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The first of the 4 games is already a given thing, Paul. We want to know the probability of the THREE next games being the same in order to know the probability of four consecutive identical games.
He really isn't. The probability calculation would go as follows:
the probability of any given setup is 1/960.
the probability of any given setup four times is 1/960^4.
the probability that the same (initially unknown) setup is repeated four times is: 960*1/960^4 = 1/960^3.
We have to multiply our probability of getting a given setup four times by the number of ways that we could have obtained the observed result. I.e. think of the coefficients in a binomial distribution for me.
Alternatively consider the following example. What is the probability of rolling the same number on two fair six sided dice?
For any particular number the probability of rolling it twice is 1/36. However we don't care which number it is, so we multiply 1/36 by six to account for the six ways that we could achieve the result. Thus we obtain 1/6.
If you throw a dice, and you get let's say a 2, the probability of getting a 2 again on the second throw is 1/6 , not 1/36....agree Paul ??
The probability of getting 2 times 2 is 1/36, but the probability of getting the same number twice is 1/6, not too difficult to understand is it?
I am sorry Paul, but you are wrong...the same way as I was wrong in the first place and was corrected by ironic_begar.
The situation is perfectly comparable to the example of the dice I gave.
I started a game of 960 chess..in position A. Started game 2 and got position A again (probability one on 960). Started game 3 and again got position A (probability 1 on 969x960). Started game 4 and AGAIN position A (probability 1 on 960x960x960) if all this was based on pure chance (which it wasn't)
I throw a dice and get a 2. Throw it again and get another 2 (probability 1 on 6) I throw it a third time and get another 2 (probability 1 on 6x6). I throw it a fourth time, and get yet another 2 (probability 1 on 6x6x6)
My original question was ' What is the probability of getting four games od chess 960 in a row, all starting with the same position'
The answer is 1 on 960x960x960
lobachevskii has it right. There are 960 ways to get the same position four times in a row, one way for each position. Each of those 960 ways has a probability of 1/960^4. The 960 ways goes into the numerator and divides out, giving you 1/960^3.
Another way to look at it (the one I usually use) is that the first probability is 1. You will get a position, some position. The probability that the second position matches the first is 1/960, and that's the same for the probabilities that the third matches the second and the fourth matches the third. Multiply them together and you get 1/960^3.
absolutely right ciljettu......UNLESS...you click on 'rematch'
Sometimes I play Chess960.
is chess960 playable with the app for iPhone?
yes. I don't have mine re-charged to check, but if memory is correct, it shows in game options on the iphone 'create challenge' same as it does on the website on that drop down option
ok, got it running now (new to the iPhone/apps...), thanks!
Could someone tell me how to castle when playing 960 on chess.com?
I mean I know the 960 castling rules, but somehow it does NOT work when I play against someone on chess.com, why is that? Am I doing something wrong?
Chess960 does not help my career of but obviously but I go back to it just in case a silly position comes up in my actual game.
@Veht.. thanks alot man. I'll try that. Hope it works!
I prefer Chess960 to regular chess- I think it might even take over in the next 50 years.
Yes it isdonyutuc. The squares between rook and king are free, as are the squares whereking and rook must end up. So queen side castling is possible. I agree it looks a bit funny.
Yes, if it became more popular than standard Chess in so many years, that would reflect success in studying its peculiarities. So far, how much has been done to categorize the openings -- I would start by categorizing according to most striking feature of each position... Examples: 1) Queen or bishop at the corner; 2) bishop duo in the center, corner or elsewhere; 3) knight duo at the corner; etc.
Categorizing is quite tricky, but I find it worthwhile as, in starting a new game, I sometimes discover significant similarities in another game played with a slighly different starting position. That helps in planning the strategy in the new game. How about that?
Why has 4+ years and counting, and chess 960 is still unavailable in live chess (non-corresspondence) on chess.com?
Other sites have it available for live play for a many years, and chess.com has already had it programmed in (for correspondence play) for many years now as well.
Surely this could be added to live play with little difficulty, and should be added in ASAP? All that would be required (or so it seems, I'm not a programmer myself) would be to add a timer to the game and make the 960 icon different from the regular chess icon (i.e. someting other than a circle).
With a reported 6.7 million members, 55,832 of which have played 960 via chess.com's correspondence/online feature, surely this feature is worth adding to live chess as well, and as soon as possible?
I prefer standard chess.
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