Here i am going to talk about Casino winning strategies. So many games in casino, let’s play DICE

If i throw 3 dices, what is the highest likelihood that a sum will appear ? Is it minimum of sum of 3 or maximum 18 respectively for each time 3 dices are thrown ?

First write a simple function of rolling a pair of dice with equal probability of 1/6.

roll <-function() 
  {

  die<- 1:6
  dice<-(sample(die,size=3, replace=TRUE, prob=c(1/6,1/6,1/6,1/6,1/6,1/6)))
  sum(dice)
}

roll()
## [1] 12

When i called the roll() function, sum will change each time. It could be 8 or 10 or etc

Now how many times of sum will each appear ? After all we want to guess the highest likelihood of a magic sum right ?

We will use simple qplot (from library(ggplot2)) and replicate function()

I am going to roll 10 times of the dice using replicate function.

roll_many_times <- replicate(10,roll())

Then plot a simple graph of 10 rolls

library(ggplot2)
qplot(roll_many_times, binwidth=1)

However if you stay casino for 24 hours and observe the number of rolls against time, the mean will change.

roll_many_times <- replicate(10000,roll())

Then plot a simple graph of 10000 rolls

library(ggplot2)

hist(roll_many_times, freq=FALSE, col=rainbow(3))
lines(density(roll_many_times), lty=2)

mean(roll_many_times)
## [1] 10.4838

The mean is therefore the likely “the sum of 3 roll dice” will appear if you stay long in Casino to watch.