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Well, I Think that we have pritty much covered this topic.
1 in 10? When I was 1600 I beat a guy who was 2200 and drew a 2100 in the same tournament.
A great achievement, but there's a 600 point and 500 point spread. The OP asks about a 1400 point spread. As x approaches zero and all that . . .
Hey wait ! It did happen ...right here.
Yes, there's a chance -- if the 2700-rated player is asleep, or in a strong charitable mode , or if the 1300-rated player is incorrectly rated (and really ought to be 2500+). Otherwise, the chance of a brick falling from the sky to hit your head is higher, so don't bet on it (if you want to keep your money, that is).
Yet again, it seems some people are confusing extremely low chance, with impossibility.
2700 > 2500
No. Some people misunderstand the limits of probability.
For instance, the common misconception that a million monkeys on a million keyboards for a million years would at some point produce the works of Shakespeare is pure rubbish. They might possibly produce in the process a couple of lines - if you don't count for line breaks or capitalization or punctuation. Random entries will not produce specific results.
You can get the 2700 player flying drunk and distract him with two lovely ladies, and he will still beat the 1300 player 100% of the time.
Statistics may provide a theoretical possibility which is infinitesimal, but that doesn't mean there is any practical chance it will occur. It's not a random matter, there is skill involved.
It's you who's misunderstanding probability, Estragon. The monkey thing is a case in point. It would probably take the monkeys longer than the age of the universe to re-create Shakespeare - but the fact of the matter is, since the probability of it occuring is non-zero, it will eventually happen. The odds of winning the lottery is about 1 in 14 million, yet people win it every week.
Tmb86: Please re-read Estragon's argument carefully. The essence of it is that Shakespeare and chess aren't subject to randomness -- rather, they are governed by skill. If it was all randomness (as is the case with lottery), then there's a small practical chance indeed.
But true randomness implies uniform probability distribution (i.e., the chance of one outcome is exactly the same as the chance of any other individual outcome). This is true about the lottery -- the chance of one number (or a set of numbers) coming up, given that we have no extra information, is exactly the same as the chance of any other number (or set of numbers).
However, this same argument cannot be applied with Shakespeare and chess -- because the chance of winning a game depends on executing a sequence of strong moves (at least stronger than your opponent's). While a single strong move here and there might just come up for the beginner, it won't suffice in the end for winning, because the game is cumulative, i.e., the moves are not independent the same way that the numbers in the lottery are.
So I suggest studying some probability theory first before commenting on the subject of it!
I'm kind of with estragon here. Just because there is a non-zero probability doesn't mean there is a 100% actuality.
The number of events (whatever probability) which will never occur is infinitely larger than the number of events which will.
(edit)The odds of winning the lottery is about 1 in 14 million, yet people win it every week.
this does not make sense, is doesn't matter how often the lotto is draw is still 1 in 14 million chance of winning it.
If the players play in such a way that their skill is separated by 1400 points, then the chance to win is zero. Not very very small, but zero.
But in practice people play above and below their ratings, are not rated correctly in the first place, do not play all positions equally well, etc. In practical terms it's a very small chance, but it's not zero.
Spoken with the precision of a true engineer. Thanks.
@Estragon has his point too. Not sure if the OP ever had one.
I liked your post, Valentin (just a touch rude with the last line). Now I'm no probability theorist - I grant you, but I picked up a thing or two during my degree. What your post makes painfully evident you don't understand (hey look, I can be rude too!) is that while you might think the sequence of letters involved in the works of Shakespeare are particularly 'skilled', and therefore improbable - the fact is they are exactly as (un)likely as any other sequence of characters of the same length. Did you know if you flip a coin 10 times, the sequence HHHHHHHHHH is just as likely as HTTHHTTTHT? Well, obviously you didn't, but it is. On every flip the probability of either outcome is 0.5, and that doesn't change because of the previous outcome. Do you see the point here?I'll outline it for you, it's exactly the same with chess. The only difference between chess and the coin toss is that, as an estimation, there are on average 30 'bad' moves in a position and maybe only 2 'good' ones. So it's kind of like flipping a coin with 30 faces. A particular sequence of a 45 move game with entirely 'good' moves is just as improbable as a particular sequence of a 45 'bad' move game. The reason you will be waiting a long time to see the 'good' game, is that they are much less numerous than the possible 'bad' games.Keep playing great chess mate.
I'll outline it for you, it's exactly the same with chess. The only difference between chess and the coin toss is that, as an estimation, there are on average 30 'bad' moves in a position and maybe only 2 'good' ones. So it's kind of like flipping a coin with 30 faces. Do you see what I mean? And a particular sequence of a 45 move game with entirely 'good' moves is just as improbable as a particular sequence of a 45 'bad' move game. The reason you will be waiting a long time to see the 'good' game, is that they are much less numerous than the possible 'bad' games.Keep playing great chess mate.
with the added complication that in a completely random situation your 30 sided coin has a 1/30 chance of hitting the good move every time, while the 1300 player would often actively discard this move. 1300's are drawn to inferior moves like GM's are drawn to good ones.
The problem with your probability is that there is an outside influence on those moves. That influence is the chess player and the player's skill level.
That's interesting, rooperi. Personally I was envisioning a random move generator, but now the question becomes who would beat a GM quicker, a random move generator, or a 1300. Lol.
...and as using a dice is prohibited by the rules, the 1300 player still has a long way to go to get his (1/30)^40 chance to draw the game
It's a draw. The answer is neither.