# I have to design a game using combinations and permutations which meets the house edge of 10-15%.

#### JxssicaLxwliet

##### New member
Hello everyone,

This is my first time posting on this website and I am unsure if I am doing this correctly. I apologise in advance.

I have to design a game using combinations and permutations which meets the house edge of 10-15%. The game I have designed requires the player to choose 3 cards from a standard deck of 52 cards. The first card has to be black (26C1), the second has to be hearts and and Ace through to 10 of hearts (10C1) and the last will decide the winning amount:

 $100 Ace of diamonds (1C1) 26C1 * 10C1 * 1C1 = 260$50 2 or 3 of diamonds (2C1) 26C1 * 10C1 * 2C1 = 520 $10 4, 5 or 6 of diamonds (3C1) 26C1 * 10C1 * 3C1 = 780$5 7, 8, 9 or 10 of diamonds (4C1) 26C1 * 10C1 * 4C1 = 1040 $2 J, Q or K of either hearts or diamonds (6C1) 26C1 * 10C1 * 5C1 = 1560 And then all the cases where the player loses: -$1 - Red (26C1), (Black, H(J/Q/K, Diamonds) and (Black, Red(A-10)) (26C1 * 42C1 * 46C1 = 50232)

After subtracting the sum of the winning hands (4160) from the total amount of hands (52C3 = 22100), I saw that the remainder was 17940. I figured out that 26C1 * 30C1 * 23C1 = 17940 but I am not sure how those numbers relate to the losing outcomes of my problem.
I want there to be an order associated with the cards (if the first card chosen isn't black, it is an automatic loss), but I don't know how to do that.
I also know that the house edge for this game is not 10-15% since the loss ratio is 81% (17940/22100) and I have simulated this game and my results have a loss ratio of 97% across 100,000 randomised hands. I don't know how to calculate the house-edge and I don't know how to change my game so that it can fit the required 10-15%.

I hope that I have explained this properly and hope to receive valuable feedback.
Thank you

Edit:
I have since changed my values. These are the new winning prizes:
 Prize: Average Percentage from Simulation of 100,000 randomised hands: Product of probability and prize $100 0.190%$0.19 $50 0.375%$0.19 $30 0.582%$0.18 $20 0.803%$0.16 $10 1.219%$0.12 -$1 96.797% -$0.97
The sum of the products in the right column equals -$0.12 which I think means that the house has a 12% profit since 1 game costs$1. I am not sure if this is correct yet and I still require help in figuring out the correct way to calculate these values.
Thank you

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