ball landing on black every spin. It does not matter when you step up to the table. You will get the same odds. Forcing this type of calculation on all aspects of the game engine is flawed. There are too many variables at play.
The idea that a probabilistic simulation is tainted because it uses dependent events rather than independent events doesn’t make any sense. I can simulate a hand of blackjack just as I can simulate a spin of a roulette table. Just because blackjack relies on dependent events that changes the “weight” of the “coin flip” for each hand played based on previous events, doesn’t mean that the game itself is moving further away from the mean and screwing its players. Blackjack has the best odds of any casino game.
TLDR: I’m guessing the engine is a complex simulation of conditional probability that calculates both dependent and independent events. This doesn't seem to be creating an unacceptable amount of bad beats.