This seem similar to "Penney's game" and the "Humble-Nishiyama Randomness Game" (https://en.wikipedia.org/wiki/Penney%27s_game https://en.wikipedia.org/wiki/Pen

This seem similar to "Penney's game" and the "Humble-Nishiyama Randomness Game" (https://en.wikipedia.org/wiki/Penney%27s_game https://en.wikipedia.org/wiki/Penney%27s_game) - betting on which coin-toss sequence appears first. For the 3-bit game there is also always a better pattern.