Casino probability

[Guest]

Bill goes to the casino to place 1 bet everyday.

He picks a number from 1 to 10.
Each number has an equal chance of occurring.
If his number is selected on the wheel he receives 10 times his original wager.
If another number is selected he loses all of his wager.
Every time Bill wins the casino takes a commission of 10% of his winnings

If Bill lost yesterday he will wager $100.
If Bill won yesterday he will wager all of his winnings(after commission) the next day.
Bill lost yesterday.

Starting today, How much will Bill lose on average per day to the casino?

[fertooos]

Each casino has a random number generator. This is how the casino works. This is normal and I don't see anything wrong with that.

[Raiden Mitchell]

An interesting question actually. Thanks for the answer. I recently watched a YouTube video about two physicists who wanted to beat the casino at roulette and were pretty close to doing it.

[Guest]

fertooos said "Each Casino has a random number generator. This is how the Casino works. This is normal and I don't see anything wrong with this."

Well, yes, each Casino has many "random number generators", considering each roulette wheel, pair of dice, or deck of cards a "random number generator"! But what in the world does that have to do with this question?

[Guest]

I suspect the "method" you mentioned was for beating twenty-one, not roulette. In casino "twenty one", where you start by dealing only two cards to the player, the dealer typically does not reshuffle the deck after each deal since that would slow the game down too much. Obviously, if you could memorize every card as it was dealt, your odds of winning would increase sharply as more cards were dealt. Most people cannot do that, but this method was based on counting the number of face cards dealt rather than all cards. Casinos now reserve the right to refuse to allow a person they suspect to be "counting cards" to play twenty-one. Many also have five or more decks of cards mixed together from which the cards are dealt to reduce the effectiveness of this method.