I really like this thought excercise, but unfortunately I don't have enough time to read through all the 72 pages of this discussion. Will you ever continue to work on your description in https://sites.google.com/site/deedlitsplace/ultracombo? Or is there a more recent description of the steps, stages and challenges so far?
At least it convinced me to finally join this message board again
I am really glad, that the current decklists do no longer seem to include effects like Grip of Chaos. I feel that cheating luck by always drawing exactly the right card is one thing, but sequntially targeting always exactly the right random target from amongst unimaginable number of available target is something else. It might be interesting to see if we could also keep track of the ballpark probability of this scenario playing out as desired. It would be great, if the probability still stays in "imaginable numbers" (that do not need fast growing hierarchies to express).
One question concering the challenge itself:
Do I assume correctly, that any possible infinite damage combo in the deck is prohibited, even if our "optimal luck" never reaches that state? i.E. if there is any imaginable way to create an infinite damage combo with the cards in the deck it is no longer legal?
Another thing about the mathematics that struck me as strange:
Is the usage of Omega in the fast growing hierarchy consistent with the definition of ordinals?
It is clear to me, how the concept of Omega introduced in the desrcription is consistent in itself and very powerful. But in the example
F_{\Omega}(64)=F_{64}(64)<F_{65}(64)
, Omega compares to be smaller than 65, and deffitely not bigger than all the nonnegative integers...
So in other words, the Omega in the fast growing hierarchy seems to introduce a new concept, which to me is not realy coupled with ordinals - except maybe for the ordinals notion of "next higher number" with Omega and Epsilon.
Can some math-savy person point me into the right direction where this is resolved?
I really like this thought excercise, but unfortunately I don't have enough time to read through all the 72 pages of this discussion. Will you ever continue to work on your description in https://sites.google.com/site/deedlitsplace/ultracombo? Or is there a more recent description of the steps, stages and challenges so far?
At least it convinced me to finally join this message board again
I am really glad, that the current decklists do no longer seem to include effects like Grip of Chaos. I feel that cheating luck by always drawing exactly the right card is one thing, but sequntially targeting always exactly the right random target from amongst unimaginable number of available target is something else. It might be interesting to see if we could also keep track of the ballpark probability of this scenario playing out as desired. It would be great, if the probability still stays in "imaginable numbers" (that do not need fast growing hierarchies to express).
One question concering the challenge itself:
Do I assume correctly, that any possible infinite damage combo in the deck is prohibited, even if our "optimal luck" never reaches that state? i.E. if there is any imaginable way to create an infinite damage combo with the cards in the deck it is no longer legal?
Another thing about the mathematics that struck me as strange:
Is the usage of Omega in the fast growing hierarchy consistent with the definition of ordinals?
It is clear to me, how the concept of Omega introduced in the desrcription is consistent in itself and very powerful. But in the example
F_{\Omega}(64)=F_{64}(64)<F_{65}(64)
, Omega compares to be smaller than 65, and deffitely not bigger than all the nonnegative integers...
So in other words, the Omega in the fast growing hierarchy seems to introduce a new concept, which to me is not realy coupled with ordinals - except maybe for the ordinals notion of "next higher number" with Omega and Epsilon.
Can some math-savy person point me into the right direction where this is resolved?