I would disagree with the answer by @kodlu. In classic differential cryptanalysis, we don't pay "probability" for the last rounds, but rather we pay for the enumeration of the involved key bits. In other words, decryption is not statistical.
And that's what makes using smaller $R$ difficuly: the key guesses. Ciphers have good diffusion and with each extra round to partially decrypt in the end, the number of key bits needed to be guessed in order to verify the output difference (now, statistically, per each key guess) grows very fast.
In addition, the shape of the output difference matters too: if it has high weight (activates many S-boxes in the consequent rounds), more key bits guesses are needed.
Note that $R$ and the number of key bits to guess are in a trade-off: smaller $R$ increases differential probability, but also increases the number of key bits to guess. Usually, the gain in differential probability by going from $R=n-1$ to $R=n-2$ does not outbalance the increase in key guess complexity when partially decrypting 2 rounds instead of 1.