brumby

A fast, allocation-free Monte Carlo model of a top-N podium finish in racing events. Derives probabilities for placing in arbitrary positions given only win probabilities. Also derives joint probability of multiple runners with arbitrary (exact and top-N) placings.

Performance

Circa 15M simulations/sec of a top-4 podium over 14 runners using the tinyrand RNG. (Per thread, benchmarked on Apple M2 Pro.) Roughly 70% of time is spent in the RNG routine.

Example

Sourced from examples/multi.rs.

/*
use brumby::capture::{Capture, CaptureMut};
use brumby::mc;
use brumby::probs::SliceExt;
use brumby::selection::Selection;

// probs taken from a popular website
let mut probs = vec![
    1.0 / 2.0,
    1.0 / 12.0,
    1.0 / 3.0,
    1.0 / 9.50,
    1.0 / 7.50,
    1.0 / 126.0,
    1.0 / 23.0,
    1.0 / 14.0,
];

// force probs to sum to 1 and extract the approximate overround used (multiplicative method assumed)
let overround = probs.normalise(1.0);

println!("fair probs: {probs:?}");
println!("overround: {overround:.3}");

// create an MC engine for reuse
let mut engine = mc::MonteCarloEngine::default()
    .with_iterations(10_000)
    .with_win_probs(Capture::Borrowed(&probs))
    .with_podium_places(4);

// simulate top-N rankings for all runners
// NOTE: rankings and runner numbers are zero-based
for runner in 0..probs.len() {
    println!("runner: {runner}");
    for rank in 0..4 {
        let frac = engine.simulate(&vec![Selection::Span {
            runner,
            ranks: 0..rank + 1,
        }]);
        println!(
            "    rank: 0..={rank}, prob: {}, fair price: {:.3}, market odds: {:.3}",
            frac.quotient(),
            1.0 / frac.quotient(),
            1.0 / frac.quotient() / overround
        );
    }
}

// simulate a same-race multi for a chosen selection vector
let selections = vec![
    Selection::Span {
        runner: 0,
        ranks: 0..1,
    },
    Selection::Span {
        runner: 1,
        ranks: 0..2,
    },
    Selection::Span {
        runner: 2,
        ranks: 0..3,
    },
];
let frac = engine.simulate(&selections);
println!(
    "probability of {selections:?}: {}, fair price: {:.3}, market odds: {:.3}",
    frac.quotient(),
    1.0 / frac.quotient(),
    1.0 / frac.quotient() / overround.powi(selections.len() as i32)
);
*/