# Backgammon Probability

## Hypothesis

As the game is computer run and the decisions are made by someone or something, its possible that the odds will favour the computer. Therefore I predict that the computer will overall recieve more double rolls.

## Method

To collect the data, 25 games of backgammon were played and the results of each roll, moves and doubles were recorded. The game was played on the Backgammon Free app, with 6 'easy' games recorded, 11 'medium' and 8 'hard'. The final outcome of the game was also recorded as well as the beginning turn of the the game.

## Results

The results collected, are conveyed through the graphs above. When the game was played on the 'Easy' level, the double rolls were recorded as 25/294 for the player, and 23/294 for the computer. For the 'Medium' level, the player received 44/561 double rolls and the computer received 45/561. Lastly, the results for level 'Hard' are 29/419 for the player and the computer obtained 53/419 double rolls.

## Analysis

Looking at the results recorded, it can be seen that overall the number of doubles the player acquired was 98/1274 and the computer had 121/1274. These results portray that the computer most definitely received more doubles, but if you look at the levels separately that thought changes. Consider 'Easy' level, the double rolls documented are similar in amounts. In fact the player actually receives 2 more double rolls than the computer. Similarly the 'Medium' level are also very close in doubles rolled, with only 1 roll being the difference, this time in favour of the computer. However when looking at the 'Hard' setting, it is seen that the computer acquires a lot more double rolls compared to the player. Not only are the double rolls uneven, but none of the players who played on the 'Hard' setting, could beat the computer. The computer always won. Although after analysing the data for the 'Easy' level, all of the players won, and for the 'Medium' level 7/11 players beat the computer.

## Conclusion

After analysing the data and focusing on the results, the computer does receive more doubles overall. Most of this unfairness was obtained in the 'Hard' level, demonstrating that the computer cheats when playing a more skillful required setting.