Here is an access to the endgame database tables.
http://www.logicalchess.com/resources/tablebase/egtb/
Try inputting ‘1n2k3/8/8/8/8/8/8/2B1KB2+w’.
It gives White wins in 49 moves!
These databases were originally generated by Ken Thompson.
I’m sure I’m missing something fundamental because my knowledge of chemistry/physics is extremely basic.
But I’ve always understood this:
6.022045 × 10^23 is the number of atoms in 12 grams of carbon-12. SO I just don’t see how if that is true we are only looking at 10^75 number of atoms in the entire universe.
Are y’all sure you have the right number or atoms. I googled a bit, and found references that match what you are saying, but that’s not proof positive. I also found this page (warning, ugly formatting) that differed. Dramatically.
the 1x10^57 kinda jumped out.
Are y’all just counting hydrogen atoms with your number?
The fundamental thing you’re missing is the concept of very large numbers and orders of magnitude.
6[sup]23[/sup] looks like it’s about a third of 10[sup]75[/sup], but it’s not. Instead of multiplying by three, you have to multiply by a thousand million million billion billion billion trillion, and you’ll still be an order of magnitude (power of 10) short.
Since 75-23 = 52, the question you should ask is, how many 12 gram units can fit in the universe? 10[sup]52[/sup] is probably in the ballpark.
I realized the error in my thinking for K+N vs. K+2B: Unless you had some bizarre underpromotion, the two bishops are going to be on different colors, so the knight can’t fork the bishops. The knight could, in principle, fork one bishop and the king, but the ecclesiastical player can always avoid that situation. But meanwhile, the knight is still going to be a royal pain in the neck (well, OK, a noble pain in the neck, but close enough), which is going to considerably slow down the checkmate.
For the other example, it still doesn’t seem to jibe with me, but that may just be due to the fact that, being human, I’m not accustomed to perfect play. In real play, one’s opponent is likely to make a mistake long before move 223 (and with that rook around, a mistake is likely to have swift consequences).
yeah well, MTG may not have Hippogriffs…
http://gatherer.wizards.com/gathererlookup.asp?set=Alliances&name=phelddagrif
But I think we can arrange something there.
hydrogen is 99.9% of the universe, isn’t it?? 
And what’s a few orders of magnitude between friends, LOL. Your estimate may differ slightly.
Probably more like 90%or so. But your point still stands – the estimate of the number of atoms in the universe is just that – an estimate. Ten percent one way or another is peanuts when we’re rounding off to the nearest power of ten anyway.
I’ve tried playing this against a computer and the moves seem quite ‘unnatural’.
Hve a look at the link I gave - the bishops stay well away from the knight - only the King closes in.
Well the player facing 2 knights might walk into a fork!
The ending of K+B+N v K is quite enchanting, and is an example of perfect play…
I’m aware of the mathematic realities, math is one thing I have no problem with. I know how exponentials work and I know that 10[sup]6[/sup] is not “twice as large” as 10[sup]3[/sup].
It’s one thousand times as large. And as we start getting into trillians and quadrillions and upwards I understand that each order of magnitude larger is a huge increase (10[sup]75[/sup] is incomprehensibly larger than 10[sup]74[/sup].)
But as it is, taking that into account I just couldn’t picture the universe being that small. That’s where my lack of physics understanding comes in to play, I’m not sure how we have this estimated size of the universe and I can’t wrap my mind around that fact that eventhough I see 10[sup]75[/sup] is a huge exponential it still seems small considering there are supposedly billions of galaxies with each galaxy having billions of stars in it.
I know how you feel.
We’re used to dealing with numbers of magnitudes up to say 100,000. When we think about millionaires, it seems a lot of money.
And 10[sup]75[/sup] looks so harmless. But if there are billions of galaxies (say 10[sup]9[/sup]), each with billions of stars (say 10[sup]9[/sup]), then that’s still only 10[sup]18[/sup]. Which is a really tiny number compared to 10[sup]75[/sup]!
Mathematicians must take credit for reducing such colossal numbers to a simple notation.
How about this:
Take a 64 square chess board. Put one grain of rice on the first square, two on the second, four on the third, eight on the fourth etc. It seems quite easy to imagine.
But if you cover each square on the whole board, you get 2[sup]64[/sup] - 1 grains in all. And that is 18,446,744,073,709,551,615.
Hard to get your head round that!
I fall into that exact same trap, so I know how you feel. In rereading my first post here, it sounds snarky, and I apologize for that. It was unintentional, I assure you.
I suppose the best way to illustrate, similar to how glee looked at it, is to reduce. (I’ve always heard 50-100 billion stars in each of the 50-100 billion galaxies. So let’s say 100(s of) billion(s) of each measure.)
If there are hundreds of billions of stars in hundreds of billions of galaxies, how can the universe only hold 10[sup]75[/sup] particles?
Divide out the billions. There are hundreds of stars in hundreds of galaxies, so how can the universe only hold 10[sup]57[/sup] particles?
Now if you’re like me, you don’t really feel a qualitative difference between 10[sup]75[/sup] and 10[sup]57[/sup]. However, “hundreds of hundreds” sounds unbelievably smaller than “billions of billions”, so the universe starts to sound much more rightly vast.
Years ago I decided that a googol was, for all intents and purposes, the equivalent of infinite, because I did the ubiquitous “layman’s calculation” for number of planck units that could fit in a sphere 12 billion light years in radius, and it came out to be less than a googol.
Thus, if the universe couldn’t even fit a googol different possible positions for an atom to exist in, (at the time I believed that space was discrete. I still kinda do, as I think it would remove several infinity problems for various equations, but that’s beside the point), then nothing over a googol was even meaningful.
Then a couple years later, I got into a debate about whether a computer would ever be able to brute force a game of chess, and I concluded it could not. (I still believe that.) My own rudimentary calculation had the number of possible moves somewhere within a few orders of magnitude of 10[sup]121[/sup], which crushed my “googol = infinity” argument into smithereens.
A billion is probably the largest number I can really even begin to imagine. I think of it this way, even though I know the numbers are way off:
09: - A billion planck units in a molecule.
18: - A billion molecules in a speck of dust.
27: - A billion specks of dust in a rock.
36: - A billion rocks in the earth.
45: - A billion earths in the solar system
54: - A billion solar systems in a cluster of stars (accounts for the space between stars)
63: - A billion star clusters in the galaxy
70: - A billion galaxies in a cluster of galaxies (accounts for space between galaxies)
79: - A billion galactic clusters in the known universe
It really gives you an appreciation for the truly staggering size of a googol. Don’t get me started on a googolplex. WTF do we even need a googolplex for, anyway?
Ah. Well computers do play chess using brute force, and they can beat 99.99% of chessplayers with it.
It transpires that you can play a very strong game of chess by just looking a few moves ahead perfectly. What I mean is that the computer analyses every possible continuation for both sides.
Say there are 30 legal moves in a typical position. Then analysing 1 move ahead for each side generates 30*30=900 positions. Call it 1000 ( 10[sub]2[/sub] ) for convenience. So 2 moves ahead generates 10[sub]4[/sub] positions.
Now count the pieces + pawns in each position, and use a simple algorithm to achieve the best result no matter what your opponent does.
And I expect the modern computer can see about 6 moves ahead (Deep Blue in 1997 could do 10[sub]8[/sub] positions per second).
Of course us carbon-based lifeforms don’t use this method. We dismiss at least 25 of the 30 moves instantly. Our judgement can be pretty good (if you watch a grandmaster playing speed chess, you’ll see this!). However we can overlook something a few moves down the line. And that’s where brute force triumphs.