Why SNGs have MORE variance than ring games

[SuitedSixes]

Thanks for posting this.

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What is "Certainty Equivalent"?

A3: Would you rather make a bet of $200 on a coin flip with an average profit of $20 or accept $5 risk-free? Would $10 risk-free persuade you not to make the bet? How about $15? Your "certainty equivalent" (or risk-free equivalent) is the amount that participation in the bet is worth to you. -- perhaps $5, $10, or $15 in this example.

The Kelly criterion with Kelly number 0.3 advises you to maximize the expected value of u(x) = x^(1-1/k) / (1-1/k), where k = 0.3 and x is your resulting bankroll. If your bankroll is $10,000 then the $200 bet gives an average value of u(x) of

55% * u(10200) + 45% * u(9800) = some number

If instead you were offered an amount "CE" risk-free the average value of u(x) would be

100% * u(10000 + CE) = some other number

These two expressions are equal when CE = $13.38. This is the "certainty equivalent" of the above bet for you if you are a Kelly better with the Kelly Number 0.3 and with a $10,000 bankroll. This amount, $13.38, is how much participation in the bet is worth to you. In particular, if the CE for this bet were negative the bet would be worth a negative amount to you and you should avoid it if possible.

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I just wish that I understood it. Is it essentially saying that for my R Game A is a better choice? If my R is higher than I assume Game B becomes a better choice.