SOCK-PUPPET: All your talk about betting strategies is irrelevant to the casino. The casino takes the money from those who just lost and gives it to those who won, from black to red or red to black. On average, every 37 times the ball hits the zero and the casino takes all the
money on the table.
Is this really how it works, Sock? As STRAW-MAN said
the last time: “ … that sounds somehow very wrong. If you lose 1/37 of your
bet on average and bet 200 dollars, then you should be down by only 200 dollars
after 37 times.” In the reality of casino gambling, you usually walk out having
lost all your money, and often the zero may not even have come up once.
STRAW-MAN: Yes, because people are not so
clever!
SOCK-PUPPET: The casino only shifts the
money from red to black or black to red. How does the stupidity of the gamblers
matter?
STRAW-MAN: Well, 1/37 is the minimum that
the casino earns anyway on average every spin. However, casinos earn much more than
that because of what we discussed about the random walk between the limits: “Gambling
means to go on a ride, a random walk of your amount of money, your “bankroll”,
away from what you started with. If betting
small amounts, the random walk is likely to stay close to the expected
average. You can likely gamble for a long time, but the expected average slowly
decreases, at a French type roulette table 1/37 of your average bet with every
spin of the wheel. … The most important is to have your Happy-Enough-Ceiling, where if you reach it, you leave with your
winnings … It must be closer to the amount that you bring to the table than the
amount you bring to the table. Why? The casino’s strict limit is all the money
you bring to the table. Your random walk
will hit most likely first whatever limit is closer to where the random walk
started. If the casino’s limit is closer than yours, you usually lose. The
casino’s limit is the money you bring to the table.”
So, where is the stupidity?
STRAW-MAN: The stupid gamblers do not have
your Happy-Enough-Ceiling. Or their
ceiling is too high. The random walk will first hit the limit that is nearer to
where they started, which is usually the limit of that the gambler runs out of
money. As you said, “Therefore, you must
walk away at some point well below having doubled your money.”
So, that is how the casinos make the big
money? Their own automatic Happy-Enough-Ceiling,
namely the gambler having lost all their money, cuts the random walk short.
STRAW-MAN: Yes. And they do not want you to
know that it is this simple! If you are clever, you turn the table on the
casino and use their own strategy against them. That is what your Happy-Enough-Ceiling is really about.
Instead of the casino cutting the random walk short, taking all your money, you
cut it short earlier and take theirs. Look, here is a plot of a quite common
outcome of a simulated run with your strategy of betting 20% of the starting
amount and leaving if your bankroll reaches 140%, which is after two bets
already if you are lucky. See the blue data? Those points are the average of
the bankrolls of 16 smart gamblers at the table, all playing your strategy.
Wow – the gamblers make some serious money.
Did you book the tickets to Las Vegas yet?
STRAW-MAN: Las Vegas? We are
going to Macao! In the private VIP rooms, the triads can secretly triple all bets –
we are going to take their money, too!
Marvelous. I am all in. I am going to try
sell this method and let the gamblers who turn lucky with it give me some of their earnings.
SOCK-PUPPET: Eh – I see – I am in, too!
STRAW-MAN: You guys are not going to gamble
with the system? Just try to sell it? Why?
Well, I think we should leave this as a new
‘didactic challenge’, like here and here and the perfect physics instructors' suicide here. As always, you can either toss around equations and suchlike, all not really convincing anybody, or, and this is what the word "didactic" is all about, you sit back and think and give us one
to three medium length sentences that make the reader go “Ohhhh – but of f’n
course!”. The sentences may start like this: Since STRAW-MAN is going to gamble
alone, let us not have 16 gamblers, but instead he gambles anew every day for 16 days.
STRAW-MAN: That is the same; there is no difference, mister pretend
to know all about many-worlds/minds theories!
Mathematically, physically, logically, yes,
but psychologically, and therefore, thinking-wise, didactically, no!
