POW with ROW who has the higher chance to mine a block? A group of $N$ miners trying to mine a block, I am one of them. In one scenario they are using a POW(proof of work) algorithm and in another, they use a ROW(race of work) algorithm.
The mining process is to execute the function $m()$. It returns a random hash number between $0 - 2^{32}$. In case of POW the first miner the find a hash smaller than some value $L$ wins. In case of ROW, the miner with the smallest hash after $T$ minutes wins.
In both scenarios I have 10% of the mining power, I manage to execute $m()$ 10% of the total time it is executed by all the miners until someone wins.
In what scenario do I have more chances to win the block, POW or ROW?
Also does the answer is changing if instead of 10% I have $p$ percent?

Assume for simplicity no ties are possible, neither in values hashed, nor in timing (i.e. two miners cannot produce a hash "at the same time", so it's always obvious who won POW). Note that in both cases, the winning miner is the one with the lowest hash: this is obvious in ROW, but also in POW since the first hash below L is less than every hash that came before it. Then, if at the time the winner is declared you computed a fraction $f$ of all the hashes, for symmetry reasons the probability that the lowest hash is among those you computed is $f$.
