> Suppose there are two branches, 0 and 0'. Miner receives 0 first. The probability of mining a block is proportional to the time spent mining. Miner thus (a) s

> Suppose there are two branches, 0 and 0'. Miner receives 0 first. The probability of mining a block is proportional to the time spent mining. Miner thus (a) starts mining 0 immediately upon notification and (b) has a greater probability of finding a block on 0 than 0'. Your mistake is in the last point. The probability of finding a block in the next X time units is completely independent of what you did in the past (unless you managed to break the underlying cryptographic hash somehow ;-)). You can think of mining as repeated coin throws (with an extremely biased coin).