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If this means locking in a small loss, then so be it, we will make it back on the next one. There is a way to minimise this problem so that it rarely happens though.
You will find with most arbs that 1 side of the bet has odds that are rare, and the other side is either pretty common, or just slightly better than the rest. If you always make sure you place the rare side first, there is a much lower risk of the 2nd bet changing odds on you.