PokerStars

After getting into BattlePoker as I mentioned in my previous blog post, I’m now sampling regular poker with fake money tables on PokerStars. Surprisingly, I was allowed to include a period in my username, so I chose this blog’s domain name: ganzir.info. If you came here after seeing my name in PokerStars, welcome 🙂

Standard

SC BattlePoker League

I’m currently participating in a competitive league for “BattlePoker,” a fan-made custom game within StarCraft II. This game seamlessly and brilliantly combines poker-style betting with auto-battle mechanics, dealing units as cards and pitting them against each other to determine whose hand wins.

I missed my first weekly game out of six, but attended my second game yesterday (June 10, 2021) and came in second place out of six. Afterwards, the replay was commentated by fellow BattlePoker players BotD and Frostacles. You can watch it here, where I play under the name “Nemesis”: https://www.youtube.com/watch?v=BK_vpxEo_bg

For more information, join the BattlePoker Discord: https://discord.com/invite/z62mka6

StarCraft II is free-to-play, and that includes access to fan-made “arcade” games like BattlePoker.

Disclaimer: I was not paid to write this, nor did anyone encourage or suggest me to do so. I’m promoting this game because I love it, and many other people do also, as testified by its bustling and content-creating community, which is extremely rare for StarCraft arcade games.

Standard

Ganzir returns

I’ve taken a break from blogging for over a month because this blog never gained nearly as many followers as I hoped. I’m back now, and in the coming days I’ll work to fix that.

Standard

Discord server

ganzir.info has a Discord server.

Keep in mind that this is not an open-access server. The members of a community are the primary determinant of how worthwhile membership in that community is, so in hopes of keeping the quality of this community high, membership is by invite only. If you’re interested in joining, contact me to request an invite. Your suitability will then be tested and, if you pass, you will receive an invite.

Standard

A hypothetical method for estimating IQ rarity on the right tail

The distribution of IQ, like that of many other quantitative traits in nature, appears to approximate a normal distribution around the mean, but deviates from normality beyond roughly plus or minus 2 standard deviations from the mean. For example, a score four or more standard deviations above the mean would occur a rate of about 1 in 30,000 if IQ were normally distributed, but such scores are far more common than that in practice. Furthermore, we can only estimate how many standard deviations above the mean that score truly is, since we have no way to directly measure “absolute” intelligence levels, only relative ones. This poses a serious obstacle to meaningfully estimating the rarity, relative to the general population, of an IQ score far above the average (and also below the average, but that’s not what I’m concerned with here).

This barrier could be overcome by combining two possible psychometric tools:

  1. An IQ test which yields a score at the interval or ratio level of measurement.
  2. A theoretical distribution which closely approximates the actual distribution of IQ in the general population, even at extreme heights.

As far as I know, neither of these things truly exist, but they both have potential substitutes which might be accurate enough to be scientifically meaningful.

Tool 1 manifests as Rasch scoring. This has already been extensively studied and even implemented in freely available psychometric test analysis software, so I won’t discuss it further here.

Tool 2 is a hitherto a subject of arcane speculation, and I’m not aware of any studies into the true distribution of intelligence at the high end. However, by combining statistical theory with knowledge about the biological underpinnings of IQ, it may be possible to determine a distribution which corresponds reasonably well to reality. Cyril Burt, studying this question in 1963, concluded that the IQs of schoolchildren matched well with a Pearson Type VII curve. Because the IQs of adults and children undoubtedly have the same biological underpinnings, like number of neurons, glucose processing efficiency, etc., I suspect that this curve would, if its parameters were correctly adjusted, also closely approximate the true distribution of adult intelligence.

Because finding the correct parameters, even roughly, for such a curve is currently beyond my research capacity, I instead propose using the log-normal distribution, for which a conversion table from the normal distribution can be found at the bottom of this webpage.

Therefore, my proposed approach for estimating the true rarity of an extremely high IQ score:

  1. Design an IQ test with generous ceiling for exceptional scorers and administer it to a sample of people known to have high IQs, possibly along with an “anchoring” sample of people with less than high IQs.
  2. Perform Rasch analysis on the test.
  3. Convert the person’s Rasch score on that test, in estimated standard deviations above the mean of the general population, to a log-normal rarity score.

Example: Person A takes this test and scores 5.33 standard deviations above the mean of the general population in “absolute” intelligence, as estimated by their Rasch score. This corresponds to a “normalized” IQ of 180. According to our normal to log-normal conversion table, this score is as rare as an IQ of 162.6 would be if intelligence were perfectly normally distributed, giving us a final rarity estimate of about 1 in 60,000.

Obviously, this is all preliminary at best. The details certainly need to be ironed out, and even the fundamental ideas may turn out to be flawed. I’m currently thinking of this as the “Bob Semple tank” of right-tail psychometrics: it doesn’t fully work, but I don’t see anyone else coming up with better ideas.

Edit (April 8, 2021): This article was inspired by a letter from Grady Towers to Darryl Miyaguchi.

Standard