; the difference variables of turtles declared
turtles-own [ heads-count tails-count total-tosses heads-fraction tails-fraction]

to setup
  clear-all
  reset-ticks
  create-turtles 1
  ask patches [ set pcolor 59]

  ask turtles
  [
    ; intial random display of Heads ot Tails
    ifelse toss?
    [ set shape "coin_heads" ]
    [ set shape "coin_tails" ]
    set size 4
  ]
end

to go
  ask turtles
  [
    ; subsequent toss random results
    ifelse toss?
    ; if toss is true, execute the following
    [
      set shape "coin_heads"
      ; rotate the coin randomly form 0 to 360) for simulation effects only
      right random 361
      set heads-count ( heads-count + 1 )
    ]
    ; if toss is false, execute the following
    [
      set shape "coin_tails"
      right random 361
      set tails-count ( tails-count + 1 )
    ]

    ; calculation of some variables
   set total-tosses ( heads-count + tails-count )
   set heads-fraction ( 100 * heads-count / total-tosses )
   set tails-fraction ( 100 * tails-count / total-tosses )
  ]

  tick
end

; to report True (for Heads) or False (for Tails) randomly.
to-report toss?
  report random 2 = 0
end
@#$#@#$#@
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"heads" 1.0 0 -14835848 true "" "plot sum [ tails-fraction ] of turtles "
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MONITOR
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TEXTBOX
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Coin Toss Experiment:\n\nAfter resetting, click on \"Toss Once\" to flip the coin once. Click \"Keep Tossing\" to keep on tossing the coin continuously. The various self-explanatory monitors display the results of the coin tosses.
17
92.0
1

@#$#@#$#@
## WHAT IS IT?

NetLogo Coin Toss Experiment - to study "the principle of a priori probability".

## HOW IT WORKS

In every go-loop, or tick, the random function is called to display either a head or tails of a Coin. An additional random call rotates the Coin by an arbitrary angle to give the likeness of a coin toss. Connection of the Coin, the agent, to it's next state is entirely random and therefore has no connection with it's earlier state. (Subject to the limitations of the random function.)

## HOW TO USE IT
1. Clear all earlier states, information, displays, etc by hitting "Reset Tosses".

2. Click on "Toss Once" to toss the coin once. Observe the outcome is the Netlogo World. Obsever monitors and graphs. Keep clicking on "Toss Once" and keep observing the outcomes. Once you have got an understanding to the displays on the monitors and graphs, you can click on "Keep Tossing" and observe the outcome of a large number of tosses. Its good to observe a million or so tosses.

### Monitors to observe
- "Total Heads" (or "Total Tails", or "Total Tosses") monitor display the total number of Heads (or Tails, or the Total number of Tosses) executed so far.

- "H-T Difference" monitor displays the diffference between Heads to Tails outcome.

- "% of Heads" (or "% of Tails") display the percentage of Heads (or Tails) outcome.


## THINGS TO NOTICE

- As the number of tosses increase, the ratio of a "Heads" (or "Tails") approach 50% of the total number of tosses.

- Sometimes you may observe a large inequality (maybe about 1,000) between "Heads" and "Tails" outcome. But such differences are small compared to the total number of tosses.

## THINGS TO TRY

Run the Experiment a few times, each time for about 1000000 ticks. Observe the "H-T Difference" and also the plot which should taper out at 50% for both Heads (or Tails).

## HOW TO CITE

If you mention this model or the NetLogo software in a publication, we ask that you include the citations below.

For the model itself:

* Borah, A. (2023).  NetLogo Coin-Toss Model, Mokokchung, Nagaland.

Please cite the NetLogo software as:

* Wilensky, U. (1999). NetLogo. http://ccl.northwestern.edu/netlogo/. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.


## REFERENCES

1. Law of Large Numbers. https://en.wikipedia.org/wiki/Law_of_large_numbers
2. Fundamental Postulate of Statistical Physics. https://en.wikipedia.org/wiki/Statistical_mechanics#Fundamental_postulate

## COPYRIGHT AND LICENSE

- Licence: Free to Copy, Modify and Distribute.
- Original Creator: Abhijit Borah, Mokokchung, Nagaland. 25th February, 2023.




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