Editing Talk:Jump Attack

==Mathematical expectation==

I'm the one who wrote the "Mathematical expectation" section. I'm not really good at math so I want you to check the program I used to calculate the data. It's written in Python 2:
 one=1
 five=2
 x5=3
 bowser=4

 import itertools

 l=[one,one,one,one,five,five,five,x5,x5,bowser,bowser]
 p=itertools.permutations(l,5)                              # change to 7, 9

 def coins(l):
     l=list(l)
     s=0
     while len(l):
         a=l[0]
         del l[0]
         if a==one:
             s+=1
         elif a==five:
             s+=5
         elif a==x5:
             s*=5
         elif a==bowser:
             s=0
             break
         else:
             raise NameError('wtf?')
     return s

 ans=[coins(l) for l in p]
 s=sum(ans)

 print s/len(ans)
 print s
 print len(ans)

The result is:

 11
 661200
 55440

 11
 18385920
 1663200

 3
 71245440
 19958400

Since the 9-Block Option has a bonus, the real number of coins earned is 6.

I daren't calculate the variance because my machine is slow. [[User:Another gossip-loving Toad|Another gossip-loving Toad]] ([[User talk:Another gossip-loving Toad|talk]]) 22:32, 20 October 2014 (EDT)


: Hi, I was curious about the expected reward as well, and when I saw the wiki page didn't list them, I ended up writing uncannily similar code as yours (I only checked the "talk" page after writing it), and found the same approximate values.
: I also saw that you'd added this to the page at first, but later removed them again since you didn't trust your numbers...I suppose my independently written code arriving at the same numbers would fully corroborate it, assuming the game does not secretly alter the game rules in the player's favor or something.
: With that caveat, I'm adding it back into the article. 
: (Here's my code, python 3)

  import numpy as np
   
  bowser = 0
  one = 1
  five = 5
  xfive = 25
  blocks = [one, one, one, one, five, five, five, xfive, xfive, bowser, bowser]
   
  def evaluate(blocks):
      total = 0
      for block in blocks:
          if block == one or block == five:
              total += block
          elif block == xfive:
              total *= 5
          else:
              return 0
      return total
   
  count = 100_000 # Number of simulated games to run, increase for more accurate average
  mode = 5 # Chance to 7 or 9
  total = sum( evaluate(np.random.permutation(blocks)[:mode]) for _ in range(count) )
  print(total/count)

--[[User:Rezuaq|Rezuaq]] ([[User talk:Rezuaq|talk]]) 05:15, December 23, 2021 (EST)
@@ Line 86: / Line 86: @@
    print(total/count)
-: --[[User:Rezuaq|Rezuaq]] ([[User talk:Rezuaq|talk]]) 05:15, December 23, 2021 (EST)
+--[[User:Rezuaq|Rezuaq]] ([[User talk:Rezuaq|talk]]) 05:15, December 23, 2021 (EST)
-:: Update: I realised you don't even need to simulate anything, it's actually faster to just compute every possible winning game and use that to get the exact expected values. I have amended the table.
-:: Python 3 code:
-    import itertools
-    import math
-    one = 1; five = 5; xfive = 25
-    winningBlocks = [one, one, one, one, five, five, five, xfive, xfive]
-    def evaluate(blocks):
-        total = 0
-        for block in blocks:
-            if block == one or block == five:
-                total += block
-            elif block == xfive:
-                total *= 5
-        return total
-    print()
-    for mode in [5, 7, 9]:
-        print('====== %d-Block Option =====' % mode)
-        count = math.factorial(11)//math.factorial(11-mode)
-        print('# of combos:', count)
-        winCount = math.factorial(9)//math.factorial(9-mode)
-        print('# of non-losing combos:', winCount)
-        # Only evaluate the winning combos-- far less than the actual total number of combinations.
-        total = sum(evaluate(perm) for perm in itertools.permutations(winningBlocks, mode))
-        print()
-        print('E[x | winning] =', total/winCount)
-        print('E[x] =', total/count)
-        if mode == 9: print('(9-block bonus multiplier: Multiply by 2 to get the in-game reward)')
-        print()
-:: --[[User:Rezuaq|Rezuaq]] ([[User talk:Rezuaq|talk]]) 06:03, December 24, 2021 (EST)