This symbol -> ! in math terms is a factorial operation from 1 to n therefore 2!+2!=4 is the same thing as (2x1)+(2x1)=4 and 3!+3!=36 is the same thing as (3x2x1)+(3x2x1)=36 possible permutations. In other words consider them as groups. (1,2,3) are the 3 different pieces and can be arranged in 6 different ways: (1,2,3),(1,3,2),(2,1,3),(2,3,1),(3,2,1), and (3,1,2) and the same as for the other side. Hope this helps.
Can someone explain the "Matrix system" better for me ???
[...] and then says 3!+3!=36 possible permutations [...]
Is this a new kind of math I've never heard of?
Indirect wrote:
This symbol -> ! in math terms is a factorial operation from 1 to n therefore 2!+2!=4 is the same thing as (2x1)+(2x1)=4 and 3!+3!=36 is the same thing as (3x2x1)+(3x2x1)=36 possible permutations. In other words consider them as groups. (1,2,3) are the 3 different pieces and can be arranged in 6 different ways: (1,2,3),(1,3,2),(2,1,3),(2,3,1),(3,2,1), and (3,1,2) and the same as for the other side. Hope this helps.
Yes that does help actually but never being good in math it's taking my brain a bit to understand it but it does make sense.
So something like 5!+5!=240. Yes or no ?
Yes.
The system created by Bernard Parham were he uses a equation for better calculating games. He explains it as 2!+2!=4 meaning 2 attackers plus 2 defenders equals 4 possibilities and then says 3!+3!=36 possible permutations and I have no idea what he's talking about. Can someone help me ?
Lets use loose change as an example. Say you have a quarter, dime, nickle, and penny, and four empty slots to put them in. How many different ways can you order them? Biggest to smallest and most valuable to least valuable are two ways for example.
Well for the first of 4 slots we have 4 choices.
No matter what we choose for the first, for the second we have 3 choices.
No matter our first two choices, now we have 2.
And for our last choice we'll always have 1.
So you can calculate it with 4x3x2x1 which can also be written as 4!
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I'm guessing Parham is saying if you have 3 attackers, you have 3 choices on your first move, 2 on your second, and 1 on your last... and the same for the opponent (so he adds them 3!+3!)... but that only makes sense to me if he's talking about captures lol. Because in chess, you can move the same piece twice!
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To do our loose change example again. Say you have 4 "slots" but you can repeat your choice e.g. you can now do quarter, quarter, penny, quarter if you want.
Now for our first choice we have 4, but because we can use the same type of coin again for our second choice we have 4, third choice we have 4 etc.
So it's just 4x4x4x4 or 4 to the power of 4. Typed as 4^4.
It seems to me Parham should use exponent not factorial.
And if he is talking about number of ways you can capture... that seems an odd way to evaluate an attack much less a position.
Although if I recall he's basing it on something like maximizing mobility... well not even that, something like maximizing force in a small area. IIRC he evaluates rooks and bishops the same, which during a game would only really be true in 1 quadrant during a combination or something.
It ignores the best way to build an attacking position, and the interplay of features, e.g. is a knight in the enemy king's quadrant always worth "1 attacker" regardless of what square it's on? Of course from our own experience we know piece placement is very important... and modern "theory" or I should say conventional chess understanding is what will help you there.
I don't know why he's interested in considering the number of ways an exchange can happen.
What you said makes sense, but not sure how it could be related to the permutations thing.
XPLAYERJX wrote:
shell_knight wrote:
And if he is talking about number of ways you can capture... that seems an odd way to evaluate an attack much less a position.
Although if I recall he's basing it on something like maximizing mobility... well not even that, something like maximizing force in a small area. IIRC he evaluates rooks and bishops the same, which during a game would only really be true in 1 quadrant during a combination or something.
It ignores the best way to build an attacking position, and the interplay of features, e.g. is a knight in the enemy king's quadrant always worth "1 attacker" regardless of what square it's on? Of course from our own experience we know piece placement is very important... and modern "theory" or I should say conventional chess understanding is what will help you there.
I have no clue who Bernard Parham is;however, I read this forum and was interested in the idea's and was just curious on an idea that I came up with of what you posted. Again I may be wrong but just to give out an idea to spark some further conversation.
I was thinking what if Parhman is talking about in terms of winning material?
You stated a few posts ago that in chess same piece can be moved which is true and gave an example of spare change which in Parhm was using 4! and with your idea of same piece moving twice would change it to 4^4
However, What if Parhman was talking about winning material? For example if you have 4 defenders on 1 pawn and I have 4 attackers on the same pawn the chances you will be able to move 1 of your defenders a second time would be highly unlikely becuase you would lose a pawn. What if he is talking about from that angle. I don't know who he is nor have I ever heard of his system of chess. But I was just curious to see people thoughts are on this idea.
This may be true but again I don't see why he would want to look at all the ways a piece can be captured
so.. basically the world as we know it isn't real. It's an illusionary world create by machines to control the human race and feed off our life force like batteries. Now..... take this red pill......
The system created by Bernard Parham were he uses a equation for better calculating games. He explains it as 2!+2!=4 meaning 2 attackers plus 2 defenders equals 4 possibilities and then says 3!+3!=36 possible permutations and I have no idea what he's talking about. Can someone help me ?