feat(misc): give every /gacha option an equal chance

The rarity tag now only styles the wish animation and the result text, so
/gacha picks like /random.

docs/deploy-coolify-selfhosted.md

@@ -88,9 +88,9 @@ reply is immediate.
 `/gacha` uses the same service and token: the bot swaps the URL's last path
 segment, so `.../api/gif` becomes `.../api/gacha`. It renders a 7-second
 `640x360` silent MP4 wish animation, posts `Wishing...` while it renders, and
-falls back to a text reply such as `★★★★★ Pizza` on the same failures. Options
-tagged `*4` or `*5` are rarer, following Genshin base rates (5★ 0.6%, 4★ 5.1%,
-3★ 94.3%) over the tiers present; untagged options are 3★.
+falls back to a text reply such as `★★★★★ Pizza` on the same failures. Every
+option is equally likely, as with `/random`; a `*4` or `*5` tag only sets the
+rarity shown in the animation and reply. Untagged options are 3★.
 
 ## 1. MongoDB Atlas (M0)
 

internal/modules/misc/gacha_command.go

@@ -26,11 +26,6 @@ const (
 	gachaDefaultRarity = gachaMinRarity
 )
 
-// gachaTierRates are Genshin Impact's base single-wish odds per mille. A
-// pick first rolls a tier among the tiers present, then an option uniformly
-// within it, so untagged input is a plain uniform pick.
-var gachaTierRates = map[int]int{5: 6, 4: 51, 3: 943}
-
 // gachaRarityTag matches a trailing "*3", "*4", or "*5" rarity tag.
 var gachaRarityTag = regexp.MustCompile(`\s*\*\s*([345])$`)
 
@@ -58,35 +53,6 @@ func parseGachaOptions(arg string) []gachaOption {
 	return out
 }
 
-// pickGachaOption returns the index of the wished option. rng may be nil to
-// use the global source.
-func pickGachaOption(options []gachaOption, rng *rand.Rand) int {
-	intN := rand.IntN
-	if rng != nil {
-		intN = rng.IntN
-	}
-	byRarity := map[int][]int{}
-	total := 0
-	for i, option := range options {
-		if len(byRarity[option.Rarity]) == 0 {
-			total += gachaTierRates[option.Rarity]
-		}
-		byRarity[option.Rarity] = append(byRarity[option.Rarity], i)
-	}
-	roll := intN(total)
-	for rarity := gachaMaxRarity; rarity >= gachaMinRarity; rarity-- {
-		tier := byRarity[rarity]
-		if len(tier) == 0 {
-			continue
-		}
-		if roll < gachaTierRates[rarity] {
-			return tier[intN(len(tier))]
-		}
-		roll -= gachaTierRates[rarity]
-	}
-	return 0 // unreachable: roll < total, the sum of present tier rates.
-}
-
 // gachaResultText renders an option as its stars followed by its label.
 func gachaResultText(option gachaOption) string {
 	return strings.Repeat("★", option.Rarity) + " " + option.Label
@@ -106,7 +72,9 @@ func gachaCommand() modules.Command {
 			if len(options) == 0 {
 				return chathelper.Reply(ctx, b, update.Message, gachaUsage)
 			}
-			winner := pickGachaOption(options, nil)
+			// Every option is equally likely; the rarity tag only styles the
+			// wish animation and the result text.
+			winner := rand.IntN(len(options))
 			results := make([]string, len(options))
 			for i, option := range options {
 				results[i] = gachaResultText(option)

internal/modules/misc/gacha_command_test.go

@@ -3,7 +3,6 @@ package misc
 import (
 	"context"
 	"encoding/json"
-	"math/rand/v2"
 	"net/http"
 	"net/http/httptest"
 	"reflect"
@@ -29,55 +28,6 @@ func TestParseGachaOptions(t *testing.T) {
 	}
 }
 
-// One option per tier must land near the Genshin base rates.
-func TestPickGachaOption_FollowsTierRates(t *testing.T) {
-	options := []gachaOption{{"five", 5}, {"four", 4}, {"three", 3}}
-	rng := rand.New(rand.NewPCG(1, 2))
-	const rolls = 200_000
-	counts := make([]int, len(options))
-	for range rolls {
-		counts[pickGachaOption(options, rng)]++
-	}
-	for i, wantPerMille := range []float64{6, 51, 943} {
-		got := float64(counts[i]) / rolls * 1000
-		if got < wantPerMille*0.85 || got > wantPerMille*1.15 {
-			t.Errorf("%s rate = %.2f‰, want about %.0f‰", options[i].Label, got, wantPerMille)
-		}
-	}
-}
-
-func TestPickGachaOption_UniformWithinTier(t *testing.T) {
-	options := []gachaOption{{"a", 3}, {"b", 3}, {"c", 3}, {"d", 3}}
-	rng := rand.New(rand.NewPCG(3, 4))
-	counts := make([]int, len(options))
-	for range 40_000 {
-		counts[pickGachaOption(options, rng)]++
-	}
-	for i, n := range counts {
-		if n < 9_000 || n > 11_000 {
-			t.Errorf("option %d picked %d times, want about 10000", i, n)
-		}
-	}
-}
-
-// Missing tiers do not dilute the odds: with only 4★ and 5★ options, the
-// 4★ share is 51/(51+6).
-func TestPickGachaOption_RenormalisesPresentTiers(t *testing.T) {
-	options := []gachaOption{{"five", 5}, {"four", 4}}
-	rng := rand.New(rand.NewPCG(5, 6))
-	five := 0
-	const rolls = 100_000
-	for range rolls {
-		if pickGachaOption(options, rng) == 0 {
-			five++
-		}
-	}
-	got := float64(five) / rolls
-	if want := 6.0 / 57; got < want*0.9 || got > want*1.1 {
-		t.Fatalf("5★ share = %.4f, want about %.4f", got, want)
-	}
-}
-
 func TestGacha_EmptyArgsRepliesUsage(t *testing.T) {
 	for _, text := range []string{"/gacha", "/gacha , ,", "/gacha *5"} {
 		t.Run(text, func(t *testing.T) {