php poker 生成的随机结果与预期不符

Question

我对扑克股票进行了研究。我所做的是使用 pokerstove 程序选择一些。并使用该程序使用枚举所有方法计算股票。所以扑克炉结果:

我还制作了一个表格来存储随机结果:

CREATE TABLE poker_results
(
id int NOT NULL AUTO_INCREMENT,
matches_id int NOT NULL,  -- just for filtering in case I will want another starting hands.
result varchar(255) NOT NULL,
winner_hands varchar(255) NOT NULL,
PRIMARY KEY (id)
) 

结果列数据如下所示:Jd,9d,Qh,5c,Kc - 这代表板上的牌。

Winner_hands 列数据如下所示:Ks-Ac,6c-Ad,3c-Ah(可以是 1 手获胜，也可以是全部 8 手获胜)。

这是将结果生成到数据库的代码。它在 codeigniter 框架上。而且为了不复制整个 poker.php，我只复制了几个从中使用的函数:

protected function get_probabilities($hands, $board_cards = array()) {
        $players = count($hands);

        $board = implode('', $board_cards);
        $board = trim($board);
        if (empty($board)) {
            $board = '-';
        }
        $hx = '';
        $hand_counter = 1;

        foreach ($hands as $hand) {
            $hx .= '&h' . $hand_counter++ . '=' . $hand[0] . $hand[1];
        }
        
        $url = 'http://' . $this->poker_server . '/?board=' . $board . $hx . '&auth=' . $this->auth;
        
        

        //Output exm. string '0.1342, 0.2042, 0.13525, 0.52635'
        //WAR!! check if alive
        $result = $this->parse_url_link($url);
        
        if (substr($result, 0, 3) == 'Err') {
            $this->utils->logging('ERROR', 'Poker server authorization failed!');
        }
        
        //echo $result;

        return array(
            'hands' => $hands,
            'prob' => explode(', ', $result),
            'board' => $board_cards
        );
    }


// protected because in child class needed
    protected function get_poker_winner($table_winners) {
        $to_return = array();
        foreach($table_winners['prob'] as $key => $val) {
            if ($val > 0) {
                $to_return[] = $table_winners['hands'][$key][0] . '-' . $table_winners['hands'][$key][1];
            }
        }
        
        return $to_return;
    }

poker_tests.php

<?php if ( ! defined('BASEPATH')) exit('No direct script access allowed');


include_once(APPPATH . 'controllers/poker.php');    
require_once APPPATH . "libraries/downloaded/Mersenne_twister.php";
use mersenne_twister\twister; 

class Poker_tests extends Poker {   
    
    public function __construct() {
        parent::__construct();
    }

    /**
     * Generates data in database with such structure:
     * CREATE TABLE matches
     * (
     * id int NOT NULL AUTO_INCREMENT,
     * player_cards varchar(255) NOT NULL,
     * 
     * PRIMARY KEY (ID)
     * )
     * 
     * CREATE TABLE poker_results
     * (
     * id int NOT NULL AUTO_INCREMENT,
     * result varchar(255) NOT NULL,
     * PRIMARY KEY (id)
     * ) 
     * 
     * 
     * Here 1 match will have many results, because we use same preflop cards.
     * 
     * Text results appended to pokerstove.txt
     * 
     * 376,992 games     0.013 secs  28,999,384 games/sec
     * 
     * Board: 
     * Dead:  
     * 
     *          equity      win     tie             pots won    pots tied   
     * Hand 0:  20.925%     20.53%  00.40%           77382       1504.50   { KhQs }
     * Hand 1:  06.215%     03.50%  02.72%           13190      10239.00   { 9c4d }
     * Hand 2:  06.396%     04.08%  02.32%           15379       8734.00   { 8d4c }
     * Hand 3:  18.906%     18.15%  00.76%           68426       2847.50   { AcKs }
     * Hand 4:  08.767%     06.91%  01.86%           26032       7019.50   { 9h2c }
     * Hand 5:  10.204%     09.83%  00.38%           37044       1424.00   { Ad6c }
     * Hand 6:  09.046%     08.67%  00.38%           32678       1424.00   { Ah3c }
     * Hand 7:  19.541%     18.08%  01.46%           68154       5514.50   { 8c7c }
     * 
     * 
     * ---
     * 
     * 
     */
    public function run() {

        $this->benchmark->mark('start');

        $this->output->enable_profiler(TRUE);

        //close the current connection, because its not needed
        $this->db->close();

        $db_poker = $this->load->database('poker_test', TRUE);

        $sql = "INSERT INTO poker_results (result, winner_hands, matches_id) VALUES (?, ?, ?)";

        // matches_id = 1. Insert new match
        $table8_hands = 'Kh,Qs,4d,9c,4c,8d,Ks,Ac,2c,9h,6c,Ad,3c,Ah,7c,8c';  // do test with this. Do those win the right amount of time?

        for ($i=0; $i < 400000; $i++) { // pradejus id 100194

            $flop = $this->poker_flop($table8_hands);
            $turn = $this->poker_turn($flop, $table8_hands);
            $river = $this->poker_stop($turn, $table8_hands);
            //echo json_encode($river) . '<br>';

            $db_poker->query($sql, array($river['river_board'],  implode(',', $river['winner_hands8']), 2));
        }
        
        $db_poker->close();

        $this->benchmark->mark('end');
        echo $this->benchmark->elapsed_time('start', 'end') . '<br>';
    }



    

    /**
     * 
     * Override - remove unneeded things for test from that function in poker.php
     * Generates 3 flop cards
     */
    public function poker_flop($table8_hands) {
            
    
        $table8_cards = explode(',', $table8_hands);
        
        $table8_results = $this->random_result($table8_cards, 3);
        
        return $table8_results;

    }

    /**
     * Generates 1 turn card
     * @param $table8_hands - same as match score in database. But here we have hardcoded in run function
     * 
     */
    public function poker_turn($table8_flop, $table8_hands) {
            
            $table8_cards = explode(',', $table8_hands);
            
            //Join players cards and opened board cards         
            $table8_reserved_cards = array_merge($table8_cards, $table8_flop);

            //Pass all opened cards and get one new board card          
            $table8_results = $this->random_result($table8_reserved_cards, 1);
            
            //Merge all opened board cards
            $table8_results = array_merge($table8_flop, $table8_results);

            // this is flop and turn both           
            return $table8_results;
            
    }

    /**
     * 
     * Generates 1 river card
     */
    public function poker_stop($table8_flop_turn, $table8_hands) {
            
        $table8_cards = explode(',', $table8_hands);
        
        $table8_reserved_cards = array_merge($table8_cards, $table8_flop_turn);
        
        $table8_results = $this->random_result($table8_reserved_cards, 1);
                    
        $table8_results = array_merge($table8_flop_turn, $table8_results);

        
        $table8_hands = $this->array_to_hands_array($table8_cards);
    
        $flop_turn_results = implode(',', $table8_results);

        // $this->benchmark->mark('code_start');
        //Get new probabilities - they will be needed to determine if hand has won or not. When prob. > 0 - then won
        $table8_prob = $this->get_probabilities($table8_hands, $table8_results);

        // $this->benchmark->mark('code_end');
        // echo $this->benchmark->elapsed_time('code_start', 'code_end');
        
        return array(
            'winner_hands8' => $this->get_poker_winner($table8_prob),
            'river_board' => $flop_turn_results
        );
            
    }


    /**
     * for second generation - new random function
     * @param  array  $reserved_cards 
     * @param  integer $cards_amount   
     * @return array
     */
    protected function random_result($reserved_cards, $cards_amount = 5) {

        $card_types = array('s', 'c', 'h', 'd');
        $card_values = array('A', 2, 3, 4, 5, 6, 7, 8, 9, 'T', 'J', 'Q', 'K');

        $deck = array();
        foreach ($card_values as $value) {
            foreach ($card_types as $type) {
                $deck[] = $value . $type;
            }
        }

        $remaining_deck = array_diff($deck, $reserved_cards);
        // make keys sequence:
        $remaining_deck = array_values($remaining_deck);

        $results = array();

        while (count($results) != $cards_amount) {          

            $rand_card_key = $this->random(0, (count($remaining_deck) - 1));
            
            $results[] = $remaining_deck[$rand_card_key];

            // remove from deck         
            unset($remaining_deck[$rand_card_key]);
            // make keys sequence:
            $remaining_deck = array_values($remaining_deck);
        }
        
        return $results;
    }


    /**
     * Picks random element from range
     * @param  integer $from        
     * @param  integer $to          
     * @return integer              
     */
    private function random($from, $to) {

        if (file_exists('/dev/urandom')) {
            $twister4 = new twister;
            $twister4->init_with_file("/dev/urandom", twister::N); 

            return $twister4->rangeint($from, $to);
        }
        else {
            return mt_rand($from, $to); 
        }
    }    
}

正如我们在 random 函数中看到的那样 - 当我在 linux 上进行测试时，我将 twister 库与 linux dev/urnadom 一起使用，而当我在 windows 上进行测试时，我将使用 native mt_rand。没有注意到差异。

所以为了选择结果，我使用这样的查询:

获取结果总数

select count(*) from poker_results where matches_id = 2 and id < 296351 

得到手牌的总赢(赢+平)是多少:

select count(*) from poker_results where matches_id = 2 and id < 296351 and winner_hands like '%Kh-Qs%' 

要得到多少手牌:

select count(*) from poker_results where matches_id = 2 and id < 296351 and winner_hands like '%Kh-Qs%' and winner_hands != 'Kh-Qs'

扑克服务器是为了获取手牌权益。通过河牌胜率，我确定手牌是否赢了 - 当手牌胜率 > 0 时，它赢了。

此工具在另一台服务器上使用 - 有运行 python 程序的 php 代码，但在这里无关紧要。

http://pokersleuth.com/programmable-poker-calculator.shtml

该工具类似于 pokerstove，但它具有命令行版本。顺便说一句，不要买这个工具，我们买了但他们没有发送许可证 key ，就像他们不在乎一样。

现在结果:

https://docs.google.com/spreadsheet/pub?key=0ArMZCQvNc-oQdEs0a1UyMkFGazVoN09KZmU1Q0FCU0E&output=html&richtext=true

现在，如果我们进行比较，手牌获胜 + 平手的次数比 pokerstove 或 pokersleuth 显示的胜率更高。当我看 ant tie % - 它比扑克炉显示大得多。样本不是那么小。 Pokerstove 使用了将近 40 万场比赛，虽然少了一点，但趋势保持不变。首先，我尝试了更小的样本，比如 10K 游戏——同样的趋势。因此，当我再生成 100K 时，如果结果保持大致相同，我并不感到惊讶。此示例也是在 linux 上生成的。但是在 Windows 上也生成了大约相同的样本，但获胜次数仍然多于扑克牌显示，获胜百分比的总和也是 110-112%。

所以我们不理解 - 我是不是生成了错误的东西或者那些程序显示错误？显示错误 Assets 的程序不太可能，因为它们被广泛使用并且可能应该已经进行了大量测试。

更新:

I think I finally understood :) Pokersleuth computes the chances of ahand (two cards) winning knowing the 5 cards on the board. You arethen comparing these chances to the real outcome (knowing the hands ofall the other players). Right?

没错。我不得不写在这里，因为它不允许在评论中进行扩展讨论。

更新:

生成了更多行 - 当前在 Linux 服务器上为 515989，% 仍然与以前大致相同。所以不动

Answer 1

您生成了 296350 个结果，但 332911 次获胜和平局。

这个过程的任何部分是否调和了这样一个事实，即当出现平局时，它是在两只或更多只手之间？看起来领带被高估了。

计算您的总赢率和平局百分比，112.3371014%。相乘(生成的结果除以胜负数)。你会得到恰好 100%。这说明什么？

另外，看看 Ad6c 和 Ah3c。他们的平手数完全相同，而且很可能是同一手牌(获胜的是一对 A)。

但对于打平的手牌，该手牌会计算/加权两次(一次用于 Ad6c，一次用于 Ah3c)。这就是为什么您的领带百分比至少是应有的两倍。您必须根据打平的手数将平局计数归一化