> To play the game right, it isn't sufficient to calculate the entropy of
the possible calls. You have to recur to the bitter end…
3Blue1Brown makes that point in his 2nd video.
On Thu, 17 Feb 2022 at 04:10, Henry Rich <henryhr...@gmail.com> wrote:
> I'm pretty sure I have a complete solution to Wordle. Some years ago I
> wrote a program to play Jotto, which has a scoring system that only
> gives you 1 point per letter matched, with no indication of what letter
> matches. I modified it for Wordle scoring.
>
> [If I'm so smart, why can't I sell my program for a million bucks?]
>
> My function for scoring Wordle is
>
> wdtouniq =: ([: {&a. a.&i. + 26 * i.~ (] - {) /:@/:)"1 NB. replace each
> letter with combination letter/# previous identical letters
> NB. Exact matches count 2 and override the result in that position.
> Otherwise, if
> NB. a letter/ordinal appears anywhere in the other word, it counts as a
> simple match
> NB. y is the guess, x is the hidden word
> wrdcmp=: ((e. + =)/@:wdtouniq)@:(({.a.)&((0 5 +/ I.@(=/)@])}))@:,: ~
>
> wrdcmp finds identical letters and replaces them with NUL. Then, it
> replaces each letter with (repeat#,letter) where repeat# is the number
> of previous letters equal to the given letter (it encodes these into 1
> byte rather than making them 2 values). Then it looks for matches.
>
> That's just the beginning.
>
> To play the game right, it isn't sufficient to calculate the entropy of
> the possible calls. You have to recur to the bitter end, calculating
> the expected # turns of each active set of words, because you are only
> allowed to call valid words.
>
> Before you start, you have to have a dictionary with a probability
> associated with each word. You could make them all identical, if you
> really think the hidden word is just as likely to be 'zloty' as 'crate';
> but I weighted the words according to their likelihood in English text,
> but reducing the weight of the most common words. Defining the
> dictionary is what really defines the game to be played.
>
> With the dictionary and probabilities I have, I can report that the
> expected number of turns for the best initial calls are
>
> tears 3.40429
> slate 3.4155
> tales 3.42104
> tries 3.4317
> stale 3.43402
> rates 3.43807
> ...
>
> Henry Rich
>
>
>
>
> On 2/16/2022 7:26 PM, Ian Clark wrote:
> > Being my usual helpful wee self, I was about to proffer this worked
> example
> > by 3Blue1Brown on calculating the best first guess:
> >
> > [1] https://www.youtube.com/watch?v=v68zYyaEmEA
> >
> > when 3Blue1Brown posted a retraction:
> >
> > [2] https://www.youtube.com/watch?v=fRed0Xmc2Wg
> >
> > He'd used the wrong hashing algorithm (if we may call it that). The video
> > details his error plus the correction, and reruns the entropy
> calculations.
> >
> >
> > AFAICS Raul has taken the necessary first step in bringing some sanity to
> > this topic. A universally-agreed acceptance test for what he calls
> *wrdcmp*.
> >
> >
> > Could some kind benefactor of humanity please expand Raul's list of
> asserts
> > to reconcile
> >
> > - the original Wordle source code, e.g. at:
> > https://www.wordleunlimited.com
> > - 3Blue1Brown's retraction, [2] above
> > - https://rosettacode.org/wiki/Wordle_comparison -which links:
> > - en.wikipedia.org/wiki/Wordle#Gameplay
> >
> >
> > WIBNI (wouldn't-it-be-nice-if) the acceptance test could be run against
> all
> > the submissions to RosettaCode.
> >
> >
> > A version of the acceptance test for Mastermind would be nice as well,
> > since there are non-isomorphic variants of that too.
> >
> >
> > Importance: medium to high. Both Mastermind and Wordle are excellent
> > paradigms for teaching Information Theory, in a form applicable to IT
> > rather than to Bayesian statistics.
> >
> >
> > What do I mean by that? The IT world needs a formulation of entropy that
> > avoids relying on the notion of probability. Moreover, Bayes Rule and
> > treatments using it are vastly simplified when expressed in bits instead
> of
> > probability ratios.
> >
> > On Wed, 16 Feb 2022 at 22:23, Raul Miller <rauldmil...@gmail.com> wrote:
> >
> >> On Wed, Feb 16, 2022 at 4:57 PM 'Pascal Jasmin' via Programming
> >> <programm...@jsoftware.com> wrote:
> >>> the score funtion is what you are looking for. is super elegant, but
> >> does not meet the spec of scoring 0 instead of 1 when there are extra
> >> copies of a candidate letter above and beyond the count in the secret.
> The
> >> elegance.
> >>> score =: e.~ + =
> >> It's viable to solve wordle using just counts of exact and inexact
> >> matches (without knowing their positions nor the letters). The
> >> approach is to start with a dictionary of possibilities and exclude
> >> everything shown to be impossible.
> >>
> >> Being able to select exact and inexact letter matches, like your
> >> approach here, is also viable. That same approach works, though the
> >> details of which dictionary words match or do not match is a bit
> >> different.
> >>
> >> Having the right dictionary is probably the most important facet of
> >> implementing a wordle solver.
> >>
> >> That said, I guess should include my current best effort:
> >>
> >> wrdcmp=: {{
> >> yw=. ;(] , ({.~1<.#)@-.)&.>/(<@I.y=/~x#~y~:x),<I.x=y
> >> 2 (I.x=y)} 1 yw} (#y)#0
> >> }}
> >>
> >> assert 1 1 2 0 0-: 'allow' wrdcmp 'lolly'
> >> assert 0 0 2 2 2-: 'bully' wrdcmp 'lolly'
> >> assert 0 0 0 1 0-: 'robin' wrdcmp 'alert'
> >> assert 0 2 1 2 0-: 'robin' wrdcmp 'sonic'
> >> assert 2 2 2 2 2-: 'robin' wrdcmp 'robin'
> >> assert 0 0 2 1 0-: 'mamma' wrdcmp 'nomad'
> >> assert 0 1 2 0 0-: 'nomad' wrdcmp 'mamma'
> >>
> >> This is a bit more elaborate than your 'score' but it's not too bad.
> >>
> >> Thanks,
> >>
> >> --
> >> Raul
> >> ----------------------------------------------------------------------
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> >>
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>
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