guess a number without actually making a secret number

[tsh73]

Playing with guess-a-number, I end up with a version that does not have "secret" variable at all.

Instead, for each number user inputs, decision is made (with different probability) to call it "secret" or not.
Of course it should keep list of discarded numbers so not to approve number already refused.
Program does not know result in advance till last moment.
---- Guess a number ----
I made up a number, (1..9)
- you guess it. That's all ;)

No! Not quite.
Actually I do not made a number.
I will deside on the go.

Make your guess (1..9): 1
Nope, try again
Make your guess (1..9): 2
Nope, try again
Make your guess (1..9): 3
You did it!
-=* thanks for playing *=-

'guessANumber
'   idea
'   instead of making a number
'   we deside on each turn
'of cource we should store numbers tried to say "no" again
'and fix probability according to not tried numbers

'logic: loop
'   get a number
'   check if number is new
'       if it is,
'       with probabilty 1/#(numbers left) say Yes and stop
'       (or else)  store it
'       else say No

print "---- Guess a number ----"
print "I made up a number, (1..9)"
print "- you guess it. That's all ;)"
print
print "No! Not quite."
print "Actually I do not made a number."
print "I will deside on the go."
print

tried$=""

while 1
   Input "Make your guess (1..9): ";guess
   if guess<1 or guess> 9 or int(guess)<>guess then
       print "Guess not valid"
       goto [cont]
   end if
   if instr(tried$, str$(guess)) then
       print "Already tried that"
       goto [cont]
   end if
   numsLeft=9-len(tried$)
   'print "1/";numsLeft,  'and the probability is
   if rnd(0)<1/numsLeft then
       print "You did it!"
       exit while
   end if
   'else
   tried$=tried$;guess
   print "Nope, try again"
[cont]
wend
print "-=* thanks for playing *=-"
end


---

Now I admit one cannot say if it uses right probabilities then picking numbers.
So next program tests it. 10000 tests. And it looks quite good, IMHO.
secret with simple random number
---------------------------------
1072  1179  1102  1067  1114  1088  1137  1086  1155
0.107 0.118 0.110 0.107 0.111 0.109 0.114 0.109 0.116
randomly approving, which move
---------------------------------
1115  1152  1082  1143  1115  1112  1184  1052  1045
0.112 0.115 0.108 0.114 0.112 0.111 0.118 0.105 0.105
randomly approving random guess
---------------------------------
1145  1086  1089  1151  1157  1168  1116  1060  1028
0.115 0.109 0.109 0.115 0.116 0.117 0.112 0.106 0.103

'guessANumber
'   idea
'   instead of making a number
'   we deside on each turn
'Probablilties test

Ntests=10000
dim r(9)    'for 1..9

'making secret with random number test
print "secret with simple random number "
print "---------------------------------"
for k=1 to Ntests
   secret = int(rnd(0)*9+1)
   r(secret)=r(secret)+1
next
for i = 1 to 9
   print using("####",r(i));"  ";
next
print
for i = 1 to 9
   print using("#.###",r(i)/Ntests);" ";
next
print


'deciding test #1
print "randomly approving, which move   "
print "---------------------------------"
redim r(9)
for k=1 to Ntests
'single test
tried$=""
move=0
while 1
   'random guess
   move=move+1
   numsLeft=9-len(tried$)
   'print "1/";numsLeft,  'and the probability is
   if rnd(0)<1/numsLeft then
   'approved guess
       'print "You did it!"
       r(move)=r(move)+1
       exit while
   end if
   'else
   tried$=tried$;guess
   'print "Nope, try again"
[cont1]
wend
next
for i = 1 to 9
   print using("####",r(i));"  ";
next
print
for i = 1 to 9
   print using("#.###",r(i)/Ntests);" ";
next
print


'deciding test #2
print "randomly approving random guess  "
print "---------------------------------"
redim r(9)
for k=1 to Ntests
'single test
tried$=""
while 1
   'random guess
   guess = int(rnd(0)*9+1)    '0..8 -> 1..9
   if instr(tried$, str$(guess)) then
       'print "Already tried that"
       goto [cont2]
   end if
   numsLeft=9-len(tried$)
   'print "1/";numsLeft,  'and the probability is
   if rnd(0)<1/numsLeft then
   'approved guess
       'print "You did it!"
       r(guess)=r(guess)+1
       exit while
   end if
   'else
   tried$=tried$;guess
   'print "Nope, try again"
[cont2]
wend
next
for i = 1 to 9
   print using("####",r(i));"  ";
next
print
for i = 1 to 9
   print using("#.###",r(i)/Ntests);" ";
next
print

end


[B+]

No secret number, no probability just pure meanness ;-))


tried$=""

while 1
   Input "Make your guess (1..9): ";guess
   if guess<1 or guess> 9 or int(guess)<>guess then
       print "Guess not valid"
       goto [cont]
   end if
   if instr(tried$, str$(guess)) then
       print "Already tried that"
       goto [cont]
   end if
   if len(tried$) >= 8 then
       print "You did it!"
       exit while
   end if
   'else
   tried$=tried$;guess
   print "Nope, but you're getting closer!"
[cont]
wend
print "-=* thanks for playing *=-"
end



[tsh73]

Mean indeed
There is a nice cyberpank novel (1997)
en.wikipedia.org/wiki/Labyrinth_of_Reflections
but I don't think it got translated to English.
(I happened to find fun translation. It is surely inofficial and I wonder if language is any good
But, chapters are numbered in binary! 001, 010, 011 etc
warm lamp feeling
)

Near the end they confront game boss (in "real" virtual reality, all that stuff)
and there was a line along
"AI is cheating. You can choose doors in any order - boss will be behind last one"

[B+]

Hi all,

I have worked this idea out for the Hi Lo Game where you have to guess a number from 1 to 100 and if your number <> secret then you are told if High or Low. I tried tsh73 probability method without a secret number to see if it plays "right". It was tricky so before I post code, I challenge others to give it a try to appreciate how it gets tricky. Meanwhile I am going to test the distribution of "secret numbers" to see if is stacking up somewhere or leaving holes as tsh73 had done.


Update: OK a nice fairly even distribution of "secret numbers" for answers so a person can not tell if the game is working with a given secret number or making things up as it goes along. Pretty cool, tsh73!

Got nice even distribution even when all my guesses remain 1 less than last guess!

[B+]

Here is a distribution of "Secret Numbers" finally determined at games end in 10,000 trials:
Secret Numbers results:
Program errors = 0
1             92
2             94
3             101
4             111
5             110
6             100
7             114
8             104
9             91
10            89
11            82
12            122
13            97
14            97
15            115
16            109
17            96
18            97
19            91
20            103
21            108
22            95
23            104
24            99
25            99
26            108
27            104
28            91
29            102
30            105
31            97
32            81
33            106
34            101
35            107
36            89
37            99
38            88
39            87
40            102
41            100
42            107
43            92
44            81
45            84
46            103
47            100
48            98
49            89
50            95
51            107
52            102
53            105
54            95
55            110
56            92
57            119
58            110
59            106
60            93
61            92
62            84
63            103
64            113
65            94
66            95
67            99
68            92
69            99
70            110
71            91
72            96
73            95
74            87
75            93
76            95
77            111
78            102
79            101
80            111
81            113
82            110
83            115
84            95
85            105
86            106
87            107
88            92
89            93
90            118
91            95
92            106
93            91
94            104
95            106
96            104
97            98
98            97
99            101
100           106
Total 10000
Lowest count 81 for i = 32
Highest count 122 for i = 12



As you can see no holes and no heavy favorites. This tells me this game plays the same as one in which a secret number is decided before the start of each game or round.

[B+]

Oct 9, 2020 6:17:39 GMT tsh73 said:

Mean indeed
There is a nice cyberpank novel (1997)
en.wikipedia.org/wiki/Labyrinth_of_Reflections
but I don't think it got translated to English.
(I happened to find fun translation. It is surely inofficial and I wonder if language is any good
But, chapters are numbered in binary! 001, 010, 011 etc
warm lamp feeling
)

Near the end they confront game boss (in "real" virtual reality, all that stuff)
and there was a line along
"AI is cheating. You can choose doors in any order - boss will be behind last one"

You know this sounds more like the movie Matrix than Neuromancer, 1984 by William Gibson which a quick Google tells me was the book Matrix was based on but wait here is more in depth answer here 
www.syfy.com/syfywire/7-classic-sci-fi-influences-on-the-original-the-matrix#:~:text=The%20biggest%20and%20perhaps%20most,%2C%20and%20other%20cyberpunky-stuff.

Hey checkout the first screen shot FX, we could do that with JB!

Matrix is legendary around here in USA.

Update: Huh! I thought I read Neuromancer but don't remember anything like Matrix might have William Gibson confused with another.

[B+]

I've got a feeling nobody is interested or maybe tsh73 is too busy with real life, so without further ado here is the Hi Lo Game without a secret number established at the beginning of each round:

' Hi Lo Game without Secret Number  B+ 2020-10-10 works now

[restart]
cls
Hi = 101: Lo = 0 '<<<<  make these higher and lower than what the secret number can be
guesses$ = ""
while Hi - Lo > 1
   input "Guess Number 1 to 100, Enter your guess "; PlayerGuess
   'if PlayerGuess = 0 then goto [restart]  ' GOOD! we split first guess of 50 both ways!
   if PlayerGuess < 1 or PlayerGuess > 100 then
       print "Your guess is out of range of this game."
       goto [cont]
   end if
   if instr(guesses$, right$("000"+str$(PlayerGuess), 3)) then
       print "You've guessed that number already."
       goto [cont]
   end if
   guesses$ = guesses$ + "," + right$("000";str$(PlayerGuess), 3)
   if PlayerGuess > Lo and PlayerGuess < Hi then
       r = rnd(0) : p = 1/(Hi - Lo - 1) ' must be inside the Lo and Hi range ie not inclusive boundaries.
       if r <= p then
           print "You Guessed!"
           Guessed = 1
           exit while
       else
           if PlayerGuess = Hi - 1 then 'guess must of been too high
               print Lo, Hi, "Your guess was too high.", r, p
               Hi = PlayerGuess
           else
               if PlayerGuess = Lo + 1 then
                   print Lo, Hi, "Your guess was too low.", r, p
                   Lo = PlayerGuess
               else 'toss coin if too high or low
                   if rnd(0) < .5 then
                       print Lo, Hi, "Your guess was too low.", r, p
                       Lo = PlayerGuess
                   else
                       print Lo, Hi, "Your guess was too high.", r, p
                       Hi = PlayerGuess
                   end if
               end if
           end if
       end if
   else
       if PlayerGuess >= Hi then Print "Your guess was too high." else print "Your guess was too low."
   end if
   [cont]
wend
if Guessed <> 1 then PRINT "Yikes! Programming error, did not find secret number."
print: input "press Enter to go again, any other + Enter to quit ";again$
if len(again$) then end else goto [restart]




and here is code to check frequency distribution of final resulting secret numbers:

' Hi Lo Game wo secret Test Distribution  B+ 2020-10-10 works now

dim secrets(100) 'check distribution of answers, also checking if we fail to arrive at answer

[restart]
'cls
Hi = 101: Lo = 0 '<<<<  make these higher and lower than what the secret number can be
guesses$ = ""
ALO = 0: AHI = 101
Guessed = 0
while Hi - Lo > 1
   scan
   'input "Guess Number 1 to 100, Enter your guess "; PlayerGuess

   'use AI to guess
   'PlayerGuess = int((AHI - ALO)/ 2) + ALO 'OK have removed blunder!

   'make all the guesses way too high ie ride the AHI down 1 by 1
   PlayerGuess = AHI - 1  'Ah still a very nice ditribution of secrets, no holes nor mountains

   'PlayerGuess = int((Hi - Lo )/ 2) + Lo  'debug what the heck is going on with ALO AHI??
   'print "Player Guesses ";PlayerGuess

   'if PlayerGuess = 0 then goto [restart]  ' GOOD! we split first guess of 50 both ways!
   if PlayerGuess < 1 or PlayerGuess > 100 then
       'print "Your guess is out of range of this game."
       'call pause 5000
       goto [cont]
   end if
   if instr(guesses$, right$("000"+str$(PlayerGuess), 3)) then
       'print "You've guessed that number already."
       'call pause 5000
       goto [cont]
   end if
   guesses$ = guesses$ + "," + right$("000";str$(PlayerGuess), 3)
   if PlayerGuess > Lo and PlayerGuess < Hi then
       r = rnd(0) : p = 1/(Hi - Lo - 1) ' must be inside the Lo and Hi range ie not inclusive boundaries.
       if r <= p then
           'print "You Guessed!"
           Guessed = 1
           'call pause 5000
           exit while
       else
           if PlayerGuess = Hi - 1 then 'guess must of been too high
               'print Lo, Hi, "Your guess was too high.", r, p
               Hi = PlayerGuess
               AHI = PlayerGuess
           else
               if PlayerGuess = Lo + 1 then
                   'print Lo, Hi, "Your guess was too low.", r, p
                   Lo = PlayerGuess
                   ALO = PlayerGuess
               else 'toss coin if too high or low
                   if rnd(0) < .5 then
                       'print Lo, Hi, "Your guess was too low.", r, p
                       Lo = PlayerGuess
                       ALO = PlayerGuess
                   else
                       'print Lo, Hi, "Your guess was too high.", r, p
                       Hi = PlayerGuess
                       AHI = PlayerGuess
                   end if
               end if
           end if
       end if
   else 'going wrong way with guessing, not narrowing down with current guess
       'if PlayerGuess >= Hi then Print "Your guess was too high." else print "Your guess was too low."
       'call pause 2000
   end if
   [cont]
   'print Lo, Hi, ALO, AHI   'OK that blunder was pretty dumb!
   'Input "Press enter to continue..." ; wait$
wend
if Guessed <> 1 then
   print "Yikes! Programming error, did not find secret number."
   programErrors = programErrors + 1
else
   secrets(PlayerGuess) = secrets(PlayerGuess) + 1
end if
trial = trial + 1
if trial < 10000 then goto [restart]

'report results
cls
Print "Secret Numbers results:"
Print "Program errors = ";programErrors
low = 10000
for i = 1 to 100
   scan
   print i, secrets(i) 'that's right in JB you can scroll output screen to review all 100
   tot = tot + secrets(i)
   if secrets(i) < low then low = secrets(i) : saveLowI = i
   if secrets(i) > high then high = secrets(i) : saveHighI = i

next
print "Total ";tot
print " Lowest count ";low;" for i = ";saveLowI
print "Highest count ";high;" for i = ";saveHighI
end

sub pause mil   'tsh version has scan built-in
   t0 = time$("ms")
   while time$("ms") < t0 + mil : scan : wend
end sub



[tsh73]

Hello B+
You code really looks correct for me
But I added a chart to frequency test - and sometimes it looks weird
You put
PlayerGuess = AHI - 1
and it looks working OK
(I use diferen number of points instead of 100 - now, set MAXX to 20)

But should frequency depend on other distributions, at all?

So
then I uncomment

'kk=kk+1
'PlayerGuess = kk

I got pretty level distibution

But then I uncomment

'PlayerGuess = int((Hi - Lo )/ 2) + Lo
I got

and then I try to use random numbers

'PlayerGuess = int(rnd(0)*MAXX) + 1
I got

And this one (going up on edges) shows on different MAXX value

' Hi Lo Game wo secret Test Distribution  B+ 2020-10-10 works now

'chart library kind-of-header
'(that is, should be included to top)
'====================================================
global Chart.xmin, Chart.xmax, Chart.ymin, Chart.ymax
global Chart.winW, Chart.winH
global Chart.slackX, Chart.slackY
global Chart.nPoints, Chart.nSeries, Chart.handle$
global Chart.windowTitle$
global Chart.colors$, Chart.widths$
dim Chart.data(1,1)
'-----------------------------------------------------
'include chart.hb to the top
'include chart.lb at the end

dim secrets(100) 'check distribution of answers, also checking if we fail to arrive at answer

[restart]
'cls
MAXX=100
MAXX=10
MAXX=20
'MAXX=30

Hi = MAXX+1: Lo = 0 '<<<<  make these higher and lower than what the secret number can be
guesses$ = ""
ALO = 0: AHI =  MAXX+1
Guessed = 0
kk=0
while Hi - Lo > 1
   scan
   'input "Guess Number 1 to 100, Enter your guess "; PlayerGuess

   'use AI to guess
   'PlayerGuess = int((AHI - ALO)/ 2) + ALO 'OK have removed blunder!

   'make all the guesses way too high ie ride the AHI down 1 by 1
   '1)
   PlayerGuess = AHI - 1  'Ah still a very nice ditribution of secrets, no holes nor mountains
   'PlayerGuess = ALO + 1  'looks pretty much the same

   '2)
   'PlayerGuess = int((Hi - Lo )/ 2) + Lo  'debug what the heck is going on with ALO AHI??
   '3)
   PlayerGuess = int(rnd(0)*MAXX) + 1
   '4)
   'kk=kk+1
   'PlayerGuess = kk

   'print "Player Guesses ";PlayerGuess

   'if PlayerGuess = 0 then goto [restart]  ' GOOD! we split first guess of 50 both ways!
   if PlayerGuess < 1 or PlayerGuess > MAXX then
       'print "Your guess is out of range of this game."
       'call pause 5000
       goto [cont]
   end if
   if instr(guesses$, right$("000"+str$(PlayerGuess), 3)) then
       'print "You've guessed that number already."
       'call pause 5000
       goto [cont]
   end if
   guesses$ = guesses$ + "," + right$("000";str$(PlayerGuess), 3)
   if PlayerGuess > Lo and PlayerGuess < Hi then
       r = rnd(0) : p = 1/(Hi - Lo - 1) ' must be inside the Lo and Hi range ie not inclusive boundaries.
       if r <= p then
           'print "You Guessed!"
           Guessed = 1
           'call pause 5000
           exit while
       else
           if PlayerGuess = Hi - 1 then 'guess must of been too high
               'print Lo, Hi, "Your guess was too high.", r, p
               Hi = PlayerGuess
               AHI = PlayerGuess
           else
               if PlayerGuess = Lo + 1 then
                   'print Lo, Hi, "Your guess was too low.", r, p
                   Lo = PlayerGuess
                   ALO = PlayerGuess
               else 'toss coin if too high or low
                   if rnd(0) < .5 then
                       'print Lo, Hi, "Your guess was too low.", r, p
                       Lo = PlayerGuess
                       ALO = PlayerGuess
                   else
                       'print Lo, Hi, "Your guess was too high.", r, p
                       Hi = PlayerGuess
                       AHI = PlayerGuess
                   end if
               end if
           end if
       end if
   else 'going wrong way with guessing, not narrowing down with current guess
       'if PlayerGuess >= Hi then Print "Your guess was too high." else print "Your guess was too low."
       'call pause 2000
   end if
   [cont]
   'print Lo, Hi, ALO, AHI   'OK that blunder was pretty dumb!
   'Input "Press enter to continue..." ; wait$
wend
if Guessed <> 1 then
   print "Yikes! Programming error, did not find secret number."
   programErrors = programErrors + 1
else
   secrets(PlayerGuess) = secrets(PlayerGuess) + 1
end if
trial = trial + 1
if trial < 10000 then goto [restart]

'report results
cls
Print "Secret Numbers results:"
Print "Program errors = ";programErrors
low = 10000
for i = 1 to MAXX
   scan
   print i, secrets(i) 'that's right in JB you can scroll output screen to review all 100
   tot = tot + secrets(i)
   if secrets(i) < low then low = secrets(i) : saveLowI = i
   if secrets(i) > high then high = secrets(i) : saveHighI = i

next
print "Total ";tot
print " Lowest count ";low;" for i = ";saveLowI
print "Highest count ";high;" for i = ";saveHighI

'-- graph code -----------------------
Chart.nSeries = 1    'for ordinary graphs, that will be
   'col0 for X, col1 etc to Y1 etc
Chart.nPoints = MAXX
Chart.nPoints = 100
redim Chart.data(Chart.nSeries, Chart.nPoints)
Chart.xmin = 1
Chart.xmax = MAXX

for i = 1 to Chart.nPoints
   Chart.data(0,i)=i
   Chart.data(1,i)=secrets(i)
next

call chartByArray

end

sub pause mil   'tsh version has scan built-in
   t0 = time$("ms")
   while time$("ms") < t0 + mil : scan : wend
end sub

'>>include chart.lb at the end
'chart library body
'to be included after main program
'(together with header included at top)

'-----------------------------------------------------
sub parametricChartByArrayInHandle handle$
'this sub RETURNS AFTER DRAWING
   Chart.handle$ = handle$
   #Chart.handle$ "down"
   'get a chart size
   #Chart.handle$ "home"
   #Chart.handle$ "posxy w h"
   Chart.winW=2*w: Chart.winH=2*h

   'now, to get Chart.ymin, Chart.ymax we have to loop
   Chart.ymin=Chart.data(2,1)
   Chart.ymax=Chart.ymin
   for s = 1 to Chart.nSeries
       for i = 1 to Chart.nPoints
           y=Chart.data(s*2,i)
           if Chart.ymin > y then Chart.ymin = y
           if Chart.ymax < y then Chart.ymax = y
       next
   next
   'for parametrics, xmax xmin should be calculated too
   Chart.xmin=Chart.data(1,1)
   Chart.xmax=Chart.xmin
   for s = 1 to Chart.nSeries
       for i = 1 to Chart.nPoints
           x=Chart.data(s*2-1,i)
           if Chart.xmin > x then Chart.xmin = x
           if Chart.xmax < x then Chart.xmax = x
       next
   next

   colorList$ = Chart.colors$
   if colorList$="" then colorList$ = "blue green red cyan pink yellow black lightgray darkblue darkgreen darkred darkcyan darkpink brown darkgray"
'add axis
   call drawAxes
   call drawTicks
   'and labeling
   ', before graphs (so then came over text)
   call drawLabels

   'now we just - plot function
   'for parametric graphs, that will be
   'col1 for X1, col2 etc to Y1, col3 for X2, col4 etc to Y2 etc
   for s = 1 to Chart.nSeries
       colr$=word$(colorList$, s)
       if colr$="" then colr$= "black"
       #Chart.handle$ "color ";colr$
       if Chart.widths$<>"" then
           w$ = word$(Chart.widths$, s)
           if w$<>""then #Chart.handle$ "size ";w$
       end if
       x=Chart.data(s*2-1,1)
       y=Chart.data(s*2,1)
       #Chart.handle$ "set ";sx(x);" ";sy(y)  'just set first dot
       for i = 1 to Chart.nPoints
           x=Chart.data(s*2-1,i)
           y=Chart.data(s*2,i)
           #Chart.handle$ "goto ";sx(x);" ";sy(y)  'then connect dots
       next
   next

   #Chart.handle$ "flush"
end sub

sub chartByArrayInHandle handle$
'this sub RETURNS AFTER DRAWING
   Chart.handle$ = handle$
   #Chart.handle$ "down"
   'get a chart size
   #Chart.handle$ "home"
   #Chart.handle$ "posxy w h"
   Chart.winW=2*w: Chart.winH=2*h

   'now, to get Chart.ymin, Chart.ymax we have to loop
   Chart.ymin=Chart.data(1,1)
   Chart.ymax=Chart.ymin
   for s = 1 to Chart.nSeries
       for i = 1 to Chart.nPoints
           y=Chart.data(s,i)
           if Chart.ymin > y then Chart.ymin = y
           if Chart.ymax < y then Chart.ymax = y
       next
   next

   colorList$ = Chart.colors$
   if colorList$="" then colorList$ = "blue green red cyan pink yellow black lightgray darkblue darkgreen darkred darkcyan darkpink brown darkgray"
   'add axis
   call drawAxes
   call drawTicks

   'and labeling
   ', before graphs (so then came over text)
   call drawLabels


   'now we just - plot function
   'for ordinary graphs, that will be
   'col0 for X, col1 etc to Y1 etc
   for s = 1 to Chart.nSeries
       colr$=word$(colorList$, s)
       if colr$="" then colr$= "black"
       #Chart.handle$ "color ";colr$
       if Chart.widths$<>"" then
           w$ = word$(Chart.widths$, s)
           if w$<>""then #Chart.handle$ "size ";w$
       end if
       y=Chart.data(s,1)
       #Chart.handle$ "set ";sx(Chart.xmin);" ";sy(y)  'just set first dot
       for i = 1 to Chart.nPoints
           x=Chart.data(0,i)
           y=Chart.data(s,i)
           #Chart.handle$ "goto ";sx(x);" ";sy(y)  'then connect dots
       next
   next

   #Chart.handle$ "flush"
end sub

sub parametricChartByArray
'this sub OPENS MODAL WINDOW and STAYS UNTIL IT CLOSED
   call genericChartByArray 1
end sub

sub chartByArray
'this sub OPENS MODAL WINDOW and STAYS UNTIL IT CLOSED
   call genericChartByArray 0
end sub

sub genericChartByArray isParametric
   oldWindowWidth = WindowWidth
   oldWindowHeight = WindowHeight
   gosub [getSlack]
   WindowWidth=oldWindowWidth:WindowHeight=oldWindowHeight
   textbox #chart.track, 1, 1, WindowWidth-Chart.slackX, 25
   graphicbox #chart.gr, 1, 25, WindowWidth-Chart.slackX, WindowHeight-Chart.slackY-25
   title$=Chart.windowTitle$
   if title$="" then title$="(modal) Chart window"
   open title$ for dialog_modal as #chart
   #chart "trapclose [quitChart]"
   #chart.track "left mouse button move for tracking"
   if isParametric then
       call parametricChartByArrayInHandle "#chart.gr"
   else
       call chartByArrayInHandle "#chart.gr"
   end if
   #chart.gr "when leftButtonMove [track]"
wait

[track]
   #chart.track ex(MouseX); " "; ey(MouseY)
wait

[getSlack]
   if Chart.slackX <>0 then return
   WindowWidth=200:WindowHeight=200
   open "" for graphics_nsb as #t:#t,"home;posxy x y":close#t
   Chart.slackX=WindowWidth-2*x:Chart.slackY=WindowHeight-2*y
return

[quitChart]
   close #chart
end sub

sub parametricChartByFunc x$,y$,tmin,tmax
'this sub OPENS MODAL WINDOW and STAYS UNTIL IT CLOSED
   nPointsWasEmpty = (Chart.nPoints=0)
   if nPointsWasEmpty then Chart.nPoints=1000 'default
   call fillArrForParametricFunc x$,y$,tmin,tmax
   call parametricChartByArray
   if nPointsWasEmpty then Chart.nPoints=0 'reset
end sub

sub parametricChartByFuncInHandle handle$, x$,y$,tmin,tmax
'this sub RETURNS AFTER DRAWING
   nPointsWasEmpty = (Chart.nPoints=0)
   if nPointsWasEmpty then Chart.nPoints=1000 'default
   call fillArrForParametricFunc x$,y$,tmin,tmax
   call parametricChartByArrayInHandle handle$
   if nPointsWasEmpty then Chart.nPoints=0 'reset
end sub

sub chartByFunc f$,xmin,xmax
'this sub OPENS MODAL WINDOW and STAYS UNTIL IT CLOSED
   nPointsWasEmpty = (Chart.nPoints=0)
   if nPointsWasEmpty then Chart.nPoints=300 'default
   call fillArrForFunc f$,xmin,xmax
   call chartByArray
   if nPointsWasEmpty then Chart.nPoints=0 'reset
end sub

sub chartByFuncInHandle handle$, f$,xmin,xmax
'this sub RETURNS AFTER DRAWING
    nPointsWasEmpty = (Chart.nPoints=0)
   if nPointsWasEmpty then Chart.nPoints=300 'default
  call fillArrForFunc f$,xmin,xmax
   call chartByArrayInHandle handle$
   if nPointsWasEmpty then Chart.nPoints=0 'reset
end sub

sub fillArrForFunc f$,xmin,xmax
   'copy to globals first
   Chart.xmin = xmin
   Chart.xmax = xmax
   'reality/default check
   if Chart.xmin=Chart.xmax then
       Chart.xmin = Chart.xmin-10
       Chart.xmax = Chart.xmax+10
   end if

   Chart.nSeries = 1    'for ordinary graphs, that will be
       'col0 for X, col1 etc to Y1 etc
   redim Chart.data(Chart.nSeries, Chart.nPoints)
   for i = 1 to Chart.nPoints
       x = i*(Chart.xmax-Chart.xmin)/Chart.nPoints+Chart.xmin
       Chart.data(0,i)=x
       Chart.data(1,i)=evalFuncX(f$,x)
   next
end sub

sub fillArrForParametricFunc x$,y$,tmin,tmax
   'reality/default check
   if tmin=tmax then
       tmin = tmin-10
       tmax = tmax+10
   end if

   Chart.nSeries = 1    'for parametric graphs, that will be
   'col1 for X1, col2 etc to Y1, col3 for X2, col4 etc to Y2 etc
   redim Chart.data(Chart.nSeries*2, Chart.nPoints)
   for i = 1 to Chart.nPoints
       t = i*(tmax-tmin)/Chart.nPoints+tmin
       Chart.data(1,i)=evalFuncX(x$,t)
       Chart.data(2,i)=evalFuncX(y$,t)
   next
end sub

'-----------------------------------------------------

'function f(x) evaluation
function evalFuncX(f$,x)
   'for LB apparently
   'evalFuncX = eval(f$)
   'exit function

   'now, for lowly JB
   select case f$
   case "1.5*x^2-2*sin(5*x)"   'single function testing
       evalFuncX = 1.5*x^2-2*sin(5*x)
   case "2*cos(x)-cos(2*x)"    'parametric, cardioid X of x[0..2pi]
       evalFuncX = 2*cos(x)-cos(2*x)
   case "2*sin(x)-sin(2*x)"    'parametric, cardioid Y of x[0..2pi]
       evalFuncX = 2*sin(x)-sin(2*x)
   case else
       evalFuncX = x 'so you clearly see it works, and works wrong
   end select
end function

'To translate X from interval [a,b] to [c,d] we'll do (X-a)/(b-a)*(d-c)+c.
'create two functions: sx(x) and sy(y)
function sx(x)
   sx=(x-Chart.xmin)/(Chart.xmax-Chart.xmin)*Chart.winW
end function
function sy(y)
   sy=Chart.winH-(y-Chart.ymin)/(Chart.ymax-Chart.ymin)*Chart.winH   'Y is inverted, so Chart.winH-...
end function
'now, two back functions for mouse tracking
function ex(x)
   ex=(x-0)/Chart.winW*(Chart.xmax-Chart.xmin)+Chart.xmin
end function
function ey(y)
   ey=Chart.ymin-(y-Chart.winH)/Chart.winH*(Chart.ymax-Chart.ymin)   'Y is inverted, so Chart.winH-...
end function

'-----------------------------------------------------
sub drawAxes
   #Chart.handle$ "color black"
   #Chart.handle$ "size 1"
   #Chart.handle$ "line ";sx(Chart.xmin);" ";sy(0);" ";sx(Chart.xmax);" ";sy(0)
   #Chart.handle$ "line ";sx(0);" ";sy(Chart.ymin);" ";sx(0);" ";sy(Chart.ymax)
end sub

sub drawLabels
   'default: numbers 7x16 pixels
   CharW=7
   CharH=16
   call textAt sx(0)+5,sy(0)-5,"0,0"
   call textAt sx(Chart.xmax)-20,sy(0)-5,"X"
   call textAt sx(0)+5,sy(Chart.ymax)+20,"Y"

   call numAt sx(Chart.xmin)+20,sy(Chart.ymin)-5,Chart.xmin
   call numRightAt sx(Chart.xmax),sy(Chart.ymin)-5,Chart.xmax

   call numAt sx(Chart.xmin),sy(Chart.ymin)-20,Chart.ymin
   call numAt sx(Chart.xmin),sy(Chart.ymax)+15,Chart.ymax
end sub

sub drawTicks
   'tbd
end sub

'-----------------------------------------------------
sub textAt x,y,text$
   #Chart.handle$ "place ";x;" ";y
   #Chart.handle$ "\";text$
end sub

sub numAt x,y,n
   text$ = formatG$(n,1)
   call textAt x,y,text$
end sub

sub numRightAt x,y,n
   'default: numbers 7x16 pixels
   CharW=7
   text$ = formatG$(n,1)
   call textAt x-len(text$)*CharW,y,text$
end sub

'-----------------------------------------------------
'scientific USING function.
'(keep in mind that there are no more then 16 digits stored in real number (Double data type)).
function usingS$(n,prec)
 if n = 0 then usingS$="0e+0":exit function
 fmt$ = "#"+left$(".",prec>0)+left$("#################",prec)   'fmt of mantissa
 s$=left$("-",n<0)
 n=abs(n)
 log10=log(n)/log(10)
 e=int(log10)-(log10<0)    'QB like INT. Makes mantissa for negative exponents start from digit (not 0 as JB do)
 p=10^e
 if left$(using(fmt$,n/p),1)="%" then p=p*10:e = e+1
 usingS$=s$+using(fmt$,n/p) +"e"+left$("+",e>0) +str$(e)   'Excel always shows "+" for exponent
end function

'there 'scientific' just not needed?
function formatG$(n,prec)
   a$=usingS$(n,prec)
   fmt$ = "#"+left$(".",prec>0)+left$("#################",prec)   'fmt of mantissa
   b$=using(fmt$,n)
   if left$(b$,1)="%" then b$=mid$(b$,2)
   formatG$=a$
   if len(b$)<len(a$) _    'nice try but 1e-3 turns to 0.000 with prec=3 - ??
       and abs(n)>1 then formatG$=b$
end function



[B+]

tsh73 Thanks for looking into this.

Hmm... I never tested just completely random guesses. Not sure what you are doing with chart.

I will play with pure random guessing and different Hi Lo starts too? If I get nothing new, I will come back to your chart thing and study what might be happening there, specially the Smiley graph! ;-))

[B+]

tsh73

Yep! My independent tests confirm the Giant's smile:

' Hi Lo Game WO Secret Number Test Random Guessing Distribution  B+ 2020-10-13

' Check tsh73 report of wackiness for pure random guessing.
' So we aren't here all day waiting for results of 1000 tests
' let us store all the guess numbers into a deck.
' Shuffle the deck before each round and use 100 numbers WITHOUT REPEAT
' to get that secret number established! That should save us a ship load
' of time and still produce results of pure random guesses.

dim secrets(100) ' Check distribution of answers, also checking if we fail to arrive at answer.
dim rg(100) '      Get our random guesses in a row! Here is our Deck!
for i = 1 to 100 ' Create our deck of random numbers to test, rg stands for Random Guess
   rg(i) = i
next

[restart]
' reinitialize all that is necessary start by reshuffle rg()
for i = 100 to 2 step -1 'forget about 0 leave it alone
   tmp = rg(i)
   r = int(rnd(0) * i) + 1
   rg(i) = rg(r)
   rg(r) = tmp
next
rIdx = 1 'reset deck index
Hi = 101: Lo = 0 '  reset, make these higher and lower than what the secret number can be
guesses$ = "" '     track what has been guessed
Guessed = 0   '     flag the number has been established!

while Hi - Lo > 1 ' Begin rounds of guesses for number
   scan

   PlayerGuess = rg(rIdx) ' 1 of 100 pure random guesses
   rIdx = rIdx + 1
   'print "Player Guesses ";PlayerGuess

   'if PlayerGuess = 0 then goto [restart]  ' GOOD! we split first guess of 50 both ways!
   if PlayerGuess < 1 or PlayerGuess > 100 then 'not going to happen
       goto [cont]
   end if
   if instr(guesses$, right$("000"+str$(PlayerGuess), 3)) then 'not going to happen
       goto [cont]
   end if
   guesses$ = guesses$ + "," + right$("000";str$(PlayerGuess), 3) 'wasting time but...
   if PlayerGuess > Lo and PlayerGuess < Hi then
       r = rnd(0) : p = 1/(Hi - Lo - 1) ' must be inside the Lo and Hi range ie not inclusive boundaries.
       if r <= p then
           'print "You guessed it!"
           Guessed = 1
           exit while
       else
           if PlayerGuess = Hi - 1 then 'guess must of been too high
               'print Lo, Hi, "Your guess was too high.", r, p
               Hi = PlayerGuess
           else
               if PlayerGuess = Lo + 1 then
                   'print Lo, Hi, "Your guess was too low.", r, p
                   Lo = PlayerGuess
               else 'toss coin if too high or low
                   if rnd(0) < .5 then
                       'print Lo, Hi, "Your guess was too low.", r, p
                       Lo = PlayerGuess
                   else
                       'print Lo, Hi, "Your guess was too high.", r, p
                       Hi = PlayerGuess
                   end if
               end if
           end if
       end if
   else 'going wrong way with guessing, not narrowing down with current guess this will happen allot!!!
       if PlayerGuess >= Hi then
           'Print "Your guess was too high."
       else
           'print "Your guess was too low."
       end if
   end if
   [cont]
   'Input "Press enter to continue..." ; wait$
wend
if Guessed <> 1 then
   print "Yikes! Programming error, did not find secret number."
   programErrors = programErrors + 1
else
   secrets(PlayerGuess) = secrets(PlayerGuess) + 1
end if
trial = trial + 1
if trial < 1000 then goto [restart]

'report results
cls
Print "Secret Numbers results:"
Print "Program errors = ";programErrors
low = 1000
for i = 1 to 100
   scan
   print i, secrets(i) 'that's right in JB you can scroll output screen to review all 100
   tot = tot + secrets(i)
   if secrets(i) < low then low = secrets(i) : saveLowI = i
   if secrets(i) > high then high = secrets(i) : saveHighI = i
next
print "Total ";tot
print " Lowest count ";low;" for i = ";saveLowI
print "Highest count ";high;" for i = ";saveHighI
end



Output:
Secret Numbers results:
Program errors = 0
1             66
2             24
3             23
4             14
5             9
6             11
7             13
8             12
9             12
10            18
11            10
12            7
13            8
14            16
15            6
16            12
17            8
18            5
19            5
20            8
21            9
22            5
23            11
24            5
25            11
26            12
27            11
28            8
29            5
30            3
31            5
32            2
33            5
34            6
35            5
36            3
37            9
38            9
39            6
40            7
41            7
42            6
43            4
44            5
45            7
46            5
47            8
48            4
49            12
50            7
51            11
52            5
53            7
54            4
55            7
56            7
57            5
58            10
59            3
60            2
61            5
62            11
63            5
64            7
65            4
66            9
67            10
68            5
69            4
70            7
71            4
72            12
73            6
74            7
75            4
76            8
77            8
78            8
79            14
80            14
81            4
82            6
83            11
84            18
85            12
86            14
87            9
88            12
89            11
90            11
91            8
92            12
93            13
94            11
95            16
96            12
97            21
98            19
99            29
100           49
Total 1000
Lowest count 2 for i = 32
Highest count 66 for i = 1



So the phenomena is definitely not just an artifact of your chart.

So what the heck??? Those boundaries are significantly favored.

[B+]

OK back from the Drawing Board and I think I have it now.

Here's why, frequency distribution of 100,000 trials:

Secret Numbers results:
Program errors = 0
1             1125
2             950
3             1065
4             976
5             1085
6             978
7             1091
8             905
9             980
10            964
11            1110
12            1017
13            1072
14            940
15            1098
16            953
17            1074
18            1104
19            1121
20            968
21            988
22            877
23            971
24            949
25            1093
26            951
27            1070
28            1074
29            1090
30            964
31            923
32            956
33            1022
34            937
35            1054
36            966
37            1000
38            910
39            1039
40            1088
41            1035
42            951
43            1018
44            1033
45            1109
46            966
47            940
48            1010
49            939
50            958
51            1083
52            909
53            971
54            927
55            1053
56            932
57            1169
58            955
59            1016
60            904
61            1073
62            976
63            1121
64            978
65            993
66            936
67            1002
68            1104
69            1062
70            957
71            977
72            911
73            915
74            914
75            967
76            933
77            1076
78            945
79            1058
80            948
81            957
82            955
83            1100
84            1023
85            919
86            966
87            972
88            1008
89            917
90            1017
91            974
92            1051
93            989
94            1070
95            993
96            1096
97            990
98            939
99            952
100           890
Total 100000
Lowest count 877 for i = 22
Highest count 1169 for i = 57



Here is the new version of Game:
' Hi Lo Game without Secret Number v2 B+ 2020-10-14
' OK the first version gets really wierd results around the boundaries 1 and 100.
' The frequency of established secret numbers jumps up very significantly!
' Back to the drawing board :)

' 2020-10-14 This time I developed the game code in the Random Number Guess Frequency Tester.
' This game has very level frequency from 1 to 100 and regular game feels right.

[restart]
cls
Hi = 101: Lo = 0 '<<<<  make these higher and lower than what the secret number can be
guesses$ = ""
while Hi - Lo > 1
   input "Guess Number 1 to 100, Enter your guess "; PlayerGuess
   'if PlayerGuess = 0 then goto [restart]  ' GOOD! we split first guess of 50 both ways!
   if PlayerGuess < 1 or PlayerGuess > 100 then
       print "Your guess is out of range of this game."
       goto [cont]
   end if
   if instr(guesses$, right$("000"+str$(PlayerGuess), 3)) then
       print "You've guessed that number already."
       goto [cont]
   end if
   guesses$ = guesses$ + "," + right$("000" + str$(PlayerGuess), 3)
   if PlayerGuess > Lo and PlayerGuess < Hi then
       r = rnd(0) : p = 1/(Hi - Lo - 1) ' must be inside the Lo and Hi range ie not inclusive boundaries.
       if r <= p then
           print "You Guessed!"
           Guessed = 1
           exit while
       else
           if PlayerGuess = Lo + 1 then
               print "Your guess was low."
               Lo = Lo + 1
           else
               if PlayerGuess = Hi - 1 then
                   print "Your guess was high."
                   Hi = Hi - 1
               else
                   'p < guess = (guess - lo -1) / range
                   range = Hi - Lo - 1
                   if rnd(0) * range <=  PlayerGuess - Lo -.5 then
                       Print Lo, Hi, "Your guess was too high."
                       Hi = PlayerGuess
                   else
                       print Lo, Hi, "Your guess was too low."
                       Lo = PlayerGuess
                   end if
               end if
           end if
       end if
   else
       if PlayerGuess >= Hi then Print "Your guess was too high." else print "Your guess was too low."
   end if
   [cont]
wend
if Guessed <> 1 then PRINT "Yikes! Programming error, did not find secret number."
print: input "press Enter to go again, any other + Enter to quit ";again$
if len(again$) then end else goto [restart]




Here is code that produced the above frequency table (It has 2 tests actually one that chooses the middle of known High's and Low's like a good AI would, the other test systematically goes down 1 number at each guess commented out):
' Hi Lo Game wo secret Test Distribution  B+ 2020-10-10 works now

dim secrets(100) 'check distribution of answers, also checking if we fail to arrive at answer

[restart]
'cls
Hi = 101: Lo = 0 '<<<<  make these higher and lower than what the secret number can be
guesses$ = ""
Guessed = 0
player = 101
while Hi - Lo > 1
   scan
   'input "Guess Number 1 to 100, Enter your guess "; PlayerGuess

   'make all the guesses way too high ie ride the AHI down 1 by 1
   'player = player - 1
   'PlayerGuess = player  'Ah still a very nice ditribution of secrets, no holes nor mountains

   PlayerGuess = int((Hi - Lo )/ 2) + Lo  'debug what the heck is going on with ALO AHI??
   'print "Player Guesses ";PlayerGuess

   'if PlayerGuess = 0 then goto [restart]  ' GOOD! we split first guess of 50 both ways!
   if PlayerGuess < 1 or PlayerGuess > 100 then
       print "Your guess is out of range of this game."
       goto [cont]
   end if
   if instr(guesses$, right$("000"+str$(PlayerGuess), 3)) then
       print "You've guessed that number already."
       goto [cont]
   end if
   guesses$ = guesses$ + "," + right$("000";str$(PlayerGuess), 3)
   if PlayerGuess > Lo and PlayerGuess < Hi then
       r = rnd(0) : p = 1/(Hi - Lo - 1) ' must be inside the Lo and Hi range ie not inclusive boundaries.
       if r <= p then
           'print "You Guessed!"
           Guessed = 1
           exit while
       else
           if PlayerGuess = Lo + 1 then
               'print "Your guess was too low."
               Lo = Lo + 1
           else
               if PlayerGuess = Hi - 1 then
                   'print "Your guess was too high."
                   Hi = Hi - 1
               else
                   'p < guess = (guess - lo -1) / range
                   range = Hi - Lo - 1
                   if rnd(0) * range <=  PlayerGuess - Lo -.5 then
                      ' Print Lo, Hi, "Your guess was too high."
                       Hi = PlayerGuess
                   else
                       'print Lo, Hi, "Your guess was too low."
                       Lo = PlayerGuess
                   end if
               end if
           end if
       end if
   else 'going wrong way with guessing, not narrowing down with current guess
       if PlayerGuess >= Hi then Print "Your guess was high." else print "Your guess was low."
   end if
   [cont]
   'Input "Press enter to continue..." ; wait$
wend
if Guessed <> 1 then
   print "Yikes! Programming error, did not find secret number."
   programErrors = programErrors + 1
else
   secrets(PlayerGuess) = secrets(PlayerGuess) + 1
end if
trial = trial + 1
if trial < 100000 then goto [restart]

'report results
cls
Print "Secret Numbers results:"
Print "Program errors = ";programErrors
low = 10000
for i = 1 to 100
   scan
   print i, secrets(i) 'that's right in JB you can scroll output screen to review all 100
   tot = tot + secrets(i)
   if secrets(i) < low then low = secrets(i) : saveLowI = i
   if secrets(i) > high then high = secrets(i) : saveHighI = i
next
print "Total ";tot
print " Lowest count ";low;" for i = ";saveLowI
print "Highest count ";high;" for i = ";saveHighI
end


And here is code I used to actually develop the new improved version of the Hi Lo Game Without Secret Number, the frequency distribution test for Random number guess. This is the test that pointed out the serious flaw in previous version of Hi Lo Without Secret Number:

' Hi Lo Game WO Secret Number Test Random Guessing Distribution  B+ 2020-10-13

' Check tsh73 report of wackiness for pure random guessing.
' So we aren't here all day waiting for results of 1000 tests
' let us store all the guess numbers into a deck.
' Shuffle the deck before each round and use 100 numbers WITHOUT REPEAT
' to get that secret number established! That should save us a ship load
' of time and still produce results of pure random guesses.
' 2020-10-13 post https://justbasiccom.proboards.com/thread/567/guess-number-secret

dim secrets(100) ' Check distribution of answers, also checking if we fail to arrive at answer.
dim rg(100) '      Get our random guesses in a row! Here is our Deck!
for i = 1 to 100 ' Create our deck of random numbers to test, rg stands for Random Guess
   rg(i) = i
next

[restart]
' reinitialize all that is necessary start by reshuffle rg()
for i = 100 to 2 step -1 'forget about 0 leave it alone
   tmp = rg(i)
   r = int(rnd(0) * i) + 1
   rg(i) = rg(r)
   rg(r) = tmp
next
rIdx = 1 'reset deck index
Hi = 101: Lo = 0 '  reset, make these higher and lower than what the secret number can be
guesses$ = "" '     track what has been guessed
Guessed = 0   '     flag the number has been established!

while Hi - Lo > 1 ' Begin rounds of guesses for number
   scan

   PlayerGuess = rg(rIdx) ' 1 of 100 pure random guesses
   rIdx = rIdx + 1
   'print "Player Guesses ";PlayerGuess

   'if PlayerGuess = 0 then goto [restart]  ' GOOD! we split first guess of 50 both ways!
   if PlayerGuess < 1 or PlayerGuess > 100 then 'not going to happen
       goto [cont]
   end if
   if instr(guesses$, right$("000"+str$(PlayerGuess), 3)) then 'not going to happen
       goto [cont]
   end if
   guesses$ = guesses$ + "," + right$("000";str$(PlayerGuess), 3) 'wasting time but...
   if PlayerGuess > Lo and PlayerGuess < Hi then
       r = rnd(0) : p = 1/(Hi - Lo - 1) ' must be inside the Lo and Hi range ie not inclusive boundaries.
       if r <= p then
           'print "You guessed it!"
           Guessed = 1
           exit while
       else

           if PlayerGuess = Lo + 1 then
               'print "Your guess was low."
               Lo = Lo + 1
           else
               if PlayerGuess = Hi - 1 then
                   'print "Your guess was high."
                   Hi = Hi - 1
               else
                   'p < guess = (guess - lo -1) / range
                   range = Hi - Lo - 1
                   if rnd(0) * range <=  PlayerGuess - Lo -.5 then
                       'Print Lo, Hi, "Your guess was too high."
                       Hi = PlayerGuess
                   else
                       'print Lo, Hi, "Your guess was too low."
                       Lo = PlayerGuess
                   end if
               end if
           end if
       end if

   else 'going wrong way with guessing, not narrowing down with current guess this will happen allot!!!
       if PlayerGuess >= Hi then
           'Print "Your guess was too high."
       else
           'print "Your guess was too low."
       end if
   end if
   [cont]
   'Input "Press enter to continue..." ; wait$
wend
if Guessed <> 1 then
   print "Yikes! Programming error, did not find secret number."
   programErrors = programErrors + 1
else
   secrets(PlayerGuess) = secrets(PlayerGuess) + 1
end if
trial = trial + 1
if trial < 10000 then goto [restart]

'report results
cls
Print "Secret Numbers results:"
Print "Program errors = ";programErrors
low = 1000
for i = 1 to 100
   scan
   print i, secrets(i) 'that's right in JB you can scroll output screen to review all 100
   tot = tot + secrets(i)
   if secrets(i) < low then low = secrets(i) : saveLowI = i
   if secrets(i) > high then high = secrets(i) : saveHighI = i
next
print "Total ";tot
print " Lowest count ";low;" for i = ";saveLowI
print "Highest count ";high;" for i = ";saveHighI
end



And here is a sample run of that distribution:
Secret Numbers results:
Program errors = 0
1             127
2             111
3             124
4             109
5             112
6             105
7             109
8             110
9             100
10            125
11            106
12            87
13            105
14            97
15            87
16            110
17            111
18            115
19            114
20            101
21            115
22            95
23            89
24            110
25            104
26            87
27            86
28            97
29            105
30            100
31            98
32            106
33            95
34            100
35            99
36            89
37            104
38            110
39            99
40            89
41            100
42            91
43            107
44            114
45            120
46            76
47            103
48            109
49            96
50            103
51            93
52            88
53            79
54            91
55            85
56            82
57            94
58            107
59            96
60            131
61            111
62            88
63            94
64            89
65            81
66            124
67            82
68            112
69            105
70            101
71            94
72            111
73            97
74            95
75            68
76            93
77            118
78            99
79            106
80            101
81            87
82            89
83            96
84            110
85            91
86            99
87            98
88            104
89            88
90            105
91            83
92            109
93            83
94            97
95            81
96            97
97            106
98            95
99            112
100           94
Total 10000
Lowest count 68 for i = 75
Highest count 131 for i = 60