Daniel Craig
Daniel Craig

Load Packages

library(mosaic)
set.seed(2026)

Rules of the Game

European Roulette Wheel European Roulette, like American Roulette consists of players placing bets on indiviual numbers or various groups of numbers, before the dealer rolls a ball in the wheel as it spins. When the ball lands any players who’s bet contained the number the ball landed on get paid depending on the type of bet they placed, for example a player who bet on black would receive a 1 to 1 payout while a player who bet on 2 would receive a 35 to 1 payout. The European Roulette wheel contains 37 slots, 18 red and 18 black, numbered 1-36, and 1 green 0.

The Specific Bet

The bet I am analysing is the even number bets which are betting on red or black, and even or odd. The payout is 1 to 1. Unlike American Roulette however, if the ball lands on the green 0 the player gets a second chance for the ball to land on their chosen bet, if it does they get the money they bet back.

The Probability Distribution

Below is a table representing the probability distribution for the bet.

Winnings Probability
+$1 18/37
0 1/37 * 18/37
-$1 18/37 + 1/37 * 19/37

There is a 18/37 chance of winning the bet, a 1/37 * 18/37 chance of getting your money back, and a 18/37 + 1/37 * 19/37 chance of losing your money.

Expected Value

The expected value, or the “average winnings” of the bet is -0.01387, which means that for every time a player bets one dollar they’ll lose an average of -0.013 cents.

x <- c(1,0, -1)
probs <- c(18/37, 1/37 * 18/37, 18/37 + 1/37 * 19/37)
expected_value <- sum(x*probs)
expected_value
## [1] -0.01387874

Tree Diagram

Tree Diagram
Tree Diagram

Being Even or Ahead

1-pbinom(4, 10, 18/37)
## [1] 0.5893746
1-pbinom(48, 98, 18/37)
## [1] 0.4335478
1-pbinom(492, 985, 18/37)
## [1] 0.1980504
1-pbinom(4921, 9843, 18/37)
## [1] 0.003659605
Number of Bets Probability of being Even or Ahead
10 0.5893746
100 0.4335478
1000 0.1980504
10000 0.003659605

Simulation

trials <- 1:10000
outcomes <- sample(x=c(1,0, -1), size=10000, prob=c(18/37, 1/37*18/37, 18/37 + 1/37 * 19/37), replace=TRUE)
even_money_european <- data.frame(trials, outcomes)
even_money_european
ggplot(even_money_european, aes(x=outcomes)) + geom_histogram()
## `stat_bin()` using `bins = 30`. Pick better value `binwidth`.

favstats(even_money_european$outcomes)

Conclusion

In conclusion, the even money bet in European Roulette feels safer because of the extra chance to recover your wager when the ball lands on zero, but the math above shows that it still favors the casino. The probability distribution, expected value, mean, and median all show a small but steady loss over the simulation. Though this amount only amounts to 1-2 cents per dollar bet. While a player may be able to get ahead, if they play many rounds the chance of breaking even or making a profit gets smaller over time. Over thousands of spins like in this simulation the house edge will still always win which is why casinos are still profitable.

Sources

Roulette, E. (2017, March 22). European roulette wheel. Gambling concept. Top view. Casino Roulette… IStock. https://www.istockphoto.com/vector/european-roulette-wheel-gm656008950-119518953

Barber, L. (2016, February 15). Which Bond does it better? Daniel Craig’s 007 wagers and winnings compared to Sean Connery, Roger Moore, Pierce Brosnan, Timothy Dalton and even George Lazenby’s gambling wins. City AM. https://www.cityam.com/which-bond-is-the-biggest-gambler-daniel-craig-sean-connery-roger-moore-pierce-brosnan-timothy-dalton-and-even-george-lazenbys-007-wagers-and-winnings-compared/

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