What the odds really mean for how long a hunt might last.
Odds tell you the chance per attempt, not a countdown. Every encounter or reset is independent, so you are never "due" a shiny. What does grow with time is the chance that you have found at least one.
The table shows how many attempts it takes before your chance of having found at least one shiny reaches a given level. Reaching the full odds number (for example 4,096 attempts at 1 in 4,096) only gives you about a 63% chance. Around 1 in 3 hunters will go past that point, which hunters call going "over odds". That is normal luck, not a bug.
The chance of at least one shiny after N attempts is 1 minus (1 minus p) to the power of N, where p is the odds as a fraction. These figures are worked out with that formula, rounded up to whole attempts.