Probabilities in Casinos and Deception
http://www.gamblingcity.net/casino-games/online-roulette/odds.php
http://www.fastodds.com/game_odds/
https://blackboard.cornell.edu/bbcswebdav/courses/ENGRD2700-Henderson-Fall2011/HW3%282%29.pdf
We got introduced to probabilities in our class, so I tried looking for practical ways people make use of probability so I researched about casino winning probabilities. And looked at roulette specifically:
After multiplying out all the payoffs and the probabilities to get the expectation we see that a player expectation is negative and that the house edge of a single zero roulette is 2.7% and for a double zero it is 5.6%.
This is why the house always win in the end.
In an even more interesting note, I have also researched and found a homework problem(from a different class) that uses probability to deceive people in a different way: where people intuitive choices may fool them.
Say there are 4, 6 sided dices. Each of them have different numbers on their sides:
the first one has number 4 on all the sides.
the second one has number 7 on 2 of the sides and number 3 on 4 of the sides
the third one has number 6 on 3 of the sides and number 2 on 3 of the sides
the fourth one has number 5 on 4 of the side and number 1 on 2 of the sides.
After doing all the calculations you would find that first die beats second die 2/3 of the time, second die beats the third die 2/3 of the time, and the third die beats the fourth die 2/3 of the time.
Now here comes the really cool part:
Intuitively, a person would think that since die 1 beats 2 and 2 beats 3 and 3 beats 4, die 1 would also beat die 4. But in reality die 4 actually beats die 1 2/3 if the time too.
So a money making game can be made where the player is told that 1 beats 2 and 2 beats 3 and 3 beats 4 two thirds of the time. And after informing the player about this, you would tell the player to pick first to give him the “advantage” since the player would think die one will be the absolute best choice. This advantage is then turned into a disadvantage when you pick die 4 if the player picks die 1. Therefore in this game, the player will only win with a probability of 1/3.
Mastering the ins and outs of probability is a critical step in becoming a master of deception ……;)
If you have the option of either playing American or European roulette, always choose European roulette. You don’t have to be a rocket scientist to realize the odds are much better when playing the European version.