How Casinos Manage Games: Roulette, Slots, Cards

Rare bets reduce turnover by an order of magnitude, and therefore the loss is also reduced.
If you play 200 spins almost every move betting, then the result will be, for example, -500$. But when you have only 5 entry points for these 200 spins, then according to the same strategy the loss will be -100$.

Rare bets are better, but the distance will make up for everything. The main thing is to increase the % of guessing or make Win stable enough to connect a small progression.

In my understanding, when playing at a distance, with a bet on any chance, the player's balance will decrease. We are talking about negative mathematical expectation.
At the same time, bet optimization is a kind of founder of the strategy. For example, when covering two dominant dozens, the chance to win the first bet is higher. But in the long run, playing flat bets, the player will still face a negative mathematical expectation. Therefore, rare bets in such a game are always better than frequent bets.
You can learn something from the lecture about this:
economy-ru.info/page/1380781332060431481...4046019031007203224/

Edwerk,
Write what you understand by mathematical expectation.

How does this not depend on the optimal bet? If each bet has a different mathematical expectation over a distance of, say, 10 spins.

Negative expectation is built into all casino games. The optimal bet has nothing to do with it. MO is calculated as Alathissa described and is the same for any bets.
Adaptive game management is added on top and the real return is greatly reduced in favor of the casino. You can write % and jackpots whatever you want, but fall into the trap of cutting off large wins and say goodbye to your money.
If only the processing of transfers eats up 10% of the casino's deposits, then blackjack, roulette, sic bo, poker and the like are clearly unprofitable with fair play. And when the real return is 60-70%, then all the casinos are happy and there is enough for everything. And for rare large wins, you can arrange painful long verifications, in the hope that the player will not endure and will merge. In extreme cases, accuse the player of violating the rules (multi-accounting without evidence) and confiscate all the winnings.

The casino advantage in different games as a percentage at the player's optimal bet.
Information from the book by Evgeniy Terentyev "How to play and win in a casino"