Dreidel

Happy Hanukkah! First we present an internationalized version of the Dreidel, a four-sided spinning top. And second we simulate a gambling dice game played with the Dreidel.

Simulate the spinning top

/ Here are labels for the 4 sides of the dreidel in three languages /
sides gets {"yiddish": ["nisht", "halb", "gants", "shtel ayn"], ...
  "english": ["nothing", "half", "gets all", "share"], ...
  "hebrew": ["נ","ה","ג","ש"]}

/ We instantiate our dreidel using one of the languages, in this case Yiddish /
dreidel gets quote(choose(sides after "yiddish"))
/ Roll the dreidel 3 times /
dreidel; dreidel; dreidel
/ Make an array with three rolls /
3 # dreidel
/ Roll it 100,000 times and compute a frequency table rounded to 2 decimal places /
100000 # dreidel |> freq |> round

sides ← {"yiddish":["nisht","halb","gants","shtel ayn"],"english":["nothing","half","gets all","share"],"hebrew":["נ","ה","ג","ש"]}

dreidel ← quote(choose(sides ∘ "yiddish"))
dreidel → "halb"
dreidel → "gants"
dreidel → "shtel ayn"
3 # dreidel → ["nisht", "halb", "nisht"]
round(freq(100000 # dreidel)) → {"gants":0.25,"halb":0.25,"nisht":0.25,"shtel ayn":0.25}

Simulate the gambling game

Second we simulate an entire game of dreidel. Our program uses the following variables:

• n is the number of players
• N is the number of turns played per game
• t is the current turn; each player gets one roll per turn
• p is current player 0..n-1
• result is the player's roll: nisht, halb, ganz or shteyl ayn
• pieces is the number of game pieces (chocolate gelt, pennies, or raisins) each player begins with
• players is an array that shows how many pieces each player has
• pot is the number of pieces in the pot
• sum is the sum of the pot plus all the players' pieces
• zerosum is a sanity check that says sum must equal n*pieces, it should always evaluate to true
• ante is the number of game pieces each player must ante every time he rolls "shteyl ayn" or when the pot is empty

A game uses the following rules:

• At the beginning of each round, every participant puts ante game pieces into pot. In addition, every time the pot is empty, every player puts ante into the pot.
• Each player spins the dreidel once during their turn. Depending on which player side is facing up when it stops spinning, they give or take game pieces from the pot:
• If נ (nun/nisht/nothing) is facing up, the player does nothing.
• If ג (gimel/ganz/gets all) is facing up, the player gets everything in the pot.
• If ה (hei/halb/half) is facing up, the player gets half of the pieces in the pot. (If there are an odd number of pieces in the pot, the player takes the half the pot rounded up to the nearest whole number.)
• If ש (shin/shteyl ayn/share) is facing up, the player adds ante game piece(s) to the pot.
• If the player is out of pieces, they get a "loan", so the number of game pieces a player has may go negative!

Initially, let's make the following assumptions: assume n=2 players, ante=1, pieces=10. The system plays for N=100 turns. Here is the input:

setup gets { ...
  init gets { n set 2; ante set 1; pot set 0; pieces set 10; N set pieces^2; p set 0; t set 1; players set n#pieces }; ...
  anteup gets { players set players-ante; pot set pot+n*ante; true }; ...
  halb gets { amount set floor(1/2*(pot+1)); pot set pot-amount; players set update(players,(players after p)+amount,p); "halb" }; ...
  ganz gets { amount set (players after p)+pot; players set update(players,amount,p); pot set 0; "ganz" }; ...
  shtelayn gets { amount set (players after p)-ante; pot set pot+ante; players set update(players,amount,p); "shtel ayn" }; ...
  nisht gets { "nisht" }; ...
  sum gets pot + sum players; ...
  zerosum gets n*pieces=sum; ...
  play gets { ...
    init; ...
    while(t<=N) { ...
      while(p<n) { ...
        anteflag set if[pot=0, anteup, true, false]; ...
        roll set d4; ...
        result set if[roll=1,halb,roll=2,ganz,roll=3,shtelayn,roll=4,nisht]; ...
        str set str + "Turn=" + t + ", round=" + p + ", ante=" + anteflag + ", result=" + result + ", players=" + stringify(players) + ", pot=" + pot + ", zerosum=" + zerosum + "\n"; ...
        p set p+1 ...
      }; ...
      t set t+1; p set 0 ...
    }; ...
    str ...
  }; ...
  "ready" ...
}

setup
play

Here is the corresponding output:

setup ← {/* Omitted for brevity */}

setup → "ready"

Turn=1, round=0, ante=true, result=ganz, players=[11,9], pot=0, zerosum=true

Turn=1, round=1, ante=true, result=halb, players=[10,9], pot=1, zerosum=true

Turn=2, round=0, ante=false, result=nisht, players=[10,9], pot=1, zerosum=true

Turn=2, round=1, ante=false, result=halb, players=[10,10], pot=0, zerosum=true

Turn=3, round=0, ante=true, result=ganz, players=[11,9], pot=0, zerosum=true

Turn=3, round=1, ante=true, result=halb, players=[10,9], pot=1, zerosum=true

Turn=4, round=0, ante=false, result=halb, players=[11,9], pot=0, zerosum=true

Turn=4, round=1, ante=true, result=halb, players=[10,9], pot=1, zerosum=true

Turn=5, round=0, ante=false, result=ganz, players=[11,9], pot=0, zerosum=true

Turn=5, round=1, ante=true, result=nisht, players=[10,8], pot=2, zerosum=true

Lots of output omitted for brevity...

Turn=95, round=0, ante=false, result=shtel ayn, players=[20,-2], pot=2, zerosum=true

Turn=95, round=1, ante=false, result=halb, players=[20,-1], pot=1, zerosum=true

Turn=96, round=0, ante=false, result=shtel ayn, players=[19,-1], pot=2, zerosum=true

Turn=96, round=1, ante=false, result=halb, players=[19,0], pot=1, zerosum=true

Turn=97, round=0, ante=false, result=nisht, players=[19,0], pot=1, zerosum=true

Turn=97, round=1, ante=false, result=ganz, players=[19,1], pot=0, zerosum=true

Turn=98, round=0, ante=true, result=shtel ayn, players=[17,0], pot=3, zerosum=true

Turn=98, round=1, ante=false, result=ganz, players=[17,3], pot=0, zerosum=true

Turn=99, round=0, ante=true, result=ganz, players=[18,2], pot=0, zerosum=true

Turn=99, round=1, ante=true, result=ganz, players=[17,3], pot=0, zerosum=true

Turn=100, round=0, ante=true, result=shtel ayn, players=[15,2], pot=3, zerosum=true

Turn=100, round=1, ante=false, result=ganz, players=[15,5], pot=0, zerosum=true

play → "done"

At this point, if you wanted to play again, you could just issue the play command.

Now let's change the following assumptions: assume n=4 players, ante=3.

NB. You could also modify the line anteflag set if[pot=0, anteup, true, false]; ... so that players must ante up if pot=0 or pot=1. Some versions of the rules call for this. We're not going to do this in our example though.

Here is the input:

setup gets { ...
  init gets { n set 4; ante set 3; pot set 0; pieces set 10; N set pieces^2; p set 0; t set 1; players set n#pieces }; ...
  anteup gets { players set players-ante; pot set pot+n*ante; true }; ...
  halb gets { amount set floor(1/2*(pot+1)); pot set pot-amount; players set update(players,(players after p)+amount,p); "halb" }; ...
  ganz gets { amount set (players after p)+pot; players set update(players,amount,p); pot set 0; "ganz" }; ...
  shtelayn gets { amount set (players after p)-ante; pot set pot+ante; players set update(players,amount,p); "shtel ayn" }; ...
  nisht gets { "nisht" }; ...
  sum gets pot + sum players; ...
  zerosum gets n*pieces=sum; ...
  play gets { ...
    init; ...
    while(t<=N) { ...
      while(p<n) { ...
        anteflag set if[pot=0, anteup, true, false]; ...
        roll set d4; ...
        result set if[roll=1,halb,roll=2,ganz,roll=3,shtelayn,roll=4,nisht]; ...
        str set str + "Turn=" + t + ", round=" + p + ", ante=" + anteflag + ", result=" + result + ", players=" + stringify(players) + ", pot=" + pot + ", zerosum=" + zerosum + "\n"; ...
        p set p+1 ...
      }; ...
      t set t+1; p set 0 ...
    }; ...
    str ...
  }; ...
  "ready" ...
}

setup
play

Here is the corresponding output:

setup ← {/* Omitted for brevity */}

setup → "ready"

Turn=1, round=0, ante=true, result=ganz, players=[19,7,7,7], pot=0, zerosum=true

Turn=1, round=1, ante=true, result=shtel ayn, players=[16,1,4,4], pot=15, zerosum=true

Turn=1, round=2, ante=false, result=halb, players=[16,1,12,4], pot=7, zerosum=true

Turn=1, round=3, ante=false, result=shtel ayn, players=[16,1,12,1], pot=10, zerosum=true

Turn=2, round=0, ante=false, result=nisht, players=[16,1,12,1], pot=10, zerosum=true

Turn=2, round=1, ante=false, result=ganz, players=[16,11,12,1], pot=0, zerosum=true

Turn=2, round=2, ante=true, result=halb, players=[13,8,15,-2], pot=6, zerosum=true

Turn=2, round=3, ante=false, result=ganz, players=[13,8,15,4], pot=0, zerosum=true

Turn=3, round=0, ante=true, result=shtel ayn, players=[7,5,12,1], pot=15, zerosum=true

Turn=3, round=1, ante=false, result=ganz, players=[7,20,12,1], pot=0, zerosum=true

Turn=3, round=2, ante=true, result=nisht, players=[4,17,9,-2], pot=12, zerosum=true

Turn=3, round=3, ante=false, result=ganz, players=[4,17,9,10], pot=0, zerosum=true

Turn=4, round=0, ante=true, result=ganz, players=[13,14,6,7], pot=0, zerosum=true

Turn=4, round=1, ante=true, result=nisht, players=[10,11,3,4], pot=12, zerosum=true

Turn=4, round=2, ante=false, result=ganz, players=[10,11,15,4], pot=0, zerosum=true

Turn=4, round=3, ante=true, result=halb, players=[7,8,12,7], pot=6, zerosum=true

Turn=5, round=0, ante=false, result=halb, players=[10,8,12,7], pot=3, zerosum=true

Turn=5, round=1, ante=false, result=halb, players=[10,10,12,7], pot=1, zerosum=true

Turn=5, round=2, ante=false, result=shtel ayn, players=[10,10,9,7], pot=4, zerosum=true

Turn=5, round=3, ante=false, result=nisht, players=[10,10,9,7], pot=4, zerosum=true

Lots of output omitted for brevity...

Turn=98, round=0, ante=false, result=nisht, players=[-13,14,91,-55], pot=3, zerosum=true

Turn=98, round=1, ante=false, result=ganz, players=[-13,17,91,-55], pot=0, zerosum=true

Turn=98, round=2, ante=true, result=nisht, players=[-16,14,88,-58], pot=12, zerosum=true

Turn=98, round=3, ante=false, result=nisht, players=[-16,14,88,-58], pot=12, zerosum=true

Turn=99, round=0, ante=false, result=shtel ayn, players=[-19,14,88,-58], pot=15, zerosum=true

Turn=99, round=1, ante=false, result=ganz, players=[-19,29,88,-58], pot=0, zerosum=true

Turn=99, round=2, ante=true, result=shtel ayn, players=[-22,26,82,-61], pot=15, zerosum=true

Turn=99, round=3, ante=false, result=nisht, players=[-22,26,82,-61], pot=15, zerosum=true

Turn=100, round=0, ante=false, result=shtel ayn, players=[-25,26,82,-61], pot=18, zerosum=true

Turn=100, round=1, ante=false, result=halb, players=[-25,35,82,-61], pot=9, zerosum=true

Turn=100, round=2, ante=false, result=ganz, players=[-25,35,91,-61], pot=0, zerosum=true

Turn=100, round=3, ante=true, result=nisht, players=[-28,32,88,-64], pot=12, zerosum=true

play → "done"

Last update: Fri Sep 23 2016