St Petesburg Paradox

You need to throw a coin.

1. If you get heads, you lose and earn 2ⁱ money being i the number of times the coin was flipped.
2. If you get tail, you continue playing and do i = i + 1.

• Mathematician Bernoulli discovered this game in 17th century
• The expected value of the income the player wins is infinite.
• This is a paradox!!!

I first set the ui.R in which I put only 2 slider inputs.

sliderInput("n_bank", "How much the Casino is charging to play", value = 500, min = 10, max = 10000)

The slider for the input is similar          

The paradox has 2 points of view:
- The player (how much you'll pay to play)
- The Casino (how much you'll charge to let them play)

The app has a plot in which:

• the X axis is the money you won in a round
• the Y axis is the numbers of times you actually won that in a round

The plot is in the server.R section in the line

    output$plot <- renderPlot({
        plot(tabla())
    })

    ```

Using 10.000 experiments this is the output

This is the fun part:

You'll need to change the sliders in order to have a “winnable” setup.

• We know the expected value of winning is infinite but: is this really true?
• The summary will simple substract the money you won and the money the casino charged you to play the game.

Example with 25$ charge of bank and 10000 time played (don't play if the bank charge 25$ ;))

[1] "You won 128776 and you paid 250000 final money -121224"

In this part I only show the table of the current game.

• outcome is the amount of money you won in 1 round.
• freq is the number of rounds that matched this money

   outcome Freq
1        2 4962
2        4 2499
3        8 1293
4       16  661
5       32  304
6       64  148
7      128   69
8      256   24
9      512   23
10    1024    7
11    2048    5
12    4096    4
13    8192    1