Normal or not normal? If a work can be found in pi, then one would think a Finite State Gambler (FSG) would succeed on the portion of pi equivalent to the work. But FSGs cannot succeed on normal sequences, meaning this sequence would be non-normal.

Of course this begs the question of whether a number normal over an infinite sequence can contain sub-sequences that are non-normal - sequences of 100 tails will occur in sufficiently large completely normal (randomized) sequences of random coin tosses, e.g.

As for the citation, there is this: http://en.wikipedia.org/wiki/Disjunctive_sequence

If this is correct, then you are correct, the conjecture would hold if pi were normal. But then wouldn't an FSG be able to succeed on the sub-sequence? Of is that acceptable, provided that the FSG fails on the overall sequence?

Normality is sufficient, but I do not think it is necessary. Normality requires that if the number is represented in any base b then each each of the b possible digits occure with density 1/b. All that is needed for every work to appear is that each digit occur at least once. They do not have to occure with equal density.