Tuesday’s pattern will require, on average, fewer flips to be achieved. The two patterns differ only in their final required elements (Heads on Monday and Tails on Tuesday). So let’s look at success and failure AFTER successfully flipping the first two elements (HT). When you flip HTH on Monday, you stop counting. But suppose you fail and flip HTT on Monday, you would have to wait until you see the next H to start hoping for the pattern again. On Tuesday, however, if you flip HTT, you stop counting. But if you flip HTH, you have failed to achieve your goal of HTT, but you are one-third of the way to achieving it again (because you got the last H which can be used as the first element of the pattern).

On average, HTH will occur in about 10 flips and HTT will occur in about 8 flips.