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@open-rgs/picks

A pick round is priced by what it removes.

Three shapes cover nearly every pick bonus, and they differ only in what ends the round: a fixed number of picks, a stop symbol, or a single wheel spin. The prizes are ordinary weighted sets, so the sampler that fills a reel fills a pick pool.

Reveals remove what they revealed

This is the whole pricing model. A pick round takes items off the board, so the odds move as the player picks. Drawing with replacement instead looks identical on screen and pays a different distribution, and the gap widens with every pick.

import { pool, pooledFrom, pickN, remainingCount } from "@open-rgs/picks";

// an explicit board
const boxes = pool(["1", "2", "5", "10", "BOMB", "BOMB"]);

// or one drawn from weights, once, before the picking starts
const drawn = pooledFrom({ "1": 50, "5": 30, "25": 15, "100": 5 }, 12, host.rng_next);

const { pool: after, picked } = pickN(boxes, 3, host.rng_next);
remainingCount(after);   // 3

Reveals are uniform over what is left, deliberately: the weights already shaped the pool when it was built, so weighting the reveal as well would apply them twice. Asking for more picks than the board holds reveals what is there, because a five-pick bonus on a four-box board is an authoring mistake and failing the round mid-flight makes it the player's problem.

Keep picking until a stop

The genre's second shape: collect prizes until the bomb. The stop is included in what was picked, because the player saw it and a report that hides it cannot be reconciled against the screen.

import { revealUntil } from "@open-rgs/picks";

const round = revealUntil(boxes, (b) => b === "BOMB", host.rng_next);

round.picked;      // everything revealed, the BOMB included
round.stoppedBy;   // "BOMB", or undefined
round.exhausted;   // true when the board ran out first

How long such a round runs is arithmetic rather than a simulation result. With three bombs in twelve boxes it reveals 2.25 prizes on average, so moving the bomb count is moving that number:

expectedPicksBeforeStop(12, 3);   // 2.25
expectedPicksBeforeStop(12, 1);   // 5.5
expectedPicksBeforeStop(12, 6);   // 0.857

Wheels

A wheel is a weighted set with a name for its shape, because that is how a designer talks about it and because the segment list is what a client renders. Equal weights make an evenly divided wheel, which is what a player assumes they are looking at.

import { wheel, wheelValue } from "@open-rgs/picks";

const w = wheel({ MINI: 50, MINOR: 30, MAJOR: 15, GRAND: 5 });

w.spin(host.rng_next);        // "MINOR"
w.probabilityOf("GRAND");     // 0.05

// what the bonus is worth, before it ships
wheelValue(w, (seg) => JACKPOTS[seg]);   // 77.5x

spin takes the generator, while Sampler.pick takes a float. The two read alike at the call site, so passing a number says so rather than failing as "next is not a function".

Pricing the round

Because reveals are uniform without replacement, every item is equally likely to be among the first n, so the expected total is the pool's mean times the number of picks. That closed form is the number a designer tunes against, and it is why the with-replacement mistake is worth naming: it pays the same mean per pick and a different distribution, and a bonus is judged on its distribution.

expectedPickTotal(pool([1, 2, 3, 9]), 2, (n) => n);   // 7.5

// the same board, simulated 20,000 times, lands on the same number