Evodice Part 1: Fitness

Hi everyone!

A while ago over at AtBC I had the notion of using dice to try and show how fitness and luck combine during the selection process. I (with the Help of Wes Elsberry) thought that using dice might be a good way to explore this and other concepts such as mutation, sexual selection etc.

So.. here we go.

Imagine a die. It has 6 sides. Let’s call these [A,B,C,D,E,F]. In the dice we all know and love each side has a number associated with it, let’s write that as [1,2,3,4,5,6]. So far so good? – so the “B” face is 2. The “E” face is 5.

Now let’s imagine the life of dice is gladiatorial and to “win” a die must roll higher than another competing die on a single trial of one on one dice combat. If he (I think of them like little people, I can’t write “it” any more) rolls a high number, his odds are better, so fitness clearly scales with numbers. So for our normal die, We’ll call him Norm, his fitness (total) is 1+2+3+4+5+6=21 and his average fitness is 21/6 sides = 3.5. Let’s imagine the Lord of the Dice is a nerdy dungeonmaster called KeithS. He hasn’t decided what happens if two dice roll “The dreaded tie” yet. Maybe dice purgatory? I just really wanted KeithS in this.

Now there’s no reason why a dice has to be [1,2,3,4,5,6]. Norm is, but let’s compare him to the other challengers:

Norm [1,2,3,4,5,6]
Uptight BiPolar [1,1,1,6,6,6]
Low SD [3,3,3,4,4,4]
IDist [1,1,4,5,5,5]

They all have the same average fitness (3.5) as I described above. How do you think they fair in head to head match ups? I’ll reveal the answers via the power of EXHAUSTIVE ENUMERATION in a while. If no one cares then You’ll never know and KeithS wins. No-one wants that!

Let’s Roll!

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88 thoughts on “Evodice Part 1: Fitness

  1. phoodoo: I predict your posts will continue to be even more mind numbingly boring than watching reruns of Mr. Bean.

    And yet you read and reply to them. What does that say about you?

    Edit to add – I see you’re still dodging making a prediction. Is the question too hard? Do you not understand it?

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  2. I said earlier based on intuition:

    I think Uptight Bipolar. High deviation from the mean gets selected for. Just my educated gambler instinct.

    At least in terms of the rules of the game it looks like Uptight BiPolar is the winner by a nose. I actually wasn’t sure he would win, just an educated guess.

    An interesting question is if something can hypothetically beat Uptight Bipolar, or whether given all possible implementations, or whether Uptight Bipolar on average is the best. I have no answer for those questions.

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  3. stcordova: An interesting question is if something can hypothetically beat Uptight Bipolar, or whether given all possible implementations, or whether Uptight Bipolar on average is the best. I have no answer for those questions.

    I used linear programming, in this case “Solver” to come up with:

    Designed [3,2,3,4,3,6], who beats Uptight Bipolar 50% of the time and loses 42% of the time.

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  4. It would be interesting to write a GA that could populate a universe of regular polygons (hmmmm, how about irregular polygons) and play them against each other.

    How about a multi-player game, modeled after Battlebots, in which designs battle each other.

    Interesting to design the arena and play, and interesting to build players.

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  5. Richardthughes,

    Naah.
    VorsprungDurchTechnik [2,2,2,3,6,6] still loses to LowSD, but it thrashes Uptight Bipolar, IDist and Matzke (& edges Dawkins)
    And ties Uniform.

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  6. Rich:

    I used linear programming, in this case “Solver”

    Studly resourceful.

    You’re a better quant than I.

    Cheers. 🙂

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  7. stcordova: 2 + 2 + 2 + 3 + 5 = 14

    not 21??????

    Gah, its supposed to be [2,2,2,3,6,6] User error! Only five sides, too 🙁 Good catch.

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  8. So the Victim drives an Audi.

    That’s a nice triangle:
    Bully[3,3,3,4,3,5] stuffs VDT [2,2,2,3,6,6], who stuffs IDist [1,1,4,5,5,5].
    But IDist stuffs Bully.

    And no, there’s no lesson there.

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  9. Rich:

    Gah, its supposed to be [2,2,2,3,6,6] User error! Only five sides, too 🙁 Good catch.

    Well, if it’s OK to eliminate sides, then this is my entry:

    DungeonMaster[6]

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  10. Frankie: I believe it is possible. The issue of whether not the variation was accidental/ happenstance is still the big issue. Natural selection requires that the variation be due to accidental/ happenstances changes.

    Yes, the issue being that some posters actually think Sal is a leading light for the ID movement.

    He says he is a creationist, who believes that intelligence for men is determined by selective pressures being higher for men in society than for woman. What does this even mean?

    He also believes, that God is bad because of the evil in the world, but also good, but the evil in the world exists because, he doesn’t know, but he loves God, but hates God, and he is not sure what evil means, but why, and

    …he is angry at Mung for not being man enough to answer everyone of Keiths non-stop demands for answers, but he can’t answer simple questions…

    What I mean is I don’t think Sal has any idea what he means. I have never seen a poster less capable of articulating what they are trying to say.

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  11. phoodoo,

    That’s nice dear.

    As you’re back:

    “If that is true then my fitness measure should be orthogonal to survivability. Do you agree, Phoodoo?”

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  12. Hahaha….Richard writes [2,2,2,3,5] when he meant to say [2,2,2,3,6,6]

    Huh?? I love it, the posts keeps getting better. Some wrong numbers, some missing numbers, whatever.

    “Honey, how do you use this click and glue thingy again! I need to steal someones idea on Wikipedia and make a hash of it! Ow, I accidentally typed on my finger, shit!”

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  13. Well, we can’t all rise the level of your technical posts, Phoodoo, but I’m working on it. Now, as you’ve expressed an opinion:

    “If that is true then my fitness measure should be orthogonal to survivability. Do you agree, Phoodoo?”

    Or would you like to dodge some more?

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  14. Richardthughes,

    Fitness is only ever determined after the fact, so your point is moot. There is no such thing as a fitness measure. There is only what survived. Dice don’t have fitness or survival, so only your crazy head knows why you ask such a meaningless question.

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  15. phoodoo: Fitness is only ever determined after the fact

    That’s already been disproven in the link I gave to Frankie. So learn and move on.

    Here’s the results, Phoodoo. (10 Monte carlo runs, population 300, each side randomly picked from a linear distribution, integers 1 – 6, fitness an average of all sides). Why don’t you walk us through the findings?

    http://postimg.org/image/uujmtho7n/

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  16. Richardthughes: phoodoo: Luck IS fitness.

    Still think this is true, Phoodoo?

    Note – fitness distribution in previous post is for the final Monte Carlo run only (#10).

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  17. I wrote a bit of code to find all sets of six numbers which fit the criteria of each number is an integer in the range 1-6 and the sum of all six numbers is 21. As it happens, there’s exactly 32 such unique number-sets. Of those 32, nine have been given names in this thread. Here’s the complete list:

    1,1,1,6,6,6 // Uptight BiPolar
    1,1,2,5,6,6 // Matzke
    1,1,3,4,6,6 // Dawkins
    1,1,3,5,5,6 // [not yet named]
    1,1,4,4,5,6 // [not yet named]
    1,1,4,5,5,5 // IDist
    1,2,2,4,6,6 // [not yet named]
    1,2,2,5,5,6 // [not yet named]
    1,2,3,3,6,6 // [not yet named]
    1,2,3,4,5,6 // Norm
    1,2,3,5,5,5 // [not yet named]
    1,2,4,4,4,6 // [not yet named]
    1,2,4,4,5,5 // [not yet named]
    1,3,3,3,5,6 // [not yet named]
    1,3,3,4,4,6 // [not yet named]
    1,3,3,4,5,5 // [not yet named]
    1,3,4,4,4,5 // [not yet named]
    1,4,4,4,4,4 // [not yet named]
    2,2,2,3,6,6 // VorsprungDurchTechnik, aka VDT
    2,2,2,4,5,6 // [not yet named]
    2,2,2,5,5,5 // [not yet named]
    2,2,3,3,5,6 // [not yet named]
    2,2,3,4,4,6 // [not yet named]
    2,2,3,4,5,5 // [not yet named]
    2,2,4,4,4,5 // [not yet named]
    2,3,3,3,4,6 // Designed
    2,3,3,3,5,5 // [not yet named]
    2,3,3,4,4,5 // [not yet named]
    2,3,4,4,4,4 // [not yet named]
    3,3,3,3,3,6 // [not yet named]
    3,3,3,3,4,5 // Bully
    3,3,3,4,4,4 // Low SD

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  18. phoodoo:
    cubist,

    1,4,4,4,4,4

    I will take this one please.The phoodoo curse.

    Not a bad pick. At the moment we have survival as a head to head match up. If we made the event a static hurdle, like “roll 3 or greater”, TPC could do very well…

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  19. cubist,

    Nice work / welcome aboard!

    One for anyone still following – do we think that across all competitors average wins will be the same, or de we expect winners and losers?

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  20. Richardthughes: One for anyone still following – do we think that across all competitors average wins will be the same, or de we expect winners and losers

    I’ll stick with my original post.

    DNA_Jock: IDist kicks ass

    😉

    Perhaps phoodoo isn’t as dumb as he looks.
    .
    .
    .
    Naaah.

    Of course, this calculation assumes that all possible dice remain equiprevalent. Depending on the tournament rules, I suspect that an evolving population would reduce down to a short loop. Not sure that such a loop would be stable in the face of a mutant arrival, though. Perhaps a subject for EvoDice Part 2
    🙂

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  21. stcordova,

    I think you need to enclose your LaTeX commands within square bracketed LaTeX tags. That is:

    square-bracket latex square-bracket LaTeX commands square-bracket slash latex square-bracket

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  22. I will note that phoodoo only makes it into the Hall of Fame thanks to his truly remarkable performance against Idiot [3,3,3,3,3,6]. Then there’s that guy in the Audi…

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  23. Rich,

    Wild guess, I think on average they’ll be all the same when all possible competitors are played with the same mean fitness. Just a guess. But if that’s the case, that would ironically illustrate COI. This would seem a good quant type question for Tom English. 🙂

    Sal

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  24. Frankie: Do you not think survivability is not predictable in life?

    Not at all – “Do you not think survivability is not predictable in life?” is a perfectly fair question, which you are dodging.

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  25. The “highest die roll wins” mode of battle seems like a reasonable way to illustrate one specific aspect of evolution. It does not do much (if anything) to illustrate other aspects of evolution, including such aspects as reproduction and mutation. Are there any plans to address those things in this simulation? Or are they beyond the simulation’s intended scope?

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  26. Interesting: if I change the scoring, such that ties lead to immediate rematches (rather than letting draws ‘stand’) then phoodoo edges out IDist, and (symmetry, man!) Idiot drops below Vorsprung. But in a diverse evolving population, phoodoo will not look impressive once the Idiots are gone.

    Maybe there is a lesson here…

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  27. cubist,

    You’re a bright one! there’s actually a working excel model with point mutations and having baby dice, but I thin its fun to break it up into bits?

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  28. Richardthughes:
    cubist,

    You’re a bright one! there’s actually a working excel model with point mutations and having baby dice, but I thin its fun to break it up into bits?

    Cool. For the record, I’m not demanding that Everything About Evolution be shoveled into the simulation all at the same time; i guess I was just curious about the “road map” for future developments.

    Possible way to incorporate mutation in the simulation: Pick one of the die’s six sides at random (because mutations, by and large, don’t seem to care which part of the genome they hit); roll a three-sided die, and add that die-roll minus 2 to the randomly-picked die-side. Or, for those of you who are conversant with dice notation in tabletop roleplaying games, add (1D3 – 2) to the randomly-picked die-side.

    WIth (1d3-2) as the mechanism that simulates mutation, 1/3 of all mutations end up being beneficial; another 1/3 end up being perfectly neutral; and the final 1/3 will be detrimental. Clearly, mutations in real biology aren’t neatly sorted into equally-large ‘bins’ like that, but since this is a toy example, adherence to specific details isn’t really the point. (1d3-2) does illustrate that not all mutations are bad, and that’s the important part. If someone really wants the simulation to model the proportions of detrimental/neutral/beneficial mutations more closely, they can replace (1D3-2) with some other mutational mechanism.

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