Some time ago I estimated the chance that John would run 100 from an open start based on his first tries for 527. That was one chance in four. In his current series at Bull Shooters, he has had 25 runs over 100. From that it is easy to estimate how many of those runs should have gotten to 200 -- simply a quarter of them, or 6.25. In fact he had 5 runs of 200 or more. Similarly, the number of runs over 300 should be about 1.6 and there has been one.
Those results say that the 1/4 probability for 100 is in the right ballpark. It is possible to estimate the number of times John has to pass 100 to have one run of 527. That is somewhere around 300 100s. It is also something like 20 runs of 300.
But those are averages and a 500 could happen on his next inning. If you play the Lotto until you win the big prize, you will probably have gotten five out of six numbers dozens of times first, but paradoxically few Lotto winners hit even one five of six before they win the big prize. If we had 2000 Schmidts starting on 2000 different tables tomorrow, it is likely that one of them would run over 527 on his first try.