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Roll the Dice

Introduction

Roll the Dice presents a straightforward gambling game, where participants wager on whether the sum of two rolled dice will be above or below a specific number of their choosing.

Rules

  1. Two ordinary six-side dice are used.
  2. Players can select any number ranging from 2 to 12.
  3. Additionally, players have the option to predict whether the next outcome will exceed or fall short of their selected number, but they cannot place bets on impossible outcomes, such as rolling below 2 or above 12.
  4. Ties LOSE

Analysis

The upcoming chart illustrates the count of potential winning combinations, the likelihood of winning, and the expected returns for all bets placed under a specified number.

Under Bets

Total Pays Winning
Combinations
Probability Return
3 35.28 1 0.027778 0.980000
4 11.76 3 0.083333 0.980000
5 5.88 6 0.166667 0.980000
6 3.53 10 0.277778 0.980556
7 2.35 15 0.416667 0.979167
8 1.68 21 0.583333 0.980000
9 1.36 26 0.722222 0.982222
10 1.18 30 0.833333 0.983333
11 1.07 33 0.916667 0.980833
12 1.01 35 0.972222 0.981944

The subsequent chart displays the number of winning combinations, winning probabilities, and returns for all bets placed above a designated number.

Over Bets

Total Pays Winning
Combinations
Probability Return
2 1.01 35 0.972222 0.981944
3 1.07 33 0.916667 0.980833
4 1.18 30 0.833333 0.983333
5 1.36 26 0.722222 0.982222
6 1.68 21 0.583333 0.980000
7 2.35 15 0.416667 0.979167
8 3.53 10 0.277778 0.980556
9 5.88 6 0.166667 0.980000
10 11.76 3 0.083333 0.980000
11 35.28 1 0.027778 0.980000

Strategy

The most advantageous bets lie on totals below 10 and above 4, offering a return rate of 98.33%.

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