Name: How many chess games are possible?
Uploaded: 2020-03-30T05:27:49.000Z
Duration: 12 min 11 s
Description: Thousands of YouTube videos with English-Chinese subtitles! Now you can learn to understand native speakers, expand your vocabulary, and improve your pronunciation...

Basic quantifiers

The comparative

than the number of atoms there are in the observable universe.

Well, the number of games of chess is known as Shannon's number

so let's find out what is Shannon's number, and how it was worked out.

Claude Shannon. He... in the 1950s he wrote a paper "How to program a computer to play chess"

...It was about how to program a computer to play chess.

And in that paper he came up with an estimate for how many games of chess there are

So he estimated that the number of games of chess would be

Ten to the power...round about ten to the power 120

Which is... well, just massive! It's billions and trillions of googles

If we compare that with atoms in the observable universe

there's about ten to the 80 atoms in the observable universe

You could assign billions of games of chess for each atom in the universe.

How did he come up with this massive figure?

So what he decided was, well, he looked at some games of chess and he said

Well, on average, at any position, there are about thirty legal moves that you can make.

So, the first player would have thirty legal moves he could make

And if you do two moves, that's the first player then the second player

Then that would be, for each move by the first player

So that would be NINE HUNDRED already, just with two moves

Some terminology here: when I'm saying *moves* I actually mean what is called a *ply*

That means that one player goes first, then the second player goes next, then the next player...

So in chess terminology a move is the white player then the black player

So another move would be the white player again, the black player again.

But we're just going to say *moves* to be: each player takes a move

It's actually called a ply in chess terminology.

So if the first player has 30 legal moves he can make

Then for each move the second player has another 30 legal moves he can make

So with just two moves there are nine hundred moves you can make altogether.

If it was three moves, it would be 30 by 30 by 30

If it was four moves, it would be 30 by 30 by 30 by 30.

Shannon said, Well, a game is about 40 moves.

Ah, that was in chess terminology, so he means 80 plays.

BRADY: Well that is the most wishy-washy...

JAMES: Yeah. It was only in passing, it was only an estimate, it was only a paragraph of the paper

And he did this rough estimate, this rough number, to show that if you had a computer

and it was trying to work out then the future of the game, and trying to work out

all the legal moves and where this game was going to go

so that it could make decisions, sort of, how to play next...

Then, the computer would never make a move

If it was calculating one game per microsecond it would be until the end of the universe

it would never play. This was the point Shannon was trying to make with this rough estimate.

So we're going to have a look at a sequence of games there are when each player takes their turn.

So...let's take the first move, and white has twenty legal moves.

So we've got...we've got one here for each pawn, so that's eight.

We've got the double move there by each pawn, so we've got sixteen.

We've got two moves there for each knight...two moves on this side here and here...

So, twenty moves for the first player. Now black takes the next turn

And for the next turn he can respond with the same twenty moves.

So for each move player 1 takes, black can take twenty moves, so you multiply, it's 20 by 20...

There are now 400 games that could have happened, already.

With just two moves there are already 400 games that could have happened.

Let's see what happens next. Then suddenly it becomes much more complicated.

When white plays next it becomes...8902 moves. Suddenly, phoof! 8000, well, nearly 9000 games that you can play, with just 3 plays.

BRADY: This sounds a lot more precise than what Shannon was doing, this is real numbers.

JAMES: Yeah, these are real numbers. With these small numbers we can work this out.

So far so good -- it's going to get harder with larger numbers.

The next move is black, and he'll have 197,742.

So after black moves again we now have 197,742 possible games that could have been played.

All the possible games we could have done in those four moves is already 200,000.

JAMES: Huge numbers already, huge numbers.

BRADY: Although, you are able to know exactly what the number is, so it just seems like

if you spend enough time on this you'll be able to...

JAMES: So OK, we can keep going can't we? So we can keep going

and these numbers are going to get bigger and bigger

Now, in theory, the total number, the largest number, the longest chess game can be...

That's invoking though, you have to invoke the 50 move rule, cause you could just go on forever,

if you just ended up with two kings, just going backwards and forths.

A game could last forever. So there is a rule that stops a game lasting forever that says:

Well, if you've played 50 moves with nothing being captured, and you're just messing about--

JAMES: Yeah it's a pawn hasn't moved, something hasn't been captured,

or you repeat the board three times. If that happens then you call it a draw.

So there's a cut-off point. Now some people have worked out what the longest possible chess game is...

It's something around 11,800. There's some disagreement, not much disagreement though,

So if you see how fast this sequence is growing, can you imagine how many games there are

altogether. Especially when you're going all the way up to nearly 12,000 moves.

Some of those games would be nonsense games, where you can win,

you've only got one move left and you can win in one move, but you don't,

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