Re: Krigman article about sevens 'due'

On Apr 23, 4:14�pm, "Mason" <mrzer0_remo...@xxxxxxxxxxxxx> wrote:
An excellent piece.  Thank you.

Another simple illustration.

You are tossing a fair coin.  The probability is .5 for heads and .5 for tails.
What are the chances of getting exactly what probability indicates when you toss
the coin.  Half the tosses would have to be tails and half heads for this to be
true.

One toss - result can not be .5 heads and .5 tails.

Two tosses - HH HT TH TT are all the possibilities.  All are equally probable.
50% of the possible results (HT TH) are what probability would indicate - .5
heads and .5 tails.

Three tosses - result can not be .5 heads and .5 tails.

Four tosses - There are 16 possibilities (list them for yourself).  All are
equally probable.  37.5% of the possible
results are now what probability would indicate - .5 heads and .5 tails.

The chances for having exactly what probability indicates become less as the
number of trials increases.  This is result counter-intuitive for those who
misunderstand probability, but is demonstrably correct.

"Intuition might suggest that the law of large numbers would increase the chance
you'll hit the theoretical average.  This turns out not to be the case."

Indeed.  The myth of "completion" is demonstrably innumerate.
--
Onward thru the fog,
Mason

"Gregg Cattanach" <rl3166...@xxxxxxxxxx> wrote in message

news:4q8Xh.5381$2v1.279@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx



Why you rarely get what you expect at craps
By Alan Krigman

Say you throw the dice randomly 36 times. According to the laws of
probability, you'll expect to get six sevens, five sixes and five eights, four
fives and four nines, three fours and three 10s, two threes and two 11s, and
one two and one 12.

Payoffs for the various bets and characteristics of the game such as the house
advantage, are based on the supposition that what you expect is what you get.
Real life, even what passes in a casino for real life, doesn't work out quite
this nicely. Which is why, in sessions or casino visits of reasonable
duration, some solid citizens win big bucks while others lose their shirts.

One reason for the uncertainty is that the expectations aren't very strong. If
you throw the dice 36 times, you may in fact obtain six sevens, five sixes,
four fives, and so on. But you might also see none, or 36, or anything in
between.

The chance of exactly six sevens is a mere 17.6 percent. The remaining 82.4
percent is the chance of throwing some other number of the li'l devils. An
intuitive way to think about this is to picture 1,000 shooters throwing 36
times each. Were these percentages to hold for the 1,000 trials, only 176
would throw six sevens. The other 824 would get fewer or more. As examples, on
the low side, 170 would shoot five sevens, 133 four, 80 three; on the high
side, 151 would throw seven, 109 eight, and 68 nine.

So why do the math mavens tell you to expect six when they know in their
hearts you can't reliably make book on it? For two reasons. First, six sevens
is the average taken over lots of shooters. Second, it's the most likely
result, as is evident from the way the figures drop above and below six
sevens.

What happens when you go to more trials? Say 360 throws, when the expected
number of sevens is 60? Intuition might suggest that the law of large numbers
would increase the chance you'll hit the theoretical average. This turns out
not to be the case. The chance of 60 sevens in 360 throws is 5.634 percent,
much less than the 17.6 percent of six sevens in 36 throws. But 60 is the
average. And it's also the most likely result, with 5.634 percent greater than
the probability of any other number of sevens. For instance, it's 5.615
percent for 59 and 5.541 percent for 61.

The way you may think the law of averages should work on larger samples seems
to hold better comparing the likelihood of five, six, or seven sevens in 36
throws with that of 50 to 70 sevens in 360 throws. The former is 49.7 percent;
the comparable range for 360 throws is a much greater 82.3 percent.

Food for thought, next time you're at a table and a bezonian at the other end
drives the dealers nuts changing bets, muttering all the while that one out of
every six rolls has to be a seven and the shooter has been throwing for a
while so a seven's gotta be due.- Hide quoted text -

- Show quoted text -

Mason wrote: "You are tossing a fair coin."

There is the problem. there is no such thing as a "fair" US coin.
All US coins are "heads heavy," meaning that the obverse or head of
every coin weighs more than the reverse or tail of every coin.

Perhaps you are using a foreign coin??


.

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