This comment is my thoughts.
-
If you have N situations, it does not automatically mean they have same probabilities. I call the mistake of not recognising it—Equiprobability mistake.
-
Outcomes have to be excluding. So people make the mistake at the very beginnign—at constructing the Ω set. Two of those situations are not excluding. One of them literally guarantees with 100% certainty, that the other will happen. When you have a correct Ω , then probability of one outcome given any other is zero. To check, whether outcomes are excluding, draw the branching universe graph and imagine a single slice in a much later point of time (Sunday), and count how many parallel universes reached that point. You will find, that only two, but thirders count the second entity twice. No matter what situation you research, the nodes which you take as outcomes CAN NEVER BE CONSEQUETIVE. If it was not the axiom, then i would be able add “I throw a dice” into the set of possible numbers that the dice shows at the end, and i would get an nonsense which is not Omega: {I throw the dice, dice shows 1, dice shows 2, shows 3, 4, 5, 6}. Thirders literally construct such an omega and thus get 1⁄3 for an outcome, just like I would get a “1/7 chance” of getting a number6 if i was also using a corrupted omega set.
-
There is a table. I place on it two apples, jar, bin, box. I pit the first apple into a jar. I put the jar into the box. I put the second apple into the bin. Comes a thirder and starts counting: “How many apples in a jar. One. How many apples in the box. One. How many apples in a bin. One. So, there are 3 apples” And forgets, that th apple in a jar and the apple in the box is THE SAME apple.
P(Monday|Tails)=P(Tuesday|Tails) is technically true, not “because two entities are equal”, but because an entity is compared to itself! It is a single outcome, which is phrased differently by using consequtive events of the single outcome.
When apple is in a jar, it guarantees that it is also in a box, the same way as <Monday and tails> situation guarantees <Tuesday and tails>.
If talking about graphs, both situations are literrally just the node sliding along the branch, not reaching any points of branching.
What if we construct generalised chess variant? Which does not bring new mechanics into the game, but expands the existing ones.
Knights, rooks, bishops stay unchanged, They are already capable of fully utilising their ability.
Queen has a combined power of 2 other piecetypes, rook and bishop. Why only two? Why these two? Instead of answering those question let’s just expand:
Queen inherits powers and characteristics of all other 5 types of pieces. (Inheritance from king and pawn explained later.)
Why pawns are in the front? Well, this is not an arbitrary structure—less valuable and more replaceable stand in the front to be a shield and prevent immediate danger on more important warriors while entering the battle. But the order of pieces on the first rank… Let’s make it fully random. 2) First row positions are fully random and not symmetrical. This way we cover classical standing, 960, and all those which do not follow the 960 limitations (king between rooks, two color bishops).
King between rooks was made in 960 to allow castling. That is the narrow ability, which is targeted by this variant. Why only rooks? Why not after moving? 3) King can pull a visible friendly target piece to the king and jump over it. Both 0-0 and 0-0-0 can be viewed as a narrow case of this rule. But in or generalised variant we should be able to pull also vertically and diagonally. Delete the limitation, that only rooks qualify, and that only once we can perform that. Queen obviously also gets this ability. Thanks to that rule 960 limitations are unnecessary: king does not need rooks on both sides to castle, and bishops can change their squarecolor by being pulled, can be used if they spawned on single color.
Pawn. Double move works ONLY from a starting position. In generalised chess we allow the double move whenever. En passant. Pawn captures a pawn, that has just crossed the attacked square. 4) Pawn can immediately capture ANY piece that has just crossed the attacked square. That means queen also can double move (which overlaps with her rook ability and brings nothing new), and en passant whoever tries to cross its huge control territory.
There is one more thing, which nerfs Queen bit. King characteristic: cannot be left in check, if impossible to avoid—you lose. Queen inherits this property automatically.
Pawn can promote to the queen, but would you want to increase the number of your pieces that are vulnerable to checks? I guess yes, if the position is under control, but better take a rook if position is complicated. Queen can also promote and turn into any other piece. Might be usefull to escape a check sequence. But if it promotes into a pawn, it becomes a dead weight as pawn cannot move backwards. (But you can use your king to pull it back 😉 )
To sum up.
Queen inherits all abilities and characteristics.
First rows are fully random.
King can pull a visible friendly target piece in a straight line up to him and jump over it.
Pawn can en-passant anyone and double move from anywhere.
Contact me if you would play this Generalised chess variant by mail/messages.