Sure, here is the step-by-step reasoning behind Shannon's estimate:

1. Assume an average chess game lasts 40 moves (this is just an estimate, actual game lengths vary)
2. Assume that on average, each player has around 10 possible reasonable moves to choose from at each turn (this is a rough estimate, the actual number varies based on the position)
3. Therefore, for each pair of moves (one by each player), there are around 10 x 10 = 100 possibilities
4. Over 40 moves, there are 40 pairs of moves
5. Therefore, the total number of possible move sequences is 100 x 100 x ... x 100 (40 times) = 10^120

This is just an estimate, and the actual number will be lower due to constraints on legal moves and repetition. But it gives an upper bound on the enormity of the game tree. The key steps are:
1) Estimate average game length
2) Estimate average branching factor (number of reasonable moves per turn)
3) Raise the branching factor to the power of the game length to get an upper bound
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