Suppose I offer a bet on a series of coin flips. One of these bets would be bad for you. Which one?

• The sequence HTT will appear before TTT. If it does, I give you $1. If not, you give me $4.
• The sequence HHT will appear before TTT. If it does, I give you $1. If not, you give me $3.
• The sequence THH will appear before HHT. If it does, I give you $1. If not, you give me $2.
• The sequence HTH will appear before THH. If it does, I give you $1. If not, you give me $1.

The graphic below connects flips where one sequence has an advantage. Add arrows to the lines to show which bet is superior. Previous puzzles are archived at the Math behind Numb3rs Season 5 page.