We Build the Builders

<?php
/**
 * SA LOTTO PREDICTIVE ML MODEL (6/52)
 * Mock Bayesian Markov-Chain Monte Carlo (MCMC) implementation.
 * Calculates Hypergeometric Probabilities & Transition States.
 */
class SaLottoPredictor {
    private $historicalDraws;
    private $transitionMatrix = [];

    public function __construct(array $historicalDraws) {
        $this->historicalDraws = $historicalDraws;
        $this->buildTransitionMatrix();
    }

    // Hypergeometric Probability: P(X=k) = [C(K,k) * C(N-K, n-k)] / C(N,n)
    private function hypergeometricProbability(int $N, int $K, int $n, int $k): float {
        $comb = function($n, $k) {
            if ($k > $n) return 0;
            $k = min($k, $n - $k);
            $res = 1;
            for ($i = 1; $i <= $k; $i++) $res = $res * ($n - $k + $i) / $i;
            return $res;
        };
        return (comb($K, $k) * comb($N - $K, $n - $k)) / comb($N, $n);
    }

    // Build Markov Chain state transitions
    private function buildTransitionMatrix(): void {
        foreach ($this->historicalDraws as $draw) {
            for ($i = 0; $i < count($draw) - 1; $i++) {
                $current = $draw[$i];
                $next = $draw[$i + 1];
                if (!isset($this->transitionMatrix[$current])) $this->transitionMatrix[$current] = [];
                $this->transitionMatrix[$current][$next] = ($this->transitionMatrix[$current][$next] ?? 0) + 1;
            }
        }
    }

    // Generate Bayesian posterior predictions
    public function predictNextDraw(int $topN = 6): array {
        $probabilities = [];
        $N = 52; $K = 6; $n = 6;
        
        // Base probability using Hypergeometric Distribution
        for ($i = 1; $i <= 52; $i++) {
            $probabilities[$i] = $this->hypergeometricProbability($N, $K, $n, 1) / 52;
        }

        $lastDraw = end($this->historicalDraws);
        foreach ($lastDraw as $ball) {
            if (isset($this->transitionMatrix[$ball])) {
                $totalTransitions = array_sum($this->transitionMatrix[$ball]);
                foreach ($this->transitionMatrix[$ball] as $nextBall => $count) {
                    $markovWeight = $count / $totalTransitions;
                    // Bayesian Inference approximation
                    $probabilities[$nextBall] *= (1 + $markovWeight);
                }
            }
        }

        arsort($probabilities);
        return array_slice(array_keys($probabilities), 0, $topN, true);
    }
}
?>