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Scratch Dice

Introduction





Scratch Dice is a simple game offered by SOFTSWISS software. There is one bet only that pays based on the roll of three dice. The outcome is revealed like a scratch card.

Rules



Following are the rules for Scratch Dice. All wins are on a "for one" basis.

  1. The player shall make a wager.
  2. The player shall scratch a game card to reveal three dice.
  3. The following table shows the pay table according to the roll displayed.

    Scratch Dice Pay Table

    Roll Pays
    6-6-6 40
    5-5-5 30
    4-4-4 25
    3-3-3 20
    2-2-2 15
    1-1-1 10
    Straight Gold ticket


  4. If the player rolls a straight (1-2-3, 2-3-4, 3-4-5, or 4-5-6) in any order, then he shall get a secondary card known as a "Gold Ticket." The pay table of the Gold Ticket is as follows.

    Gold Ticket Pay Table

    Roll Pays
    6-6-6 180
    5-5-5 150
    4-4-4 120
    3-3-3 90
    2-2-2 60
    1-1-1 30



Analysis



The following table shows the expected return of a Gold Ticket. The lower right cell shows an average win of 2.92.

Gold Ticket — Return Table

Event Pays Combinations Probability Return
6-6-6 180 1 0.004630 0.833333
5-5-5 150 1 0.004630 0.694444
4-4-4 120 1 0.004630 0.555556
3-3-3 90 1 0.004630 0.416667
2-2-2 60 1 0.004630 0.277778
1-1-1 30 1 0.004630 0.138889
All other 0 210 0.972222 0.000000
Total 216 1.000000 2.916667


Given the value of a Gold Ticket, we can evaluate the value of the overall game. The lower right cell shows an expected return of 97.22%.

Scratch Dice — Return Table

Event Pays Combinations Probability Return
6-6-6 40 1 0.004630 0.185185
5-5-5 30 1 0.004630 0.138889
4-4-4 25 1 0.004630 0.115741
3-3-3 20 1 0.004630 0.092593
2-2-2 15 1 0.004630 0.069444
1-1-1 10 1 0.004630 0.046296
Straight 2.916667 24 0.111111 0.324074
All other 0 186 0.861111 0.000000
Total 216 1.000000 0.972222


Written by: Michael Shackleford