Ame-Shikō is four Bright cards including the Rain Man (November). It is worth 7 points, one less than Shikō, because the Rain Man is the “weak” Bright.

November · Rain Man

January · Crane on Pine

March · Cherry Blossom Curtain

August · Full Moon
The Rain Man (willow, Ono no Michikaze with an umbrella) plus any three of: Crane and Sun, Curtain, Moon, Phoenix.
Ame-Shikō replaces any smaller Bright yaku. If you capture the fifth Bright later in the round, it becomes Gokō (10 points).
Three Brights with the Rain Man do not count as Sankō. The Rain Man only helps once you hold four Brights. That's why experienced players don't rush to take it unless they already have the other Brights, or need the November capture for another reason.
Holding three Brights plus a willow card in hand is a good moment: if the Rain Man is on the field, capturing it gives you an instant 7-point yaku.
Willow is an awkward month: Bright, Swallow, ribbon and Lightning chaff share it. When you need the Rain Man, prefer keeping a willow match in hand rather than spending it early on a low-value capture. Conversely, if you only have two Brights, leaving the Rain Man for later often saves you from painting a target without a score.
Ame-Shikō uses the same Nintendo-style Koi-Koi scoring on Hanafuda Legends whether you play ranked, casual, private rooms, or vs computer. Set yaku replace smaller versions of the same family (you do not score Sankō and Shikō together), while unrelated yaku such as ribbons, animals and chaff still add to your total when you stop.
If you are new to the combination, practise in the tutorial or against the computer first, then take it into online play. How to Play covers the turn structure, matching, and when to call Koi-Koi versus stopping for points.