1. ## Shark Attack! statistics/odds/prizes/betting

Imagine you are playing a computer game called Shark Attack!

There are 10 sets of waves (called tides), and each tide has 10 waves. Within each tide there will always be a shark which appears at random in one of those ten waves.

At the beginning of each tide, the player rolls a single 10-sided dice. At the end of each tide, the player will roll another dice to try and match the shark in the next tide. The object is for the player's dice roll to match the wave which contains the shark. If the player "wins" a tide because their dice roll matches the wave where a shark appeared, they gain 1 in their score. At the end of 10 tides their score is totaled. For each point they have won, they get to roll a single 10 sided dice, and the result of their roll will determine what bag number they win.

Now the big issue is the prize rewards. The money system is in gold pieces. For the game, 1 million gold in currency is a pretty standard amount and common to have. Imagine there are 10 bags, ranked from least to greatest (1 being least and 10 being greatest. Let's pretend a buy-in amount for a player to play a whole game (10 tides with 10 waves each tide) is 500,000 gold.

For the bag prize amounts, consider maybe:

bag 1 100,000 gold
bag 2 300,000 gold
bag 3 500,000 gold
bag 4 600,000 gold
bag 5 700,000 gold
bag 6 800,000 gold
bag 7 900,000 gold
bag 8 1 million gold
bag 9 2.5 million gold
bag 10 5 million gold

Since I know very little about statistics/gambling, do those prize amounts seem fair to both the player and dealer? From what I can tell, the player always has 1/10 chance of getting the correct wave that contains a shark. Beyond that, there's a few things I cannot quite understand. Are those prize amounts fair? What are the odds of a player hitting the bat #10 with 5 million gold when they roll? Is there a better way to handle the prizes, for example..different amounts for prizes that makes it equally fair to the dealer and the player?

2. ## Re: Shark Attack! statistics/odds/prizes/betting

Simplify your problem. As far as I can see you are doing the equivalent of rolling 10 D10 and counting the number of 1's that come up. This has a binomial distribution B(10,0.1). Hence you can calculate the probability mass function for any number of wins at this stage from 0, .., 10, you can look this up on Wikipedia. But the mean number of wins is 1.

For the next stage we need to ask are there just 10 bags, and if you roll the same number twice you only wing the bag once?

If you don't understand the statistics the sensible thing to do is simulate the game.

.

3. ## Re: Shark Attack! statistics/odds/prizes/betting

By the way, it should be "one die". "Dice" is the plural of "die".