Hello Alan and all,
Given below is what Wikipedia offers.
For anyone wishing to access the original page:
https://en.wikipedia.org/wiki/Shannon_number
Paul Benson.
"
Shannon number - Wikipedia - en.wikipedia.org.
The Shannon number, named after Claude Shannon. , is a conservative lower
bound (not an estimate) of the game-tree complexity. of chess. of 10120,
based on an average of about 103 possibilities for a pair of moves consisting
of a move for White followed by one for Black, and a typical game lasting about
40 such pairs of moves.
Contents.
1 Shannon's Calculation.
2 Number of sensible chess games.
3 See also.
4 Notes and references.
5 External links. Shannon's Calculation[ edit. ].
Shannon showed a calculation for the lower bound of the game-tree complexity of
chess, resulting in about 10120 possible games, to demonstrate the
impracticality of solving chess. by brute force. , in his 1950 paper
"Programming a Computer for Playing Chess". [1]. (This influential paper
introduced the field of computer chess. .)
Shannon also estimated the number of possible positions, "of the general order
of 64 ! 32 ! 8 ! 2 2 ! 6 {\displaystyle \scriptstyle {\frac
{64!}{32!{8!}^{2}{2!}^{6}}}} \scriptstyle {\frac {64!}{32!{8!}^{2}{2!}^{6}}},
or roughly 1043". This includes some illegal positions (e.g., pawns on the
first rank, both kings in check) and excludes legal positions following
captures and promotions. Taking these into account, Victor Allis. calculated
an upper bound of 5×1052 for the number of positions, and estimated the true
number to be about 1050. [2]. Recent results [3]. improve that estimate, by
proving an upper bound of only 2155, which is less than 1046.7 and showing [4].
an upper bound 2×1040 in the absence of promotions.
Allis. also estimated the game-tree complexity to be at least 10123, "based on
an average branching factor of 35 and an average game length of 80". As a
comparison, the number of atoms in the observable universe. , to which it is
often compared, is roughly estimated to be 1080.
Number of movesNumber of possible games
1 20
2 400
3 8,902
4 197,281
5 4,865,609
6 119,060,324
7 3,195,901,860
8 84,998,978,956
9 2,439,530,234,167
10 69,352,859,712,417
After each player has moved 5 times there are 69,352,859,712,417 possible games
that could have been played. Number of sensible chess games[ edit. ].
As a comparison to the Shannon number, if chess is analyzed for the number of
"sensible" games that can be played (not counting ridiculous or obvious
game-losing moves such as moving a queen to be immediately captured by a pawn
without compensation), then the result is closer to around 1040 games. This is
based on having a choice of about three sensible moves at each ply (half a
move), and a game length of 80 ply (40 moves). [5].
"
-----Original Message-----
From: Alan Dicey - Email Address: adicey@xxxxxxxxxxxxx
Sent On: 29/08/2018 17:36
Sent To: usbca_chess@xxxxxxxxxxxxx - Email Address: usbca_chess@xxxxxxxxxxxxx
Subject: [usbca_chess] Dear Jim, Whoa! Thanks for the cool facts!_chess] Re: A
couple of Chess facts!
Dear Jim,
Whoa!
Thanks for the cool Facts!
Jim, or anyone else.
Anyone care to Google something called:
"The Shannon Number"?
It is the number of legal Chess games that are possible to play!
Some one sent it to me one time, but I think I put his message and the
definition on my other T - Drive which is in the closet!
With best regards
God Bless
Alan
Plantation, Sunny South Florida
----- Original Message -----
From: JT
To: usbca_chess@xxxxxxxxxxxxx
Sent: Wednesday, August 29, 2018 2:20 AM
Subject: [usbca_chess] Re: A couple of Chess facts!
I love this stuff. And here are some interesting correlations:
First of all, I shall attempt to put that ridiculously long number, the
number of possible different moves through the first ten moves of a chess
game, into English. Here goes:
169 octillion;
518 septillion;
829 sextillion; (I hope I spelled that right!)
100 quintillion;
544 quadrillion
Move possibilities.
Now, many of us have a hard time envisioning a number no larger than a
million. So, to get a frame of reference, here are a couple tidbits that
might help.
I recently read that it was either Amazon or google, I forget which, but
whichever it was, it was the first company ever to amass a trillion dollars
in worth.. A trillion, in case anyone wonders, is a million millions. If I
had a million millions, I could afford to go to Monaco for their dandy
tournament, coming up the end of October. I could even take a few people
with me!
Anyway, I asked Alexa, as a point of comparison, how much was the US
National Debt. Her answer: as of 2016 statistics, the US National Debt was
18+ trillion dollars. That's 18 million millions. Man! How much could I
travel if I had that much!
So, one septillion is a trillion trillions!
One octillion is a thousand trillion trillions.
That means that there are 169 thousand 518 trillion trillions of possible
different moves that could occur during the first ten moves of a chess game.
One more correlative: according to Alexa, again, light's top speed, in feet
per second, is 983,571,056. That's 983 million, 571 thousand, 56 feet per
second, just under a billion feet per second. I always thought the speed of
light was 186,284 feet per second, but maybe light has gotten faster as I've
gotten older. Sure seems like everything else has, so why not! Anyway, if we
sent light on a trip of 169 octillion, 518 septillion, 829 sextillion, 100
quintillion, 544 quadrillion feet, it would be a journey of roughly 33
septillion miles. How incomprehensible is that!?
Try this. We all know there are 60 seconds in a minute, 60 minutes in an
hour, 24 hours in a day. That translates to 1,440 minutes in a day. And that
translates to 86,400 seconds in a day. Once again according to Alexa, the
earth is 4.54 billion years old. That's 4 billion 540 million years. I
recall from my Geology classes back in college that the oldest rock on hand
successfully carbon dated was thought to be 3.2 billion years old. Well, I
was in college a long, long time ago. Now, if, at 4.54 billion years ago,
mentioned by Alexa, God had commenced counting the days, we've all done
that, right? Counting the days, year after year, for 4 billion 540 million
years, how many days would he have counted? 365.25 times 4.54 equals
1,658-235. 365.25 is the number of days per year, factoring in leap years.
That comes to one thousand 658.235 billions, or, one trillion, 658 billion
235 million days. That's 1,658,235 plus six zeroes. You'd think the number
would be bigger than that, wouldn't you? I mean, the US owes, or owed as of
2016, 18 trillion dollars and change. That's 18 times more dollars than the
number of days that have passed since the earth began! But check this out.
If God had started counting seconds, counting by billion, a billion each
second, over the 4 billion 540 million years elapsed from that day to this…
Remember I said there were 86,400 seconds in a day? So if you increment a
billion 86,400 times, you come up to 86 trillion, 400 billion. That's 864
plus 11 zeroes. The easy way to do it is to multiply 864 by 1,658.235, then
tack on the zeroes. You can use a calculator; I did. 864 times 1,658.235
equals 1,432,715. One million, 432 thousand, 715. Now we have to add on the
zeroes. There were 17 of them, so we'll have to shift commas a bit.
1,432,715 is seven digits, plus 17 zeroes equals 24 digits. That works out
to 143,271,500,000,000,000,000,000. Or,
143 sextillion (I tried several times to get Alexa to spell sextillion, but
she wouldn't.)
271 qintillion
500 quadrillion
000 trillion
000 billion
000 million
000 thousand
000.
If you're still reading, then you've come to the pot at the end of the
rainbow. If Alan's number is correct, and if my number is correct, and I'm
pretty sure of mine, you could multiply my number by a million, in other
words add six more zeroes, and you would still be a bit shy of Alan's
number. Yep, you could count the number of seconds in 4.54 billion years,
counting a billion for each second, and the number you would come up with,
143,271,500,000,000,000,000,000 would be less than one millionth of the
number of possible variations achievable in just the first ten moves of a
chess game. Strikes me as being a fine reason for studying the openings that
we are fairly sure are at least playable. There are simply way too many
opportunities to get lost in random experimentation.
And there's one other ray of hope. With numbers that large, we can hope that
it will yet be a while before some blasted computer comes up with the
unbeatable variation. How long do you suppose it would take light to travel
169,518,829,100,544,000,000,000,000,000 feet? If light started its journey
at the birth of the earth, and if scientists are anywhere close to right on
the age of the earth, light still has a really long way to go! I mean a
really, really, really long way!!!
Jim T
From: usbca_chess-bounce@xxxxxxxxxxxxx
[mailto:usbca_chess-bounce@xxxxxxxxxxxxx] On Behalf Of mordue andrew ;
(Redacted sender "tyson.mordue" for DMARC)
Sent: Tuesday, August 28, 2018 6:31 AM
To: usbca_chess@xxxxxxxxxxxxx; Alan Dicey <adicey@xxxxxxxxxxxxx
Subject: [usbca_chess] Re: A couple of Chess facts!
All,
This is why it is important to learn your openings in case you meet a
Chinese opponent!
Tyson
On 28 August 2018 at 00:29 Alan Dicey <adicey@xxxxxxxxxxxxx wrote:
A few Chess facts
There are 318,979,564,000 different ways of playing the first four moves
by
each player in a game of chess.
There are 169,518,829,100,544,000,000,000,000,000 different ways of
playing
the first ten moves by each player in a game of chess.
- - - -
There are over 200 million inhabitants of China that are keen chess
players.
- -
The word "Checkmate" comes from the Persian phrase "Shah Mat", which means
"the king is dead".
- -
With best regards
God Bless
Alan
Plantation, Sunny South Florida
