Guessing Strategies (Useless for Casino Roulette)

Another way is adaptive responses of casinos to players' bets.

Hmm...adaptive casino (the great and terrible). Does he need it?

Catch a mouse and stomp slowly. The player's capital spins around one point back and forth, and the casino smoothly takes its percentage (the point slowly shifts towards the player's loss). If the capital is intended for the game, and not for hungry children, then there will be no scandals and suicides. The player gets adrenaline-casino money. This is the casino's dream.

The bias in favor of the player is controlled by limiting the upper bet. Yes, that's right.

If the player's capital is considered as a random walk, then the longer he plays, the more likely it is that the point will return to its original position: the ratio of paths not passing through zero to the total number of options is less and less, count for yourself...

Moreover, 0 creates a condition for 100% loss of the player, but slowly, smoothly. And everyone is happy, unless the children and wife are sitting at home hungry...

Dealer's handwriting:
Henri Poincaré, instead of the immensely complex flight of a coin, considered a very simple movement - the rotation of the arrow of a primitive roulette. Let there be a horizontal circle, divided into equal sectors - white and black; in the center of the circle on the vertical axis there is an arrow, which can be spun and allowed to rotate freely. What is the probability p that it will stop in the white sector? If there are an equal number of white and black sectors, and the arrow is spun strongly enough, then everyone will say: p = 1/2. Poincaré formalized this intuitively clear position: if the initial velocity v is large enough, then the proportion of time spent by the arrow in the white sectors (and with it - the probability of stopping in one of them) is close to the proportion of these sectors themselves in the circle. On the contrary, the dependence of the stopping angle Ф(v) on the initial speed v and the nature of the deceleration (type of friction, etc.) is insignificant and disappears altogether in the limit.

More precisely: for any accuracy of roulettement of angle and momentum, there exists such a value of momentum (and with it the number of revolutions) that there are indistinguishably close initial conditions leading to different outcomes.

Therefore, a short spin is immediately blocked, and if the ball is launched with sufficient speed, it is back 50/50.

Vladimir wrote: Moreover, 0 creates a condition for 100% loss of the player, but slowly, smoothly. And everyone is happy, unless the children and wife are sitting at home hungry...

What does "0" have to do with it? It's a regular number, only painted green. Only for playing on simple chances it's a killer of all options, but who makes you play on chances?

In regards to the questions about the availability of adaptive, it is very strange to hear that people should be satisfied with cars that drive at a speed of 20-30 km/h. We live in a different century.

0 is a synonym for unfair payout. Unfair play leads to 100% ruin in a limited period of time. Let's replace the word adaptive with dispersion and everything will fall into place.

Once again about dispersion (adaptive). Adaptive happens not only in casinos. It can happen at your home too. Honest RNG 5000 events probability +=2/3; probability-=1/3. Two series of 60-100 tests in which +/- went 50 to 50. If this happened in a casino, there would be only one conclusion: they are rigging, taking the last hard-earned money... But there are also opposite stripes, no one complains about that.