1. Make the first toss to find the probability (\(p\)) that Alice wins in a single toss
- we cannot choose an arbitrary \(p\) because we know that we obtained the intermediate observation \(A=5;B=3\)
- … so what we do is:
- choose a \(p\) randomly between 0 and 1
- simulate 8 throws and count how often Alice won
- keep the \(p\) if Alice won 5 times
logArray = rep(FALSE, 8)
while ( sum(logArray) != 5 ) {
pInit = runif(1, min = 0, max = 1) # choose some p from a uniform distribution on (0,1)
pNext8 = runif(8, min = 0, max = 1) # throw 8 times, Alice wins every time the real number is below pInit
logArray = (pNext8 < pInit) # how many times did Alice win? Loop stops if this is 5
}
sum(logArray) == 5 # this is TRUE now, i.e. we have a good pInit because Alice won 5 times with it
## [1] TRUE
cat(paste("The initial toss came up with p =", round(pInit,3) , "\n"))
## The initial toss came up with p = 0.285
- it is convenient to collect these commands in a function:
get_pInit <- function() {
logArray = rep(FALSE, 8)
while ( sum(logArray) != 5 ) {
pInit = runif(1, min=0, max=1)
pNext8 = runif(8, min=0, max=1)
logArray = (pNext8 < pInit)
}
return(pInit)
}
- we can have a look at the empirical distribution of \(pInit\)
trials = 5000
pInitArray = numeric(trials )
for (i in 1:trials ) pInitArray[i] = get_pInit()
hist(pInitArray, col = "red", breaks = 40, main = "Distribution of pInit knowing A=5 ; B=3") # posterior distribution
![](data:image/png;base64,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)
2. Play the game one time
- to start with, let us play one game
- we start with the result already obtained: \(A=5;B=3\)
pInit = get_pInit() # prior knowledge already included (via the distribution of pInit)
AlicePoints = 5 # current score
BobsPoints = 3
while ( (AlicePoints < 6) && (BobsPoints < 6)) {
nextThrow = runif(1, min = 0, max = 1) # one toss
if ( nextThrow <= pInit) {AlicePoints = AlicePoints + 1} else {BobsPoints = BobsPoints + 1}
}
AliceWins = (AlicePoints == 6)
BobWins = (BobsPoints == 6)
if(AliceWins) cat("Alice won.") else cat("Bob won.")
## Alice won.
3. Play the game many times
- now, play a lot of games and see how often both players win
- in every game, we choose a new initial \(p\) by rolling the first ball (important!)
- we save the initial probabilities to check if the posterior distribution was correct
NumberAliceWins = 0
NumberBobWins = 0
numberGames = 5000
pInitArray = numeric(numberGames)
for (i in 1:numberGames) {
pInit = get_pInit() # renew in each game!
pInitArray[i] = pInit # save for histogram of posterior distribution
AlicePoints = 5 # current score
BobsPoints = 3
while ( (AlicePoints < 6) && (BobsPoints < 6)) { # play this game until one participant wins
nextThrow = runif(1, min = 0, max = 1)
if ( nextThrow <= pInit) {AlicePoints = AlicePoints + 1} else {BobsPoints = BobsPoints + 1}
}
if(AlicePoints == 6) {NumberAliceWins = NumberAliceWins + 1} else {NumberBobWins = NumberBobWins + 1}
}
(NumberAliceWins + NumberBobWins) == numberGames # This must be TRUE
## [1] TRUE
4. Results
- look at the posterior distribution generated above
hist(pInitArray, col="red", breaks=40, main="P(p|A=5,B=3)")
![](data:image/png;base64,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)
odds = NumberAliceWins/NumberBobWins
cat(paste("The odds was", signif(odds, 3), "\n"))
## The odds was 9.92
- we cannot expect that the odds simulated here exactly agrees with the theoretical prediction
- neither will we obtain the same result if the algorithm is run repeated times
- however, in the vast majority of the cases, the result will be closer to the Bayesian prognosis
- the higher the number of games played, the bigger the probability that the result comes closer to the Bayesian prediction
mailto:uwe.menzel@matstat.de