Extremely pleased to have cracked this one!
Here's how I solved it:
Solution attached. I was disappointed that the solution provided did not respond to the question from @alex and give a definitive answer regarding the correct probabilities. I know I’m way late to the party, but I’ll weigh in and agree that Alex has the correct probabilities. It looks like the solution from @patrick_digan did not exclude paths that go out of bounds.
Assuming that the question is which start slot has the highest probability of landing the Alteryx chip where it is in the diagram (i.e. Finish Slot 2), then the answer would be Start Slot 1 with a probability of 38.1%.
@Kenda did you have a chance to look at the second hint provided with the original problem labeled "Reshaping approach"? It explains the issue with the approach you described.
In your example of Start Slot 1 and row 3, one of the 4 possible paths goes out of bounds, but in your picture you have pointed it back in bounds and counted the same path twice. When starting in Slot 1, there are only three possible paths to row 3, not 4, so the probability that you calculated should be 2/3, not 3/4. Here is an excerpt from the hint that explains it, using row 4 as an example. As it shows, on each row you need to subtract paths that go out of bounds and account for the adjustments in all subsequent calcs. Hope that is helpful.
I've been keeping this challenge on hold, as when I first came to it I thought it would be a nice use case for the Python SDK tool. Now that I more or less have it, I should try with the new Python tool...
(the tool needs some polishing --and clarification of what the "position" actually means-- but that's for another day)
Here is my solution - short, simple and generic
All you need to change are 2 parameters in Text input tool: Number of slots and Number of rows
Main workflow to run batch macro with list of slots in initial row as control parameter
Batch macro that runs iterative macro for every slot in initial row
And finally iterative macro that takes possible slots with their probabilities in previous row and calculate possible slots and their probabilities in the next row