I would argue that the sequence that appears has a probability 100%. This is a bogus probability problem.
A real problem would be the probability of the sequence appearing again after a second shuffle.
Shuffling cards is not a really random process. Each way of doing it leads to limited options. Itās difficult to Calculate. For example of I take two new deck of cards and riffle shuffle both once. The chance of getting the same arrangement is not as low as you calculate. 
ā¦ the reason is because of the same initial conditions and a similar method of shuffling.
And the probability of certain features evolving is 100%, because it evolved. This is the point that Behe usually fails to understand.
You left out natural selection again.
You havenāt shown any mutations that would have to happen simultaneously in order for the eye to evolve.
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The analogy assumes that all possible outcomes are equal.
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Assumptions need not be true.
Nits need not be picked.
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Itās realityā¦
Edit : As per mathematicians, a deck of cards needs to be shuffled 7 times to get a truly Ra Dom distributionā¦
https://www.nytimes.com/1990/01/09/science/in-shuffling-cards-7-is-winning-number.html
@swamidass: another non intuitive discovery by scienceā¦
No, but if we could demonstrate this through knock out experiments would you agree the hypothesis is falsified?
Do you see your reasoning is circular here?
By his logic, if I have a vocabulary of 200 words, then the chances of me repeating a word in an essay is 1 out of 200 factorial. Is it correct science to assume all mutations are equally possible?
Are you suggesting biologists look at mutations that way?
This is an interesting piece of trivia. But it canāt be science.
Edit: Besides, itās not like any particular combination is required. The important combinations would be those that cause a functional difference.
The problem is in-between the steps of selection.
Itās an analogy. Nit picking the analogy does nothing to change the main argument.
How is it a problem?
Not all mutations are equally probable. With respect to substitution mutations, CpG mutations have a much higher chance of occuring, and transition mutations will outnumber transversion mutations for the non-CpG mutations. Genetic recombination has a much higher chance of occuring in repeat regions due to complementary sequence. Transposons have a much higher chance of producing duplications than non-transposons.
However, the main argument still stands. The human population is large enough that we can still expect to see nearly every possible non-lethal substitution mutation in at least one human.
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Yes, but which mutations are significant in terms of function? Any random mutation is useless for evolution.
Tying mutations to differences in function is very difficult. However, there is no doubt that differences in function are due to differences in DNA sequence.
Would you agree that the differences between humans is due to differences in the DNA sequence of their genomes?
You are doing a blind search between selection steps through a sequence.
And how is that a problem?
I have already shown you that you are dealing with functional space that is a fraction of search space.
So arenāt you making a case against evolution?. Out of a really huge set of possible mutations ,only an unknown (much smaller?) number is functionally Significantā¦ this making the probability of getting functionally significant mutations potentially lower than the no: of molecules in the universe!
You canāt just do hand waving and say differences in humans is due to differences in DNA. What about environment , food habits, pollution, psychological condition, world view, religious beliefs, no: of siblings, marital status of parents etcā¦ all of these and more are statistically proven to cause differences between humans. The genotyoe phenotype connection is not air tight. Genetic difference might or might not cause phenotypic variation. Other causes also cause phenotypic variation.