Re: Krigman article about sevens 'due'

alan wrote:
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??

Sheesh. alan: reworded just for you: 'PRETEND' you are tossing a fair
coin. It's a theoretical experiment, not a game you can play in a casino.

--
Gregg C.


.

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