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Dice Arena

Introduction

Dice Arena is a simple dice game I noticed at the Bovada Internet casino on July 7, 2025. The goal is to get a higher dice total than the dealer.

Rules

  1. The player must choose a mode to play in. Following are the choices:
    • Medium -- Player two dice vs. dealer two dice.
    • Low -- Player two dice vs. dealer one die.
    • High -- Player one die vs. dealer two dice.
  2. Dice will be rolled according to the mode chosen.
  3. If the player has the higher total, he wins according to the total rolled.
  4. If the player and dealer tie, the player will win according to the mode chosen.
  5. If the dealer has the higher total, the player loses.
  6. Following are the specific pay tables according to the mode chosen.

The following table shows what wins pay (on a "for one" basis) in Medium mode. All ties pay 1 for 1.

Medium Mode
Player Total Win Pays
3 21
4 10
5 5
6 2.5
7 1.3
8 1.2
9 1.2
10 1.2
11 2
12 4

 

The following table shows what wins pay (on a "for one" basis) in Low mode. All ties pay 1 for 2.

Low Mode
Player Total Win Pays
2 10
3 4
4 2
5 1.2
6 0.9
7 0.6
8 0.6
9 0.9
10 1.2
11 1.5
12 3

 

The following table shows what wins pay (on a "for one" basis) in High mode. All ties pay 2 for 1.

High Mode
Player Total Win Pays
3 46
4 20
5 6
6 4

 

Please note the game help screen incorrectly state a winning 6 pays 1 for 1. It actually pays 4 for 1.

Example

 

In the image above I bet $1 in "high" mode, meaning my one die against two dealer dice. My six beat the dealer's total of 5. My win was 4 for 1.

Analysis

The following table shows my analysis in Medium mode. The right column shows the expected return for that the roll of that row. The lower right cell shows an expected return of 98.06%.

Medium Mode
Player Total Win Pays Prob. Roll Prob. Win Prob. Tie Prob. Loss Exp. Ret.
2   0.027778 0.000000 0.027778 0.972222 0.000772
3 21 0.055556 0.027778 0.055556 0.916667 0.035494
4 10 0.083333 0.083333 0.083333 0.833333 0.076389
5 5 0.111111 0.166667 0.111111 0.722222 0.104938
6 2.5 0.138889 0.277778 0.138889 0.583333 0.115741
7 1.3 0.166667 0.416667 0.166667 0.416667 0.118056
8 1.2 0.138889 0.583333 0.138889 0.277778 0.116512
9 1.2 0.111111 0.722222 0.111111 0.166667 0.108642
10 1.2 0.083333 0.833333 0.083333 0.083333 0.090278
11 2 0.055556 0.916667 0.055556 0.027778 0.104938
12 4 0.027778 0.972222 0.027778 0.000000 0.108796
Total   1.000000       0.980556

 

The following table shows my analysis in Low mode. The right column shows the expected return for that the roll of that row. The lower right cell shows an expected return of 98.15%.

Low Mode
Player Total Win Pays Prob. Roll Prob. Win Prob. Tie Prob. Loss Exp. Ret.
2   0.027778 0.166667 0.166667 0.666667 0.048611
3 4 0.055556 0.333333 0.166667 0.500000 0.078704
4 2 0.083333 0.500000 0.166667 0.333333 0.090278
5 1.2 0.111111 0.666667 0.166667 0.166667 0.098148
6 0.9 0.138889 0.833333 0.166667 0.000000 0.115741
7 0.6 0.166667 1.000000 0.000000 0.000000 0.100000
8 0.6 0.138889 1.000000 0.000000 0.000000 0.083333
9 0.9 0.111111 1.000000 0.000000 0.000000 0.100000
10 1.2 0.083333 1.000000 0.000000 0.000000 0.100000
11 1.5 0.055556 1.000000 0.000000 0.000000 0.083333
12 3 0.027778 1.000000 0.000000 0.000000 0.083333
Total   1.000000       0.981481

The following table shows my analysis in High mode. The right column shows the expected return for that the roll of that row. The lower right cell shows an expected return of 98.15%.

High Mode
Player Total Win Pays Prob. Roll Prob. Win Prob. Tie Prob. Loss Exp. Ret.
1   0.166667 0.000000 0.000000 1.000000 0.000000
2 0 0.166667 0.000000 0.027778 0.972222 0.009259
3 46 0.166667 0.027778 0.055556 0.916667 0.231481
4 20 0.166667 0.083333 0.083333 0.833333 0.305556
5 6 0.166667 0.166667 0.111111 0.722222 0.203704
6 4 0.166667 0.277778 0.138889 0.583333 0.231481
Total   1.000000       0.981481

Written by: Michael Shackleford