GyaradosPlatinum

Every encounter has the same shiny chance, the Shiny Odds Per Try shown above. Each one is a separate roll that does not care how many you have already done, so the more you hunt, the higher your overall chance of at least one shiny. The formula below turns your odds and your number of tries into that combined chance.

chance after N tries = 1 − (1 − p)^N,  where  p = 1 / odds per try

Example at 1 in 8,192 (classic full odds): about 864 encounters for a 10 percent chance, 5,678 for 50 percent, and 18,862 for 90 percent.

The table above flips that around: it shows how many encounters it takes to reach a 10, 25, 50, and 90 percent chance at your current odds. Turning on boosts like the Shiny Charm, sandwiches, or chains improves your odds, so the encounter numbers drop.

These are estimates, not promises. Most games have no pity counter, meaning no guaranteed shiny no matter how many you hunt, so even Very Likely is not guaranteed: some hunters find one early, others go well past that point.