Egg Cell Roulette: What is Player 1’s Probability of Winning Pharaoh Casino?

Egg Cell Roulette is a popular game played at Pharaoh Casino, where two players take turns throwing eggs at a spinning roulette wheel. The goal is to hit an egg cell, which will start to hatch, and the first to hatch fully will determine the winner. Player 1 throws first, and Player 2 throws second. In this article, we will examine what Player 1’s probability of winning is in Egg Cell Roulette at Pharaoh Casino.

The Rules of Egg Cell Roulette

Before we begin, let’s establish the rules of Egg Cell Roulette at Pharaoh Casino. The game is played with a roulette wheel that has eight egg cells on it. The egg cells are evenly spaced, and each egg cell has a different color: red, blue, green, yellow, pink, purple, orange, and black.

To play the game, two players take turns throwing eggs at the roulette wheel, trying to hit one of the egg cells. When an egg hits an egg cell, the egg cell will start to hatch. The first egg cell to hatch fully will determine the winner.

Player 1 throws the first egg, and Player 2 throws the second egg. If neither player hits an egg cell, the game is a tie. If both players hit the same egg cell, the game continues until one player hits a different egg cell.

Calculating Player 1’s Probability of Winning

To calculate Player 1’s probability of winning Egg Cell Roulette at Pharaoh Casino, we need to consider a few factors. First, we need to determine the probability of Player 1 hitting an egg cell on their first throw. Second, we need to consider the different outcomes that can occur once an egg cell has been hit.

Probability of Player 1 Hitting an Egg Cell on Their First Throw

There are eight egg cells on the roulette wheel, so the probability of Player 1 hitting any one of them on their first throw is 1/8 or 12.5%. Therefore, the probability of Player 1 missing all of the egg cells on their first throw is 7/8 or 87.5%.

Different Outcomes Once an Egg Cell Has Been Hit

Once an egg cell has been hit, there are three possible outcomes:

1. Player 1’s egg hits an unoccupied egg cell.
2. Player 1’s egg hits the same egg cell as Player 2’s egg.
3. Player 1’s egg hits a different egg cell than the one hit by Player 2’s egg.

Player 1 Hits an Unoccupied Egg Cell

If Player 1’s egg hits an unoccupied egg cell, Player 1 has a 1/8 chance of winning the game. This is because there is only one egg cell that Player 1 can hit to win the game.

Player 1 and Player 2 Hit the Same Egg Cell

If Player 1’s egg hits the same egg cell as Player 2’s egg, the game continues until one player hits a different egg cell. Therefore, Player 1’s probability of winning depends on how long the game continues.

Assuming that the game continues until one player hits a different egg cell, the probability of Player 1 winning in this scenario is 1/7 or 14.3%. This is because there are seven remaining egg cells that Player 1 can hit to win the game.

Player 1 Hits a Different Egg Cell than Player 2

If Player 1’s egg hits a different egg cell than the one hit by Player 2’s egg, Player 1 has a 1/7 or 14.3% chance of winning the game. This is because there are seven egg cells remaining that Player 1 can hit to win the game.

Final Calculation

To calculate Player 1’s overall probability of winning Egg Cell Roulette at Pharaoh Casino, we need to consider all of the possible outcomes and their probabilities. Here is the calculation:

Player 1's Probability of Winning Egg Cell Roulette at Pharaoh Casino = Probability of Player 1 Hitting an Egg Cell on Their First Throw * (Probability of Player 1 Winning if they Hit an Unoccupied Egg Cell + Probability of Player 1 Winning if they and Player 2 Hit the Same Egg Cell + Probability of Player 1 Winning if they Hit a Different Egg Cell than Player 2)

Substituting in the probabilities we calculated above, we get:

Player 1's Probability of Winning Egg Cell Roulette at Pharaoh Casino = 12.5% * (12.5% + 14.3% + 14.3%) = 4.91%

Therefore, Player 1’s probability of winning Egg Cell Roulette at Pharaoh Casino is approximately 4.91%.

Conclusion

In conclusion, Egg Cell Roulette is a fun and exciting game played at Pharaoh Casino. However, Player 1’s probability of winning is relatively low at approximately 4.91%. This is due to the low probability of hitting an egg cell on their first throw and the various outcomes that can occur once an egg cell has been hit. Nevertheless, with a bit of luck and skill, any player can win Egg Cell Roulette at Pharaoh Casino.