R 提高圣彼得堡模拟的速度

我正在try 编写R函数来模拟圣彼得堡悖论.在这个悖论中，我们抛出一枚公平的硬币，直到第一次出现 tail .每一轮，我们得到2^N美元.

为此，我编写了一个R函数:

    simulate_games <- function(n = 1000, max_turns = 10) {
    results <- data.frame(game_number = integer(), number_of_turns = integer(), final_reward = 

    numeric())
  
    for (i in 1:n) {
    turns <- 0
    reward <- 0
    
    while (turns < max_turns && runif(1) > 0.5) {
      turns <- turns + 1
      reward <- 2^(turns )
    }
    
    results <- rbind(results, data.frame(game_number = i, number_of_turns = turns, final_reward = reward))
    }
  
  return(results)
}
results <- simulate_games()

我感兴趣的最终结果是:

c(mean(results$number_of_turns), mean(results$final_reward))

现在，我正在try 加快对大量"n"的模拟:

library(doParallel)
library(foreach)

simulate_games_parallel <- function(n = 1000000, max_turns = 10) {
    cl <- makeCluster(detectCores() - 1) 
    registerDoParallel(cl)
    
    results <- foreach(i = 1:n, .combine = rbind, .packages = "doParallel") %dopar% {
        turns <- 0
        reward <- 0
        
        while (turns < max_turns && runif(1) > 0.5) {
            turns <- turns + 1
            reward <- 2^(turns)
        }
        
        data.frame(game_number = i, number_of_turns = turns, final_reward = reward)
    }
    
    stopCluster(cl)
    return(results)
}

results <- simulate_games_parallel()

我做得对吗？有没有更有效的方法来做到这一点？