The most crucial to happy gambling
generally (apart from being prepared for losing, since you create a losing copy
of yourself with certainty) is your Happy-Enough-Ceiling, where if you reach it, you leave with your winnings. The trivial
example is entering the casino with three dollars and playing Martingale
roulette, leaving as soon as four dollars are won – the Many Worlds/Minds
(MW/M) tree then looks like this:
The large circled numbers are the bankroll,
starting at 3 dollars, de/increasing by the bet amount when losing/winning. The
small black numbers are the expected number of days if trying for 32 days. I
win on about 24 days and only lose on eight.
STRAW-MAN: But, wanting to play less boring
games, where should our Happy-Enough-Ceiling generally be?
Well, remember that 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. That expected average of your funds slowly decreases. At a
French type roulette table, 1/37 of your bet is lost on average with every spin of the
wheel.
But: The larger the bets, the more will the random walk jump widely and thus wildly up and
down.
Now, thinking about this random walk, our Happy-Enough-Ceiling 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 your limit, you usually lose.
The casino’s limit is the money you bring to the table. Therefore,
you must walk away at some point well
below having doubled your money. That is why my Happy-Enough-Ceiling is at
a modest 4 dollars if I start Martingale with 3 dollars – not because of Zen
modesty.
STRAW-MAN: But is it Zen? If you are down
to 2 dollars, you are in a new Here-and-Now
with a new starting amount. Why go on playing with a 4 dollar ceiling? That
limit is now as far as your new “starting amount”. There should be a personal
lower limit, too, one above zero.
If you stop playing at 2 dollars, your
lower limit is as close to the 3 dollars at the start as the ceiling at 4
dollars. So your random walk loses most
days! Remember – we started this whole series with wanting to ensure
more happy days than sad ones drowned in fermented spirits.
STRAW-MAN: But look, you said “Your random walk will hit most likely first
whatever limit is closer to where the random walk started.” So, why not
just have my ceiling, my upper limit, closer to my starting amount than my
lower limit?
If you have a personal lower limit, why
bring those dollars in the first place if you will not touch them? Like getting
mugged? Moreover, if you re-evaluate the Here-and-Now again every time, you
would also increase your ceiling after winning. That is the same as not having
a ceiling and thus losing almost always.
STRAW-MAN: Ok, so the important is that I walk away at some point well below having
doubled my money.
Yes. This explains differently why putting
everything on red loses most days. Winning on red pays out double your bet,
therefore, the upper limit is automatically at least as far away as the amount
that you bet. If I bet all I have, my upper ceiling is automatically as far
away from my starting amount as my starting amount is from zero. My ceiling is
then as close as the casino’s zero limit. The start of the random walk is in
the middle of these two borders, and so I lose again.
So,
we must bet some amount well below our starting amount.
STRAW-MAN: But you also said that we must
bet large amounts in order to avoid going down with the expected 1/37 on every
spin of the roulette wheel. So, bringing 1000 dollars, bets should be well
below this but high, say 500 dollars, and our upper ceiling is therefore
automatically at 1500 dollars. You sure you win most days this way?
Well, draw the MW/M diagram. B is your bet.
Your starting amount is 2B and your Happy-Enough-Ceiling at 3B. You win about 2
out of 3 days:
You could also bet 200 dollars on red each
time, and walk out when hitting 1400 dollars. Most days, you go home with 1400
dollars.
STRAW-MAN: And how much do I still bring home
on the other days?
Well, if we play for only 10 rounds before
getting bored, those amounts vary, but if we stay about 25 to 30 rounds, we go
almost always home with either 1400 dollars or zero.
STRAW-MAN: Hmm – 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.
Yes, this is one example for why
understanding deviations Δx is so important, why averages
enough, although averages are already beyond most university students in the
arts and humanities and so misunderstood as to be looked down upon as being
racism and sexism.
STRAW-MAN: Oh, let’s not go there today.
Back to justifying this as potentially useful. I need a 100 kilo-dollar
lifesaving surgery but only have 90 thousand. What can I do at the roulette
table in order to maximize the number of worlds where I survive? The Happy-Enough-Ceiling
is now forced upon me; it is 100 thousand; and all I learned here otherwise is to use large
amounts.
Yes, but if you bet more than what you need
in order to reach your Happy-Enough-Ceiling, you have less to proceed betting in case you
lose. So, it is actually very easy as far as I can see.
STRAW-MAN: Bet 10 thousand dollars! Then,
after losing, re-evaluate in the new Here-and-Now and bet 20 thousand, then 40 thousand?
A desperate
Martingale, yes, and finally betting the last 20 thousand fully. Always bet the
amount that is still missing or, if you have already less than that, all you
have. As death approaches, re-evaluating the Here-and-Now becomes more important than deceiving yourself about that you are still the one who entered the casino in order to fool yourself about being a winner relative to him.
