Cheat Dice

A game of dice against the computer where the computer can be configured to sustain a certain win rate.

Multiplayer support ?

• yup.

Can the Human player cheat ?

• absolutely.
  
  If you set your player name to "AlphaDice" the computer will help you win

Installing

• go get github.com/zkynet/cheatdice

Running the game

• go run main.go

Game rules

1. The game is divided into “rounds.” During each round, each player gets one “turn.”
2. On a turn the player rolls two six-sided dice.
3. The player wins the round that gets a double (or higher double if many players get doubles). If no player gets a double then the higher total wins. If two have the same total, then the player with the highest number on a die wins. If two players rolled the same numbers on their dice then the round is a draw and no player gets a point.
4. On the next round the players switch turns, i.e. player indexed 0 always starts, followed by 1 then 2 then 3 .. etc.
5. The rounds continue until a human player decides to quit.

How the computer cheats

When it cheats

The computer will start cheating once it passes the configured "FirstCheatRound". Once it has passed it will only cheat if it is under the set "WinningPercent".

How it cheats

When it is the computers turn, it will roll a dice (dice inception intended) to determine one of three methods it can use to cheat.

• The first method ( Double )
  • The computer performs a normal roll but will then set one dice to be equal to the other.
• The Second method ( Highest total )
  • the computer performs a normall roll but wil then check if any dice are lower then 3, if they are the set them to 3. Once both dice have been checked and possibly raised above 3, they get +1 to their value.
• The third method ( Highest Dice )
  • The computer performs a normall roll but then set's once dice to be equal to 5. I thought about using 6 here but the density of sixes in the roll log was too high with that setting. 5 seemed to fit better and still produce optimal win rates.

Why it seems random

1. This kind of cheating does not rely on reading the apponents dice, thus there is no 1-1 relation between the human dice roll and the cheat methods.
2. The cheating interval, win percentage and number of cheating method can be adjusted for each game. This makes it even more difficult to detect if optimized properly.

Small footnotes on cheating

The higher the difficulty of the game the harder it is to achive high win percentages while making it seem random. For example if the player count goes from 2 to 4 you will see about 20% lesser win rate then the rate you set it for. Same goes for the number of cheat methods, how often you can cheat in a row and what round you start cheating on. All of these settings affect the win rate and can be tuned in various ways.

How to adjust cheat rate

type Game struct {
    ...
	CheatsInARow         int // how many times the computer can cheat in a row ( 0 means no limit )
	WinningPercent       float64 // the precentage of wins ( 0.1 to 0.9 )
	FirstCheatRound      int // when to start cheating
	NumberOfCheatMethods int // how any different methods to use for cheating
}

Testing

• go test -v

1.000.000 game test with 70% win rate

settings

globalGame.FirstCheatRound = 1
globalGame.WinningPercent = 0.7
globalGame.CheatsInARow = 0
globalGame.NumberOfCheatMethods = 3

output

=== RUN   TestCheating70PercentWin5PercentError1MillionRounds
Win rating: 0.699997
--- PASS: TestCheating70PercentWin5PercentError1MillionRounds (10.14s)

1.000.000 game test with 80% win rate

settings

globalGame.FirstCheatRound = 1
globalGame.WinningPercent = 0.8
globalGame.CheatsInARow = 0
globalGame.NumberOfCheatMethods = 3

output

=== RUN   TestWinningPercentage1000000Rounds
Win rating: 0.7957014298570143
--- PASS: TestWinningPercentage1000000Rounds (10.37s)

1.000.000 game test with 90% win rate

90% win rating is hard to reach while making it seem random. To get to 90% I lower the number of methods to be used for cheating. By default the weakest method is removed first.

• I only get up to about 85% win rate with 2 methods.

settings

globalGame.FirstCheatRound = 1
globalGame.WinningPercent = 0.9
globalGame.CheatsInARow = 0
globalGame.NumberOfCheatMethods = 2

output

=== RUN   TestWinningPercentage1000000Rounds
Win rating: 0.8492200779922008
--- PASS: TestWinningPercentage1000000Rounds (12.38s)

• Using only the best win method we can reach 90%, but it's not looking very random at this point.

settings

globalGame.FirstCheatRound = 1
globalGame.WinningPercent = 0.9
globalGame.CheatsInARow = 0
globalGame.NumberOfCheatMethods = 1

output

=== RUN   TestWinningPercentage1000000Rounds
Win rating: 0.89999600039996
--- PASS: TestWinningPercentage1000000Rounds (11.35s)

100 game test

settings

globalGame.FirstCheatRound = 1
globalGame.WinningPercent = 0.7
globalGame.CheatsInARow = 0
globalGame.NumberOfCheatMethods = 3

output

=== RUN   TestCheating70PercentWin10PercentError100Rounds
Win rating: 0.67
--- PASS: TestCheating70PercentWin10PercentError100Rounds (0.00s)

Example test suit output

zkynets-MacBook-Pro:cheatdice zkynet$ go test -v -bench=.
=== RUN   TestDiceRoll3000000TimesMax6
--- PASS: TestDiceRoll3000000TimesMax6 (2.89s)
=== RUN   TestDiceRollWithATie
=== RUN   TestDiceRollWithATie/Players_tie
=== RUN   TestDiceRollWithATie/Players_tie#01
--- PASS: TestDiceRollWithATie (0.00s)
    --- PASS: TestDiceRollWithATie/Players_tie (0.00s)
    --- PASS: TestDiceRollWithATie/Players_tie#01 (0.00s)
=== RUN   TestDiceRollWinMethodHighestDice
=== RUN   TestDiceRollWinMethodHighestDice/Player_0_wins_with_the_highest_dice
=== RUN   TestDiceRollWinMethodHighestDice/Player_0_wins_with_the_highest_dice#01
=== RUN   TestDiceRollWinMethodHighestDice/Player_0_wins_with_the_highest_dice#02
=== RUN   TestDiceRollWinMethodHighestDice/Player_1_wins_with_the_highest_dice
--- PASS: TestDiceRollWinMethodHighestDice (0.00s)
    --- PASS: TestDiceRollWinMethodHighestDice/Player_0_wins_with_the_highest_dice (0.00s)
    --- PASS: TestDiceRollWinMethodHighestDice/Player_0_wins_with_the_highest_dice#01 (0.00s)
    --- PASS: TestDiceRollWinMethodHighestDice/Player_0_wins_with_the_highest_dice#02 (0.00s)
    --- PASS: TestDiceRollWinMethodHighestDice/Player_1_wins_with_the_highest_dice (0.00s)
=== RUN   TestDiceRollWinMethodHigherTotal
=== RUN   TestDiceRollWinMethodHigherTotal/Player_0_wins_with_a_higher_total
=== RUN   TestDiceRollWinMethodHigherTotal/Player_1_wins_with_a_higher_total
--- PASS: TestDiceRollWinMethodHigherTotal (0.00s)
    --- PASS: TestDiceRollWinMethodHigherTotal/Player_0_wins_with_a_higher_total (0.00s)
    --- PASS: TestDiceRollWinMethodHigherTotal/Player_1_wins_with_a_higher_total (0.00s)
=== RUN   TestDiceRollWinMethodDouble
=== RUN   TestDiceRollWinMethodDouble/Player_0_wins_with_a_double
=== RUN   TestDiceRollWinMethodDouble/Player_1_wins_with_a_double
=== RUN   TestDiceRollWinMethodDouble/Player_0_wins_with_a_higher_double
=== RUN   TestDiceRollWinMethodDouble/Player_1_wins_with_a_higher_double
--- PASS: TestDiceRollWinMethodDouble (0.00s)
    --- PASS: TestDiceRollWinMethodDouble/Player_0_wins_with_a_double (0.00s)
    --- PASS: TestDiceRollWinMethodDouble/Player_1_wins_with_a_double (0.00s)
    --- PASS: TestDiceRollWinMethodDouble/Player_0_wins_with_a_higher_double (0.00s)
    --- PASS: TestDiceRollWinMethodDouble/Player_1_wins_with_a_higher_double (0.00s)
=== RUN   TestCheating70PercentWin10PercentError100Rounds
--- PASS: TestCheating70PercentWin10PercentError100Rounds (0.00s)
=== RUN   TestCheating70PercentWin10PercentError1MillionRounds
--- PASS: TestCheating70PercentWin10PercentError1MillionRounds (3.38s)
=== RUN   TestCheating70PercentWin5PercentError1MillionRounds
--- PASS: TestCheating70PercentWin5PercentError1MillionRounds (3.34s)
=== RUN   TestMultiplayerCheating50PercentWin10PercentError1MillionRounds
--- PASS: TestMultiplayerCheating50PercentWin10PercentError1MillionRounds (5.70s)
=== RUN   TestMultiplayerCheating50PercentWin5PercentError1MillionRounds
--- PASS: TestMultiplayerCheating50PercentWin5PercentError1MillionRounds (5.74s)
goos: darwin
goarch: amd64
pkg: github.com/zkynet/cheatdice
Benchmark4PlayerGame-4            200000              5699 ns/op
Benchmark2PlayerGame-4            500000              3368 ns/op
BenchmarkDiceRoll-4              2000000               931 ns/op
PASS
ok      github.com/zkynet/cheatdice     26.806s

Roll log for 100 games

44-34
33-24
24-44
11-31
31-45
22-45
56-33
44-64
61-23
52-55
56-14
42-21
44-11
45-26
66-13
64-22
62-51
25-24
45-54
54-36
53-54
46-33
45-65
56-41
34-64
64-24
66-46
33-11
52-16
66-24
45-24
45-46
64-61
45-16
64-25
66-21
34-22
46-22
56-42
52-46
44-42
33-14
23-65
55-34
54-25
45-34
44-53
64-53
62-41
22-25
66-12
14-56
64-46
53-44
46-14
44-22
45-32
35-11
44-56
46-43
63-63
52-45
64-11
56-64
56-24
64-52
62-11
51-45
56-51
14-12
66-31
56-45
42-32
56-52
11-61
55-61
66-22
45-61
65-54
56-43
22-65
22-22
51-25
44-64
25-41
44-33
56-22
26-31
52-31
66-55
43-41
64-13
46-65
34-52
55-16
22-36
12-41
54-46
54-42
61-51