So why aren't ranks rational. I mean it would make for so many better games if a player was 1.5 kyu and another 2.1 to play essentially even.

Hhm! For one thing, 1.5 and 2.1 are decimal, not rational. And secondly, the difference is 0.6 which rounds to 1 and so they should play on a one stone handicap.

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Still officially AGA 5d but I play so irregularly these days that I am probably only 3d or 4d over the board (but hopefully still 5d in terms of knowledge, theory and the ability to contribute).

I think this is how AGA ranks work, they are fractional numbers and you round to see what handicap to use. I've heard some go servers will also use custom komi/reverse-komi to make up for fractional difference in rank.

See for example, the handicap section of the AGA On-Line Self-Paired Tournament Rules.

To be fair (and pedantic ), they are rational numbers (numbers that can be expressed as ratios), 3/2 and 21/10. But maybe fractional would be a clearer term to use.

Pedantic++

They are decimal representations of rational numbers.

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Geek of all trades, master of none: the motto for my blog mostlymaths.net

Agreed, they are both rational and decimal.

The answer is typically "tradition" however some places do use the rating difference in lieu of ranking difference. As mentioned, AGA self paired tournaments do this, and I believe IGS does as well (or at least they used to).

Yes, yes, rational numbers are like PhDs degrees, on paper only.

This is why daddy drinks.

But to go to the highest possible point of pedantry, with vain hopes that it will end this, 2.1 is a number (of what sort, we probably can't say, though it's not an integer). '2.1' is a linguistic entity that represents a number (you might call it a decimal representation, though you might also reserve that for a particular type of abstract object).

As to the original question, I hold the apparently unpopular opinion, (influenced by playing a lot of other abstracts and the OGS ladders) that reduced handicaps are good. So I'm (good god, what is happening?) in partial agreement with you, SmoothOper.

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Occupy Babel!

My next ranking goal is going to be 5i!

Why think small? Why not try the quaternions?

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Still officially AGA 5d but I play so irregularly these days that I am probably only 3d or 4d over the board (but hopefully still 5d in terms of knowledge, theory and the ability to contribute).

Abyssinica is just admitting what we all know in our hearts, for us amateurs our ranks are all imaginary anyway.

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Dave Sigaty
"Short-lived are both the praiser and the praised, and rememberer and the remembered..."
- Marcus Aurelius; Meditations, VIII 21

I felt the universe shaking

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Geek of all trades, master of none: the motto for my blog mostlymaths.net

I thought my rank (5.98343) was rational (598343/100000), but actually it's irrational (11 * sqrt(6 * log(pi)/pi)/e).

Can I be a pi dan?

No, but if your rank is purely gained online you can be an e-dan.

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Still officially AGA 5d but I play so irregularly these days that I am probably only 3d or 4d over the board (but hopefully still 5d in terms of knowledge, theory and the ability to contribute).

If you use a concrete brand of mobile devices and use them to play go, an iDan

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Geek of all trades, master of none: the motto for my blog mostlymaths.net

Or, if you're on a budget, you can always get the iKyuu.

Dgs has the option to adjust komi to account for rank differences.