move on, come rain or shine

A change of tact delayed this month’s posting - apologies. Perusing the high stakes forum at 2+2, I ran across this interesting post. Though he admits to not following his own advice, the author concludes:

Anyway - when you running very bad or very hot - it's harder to get the maximum EV from this situation compared to when you running normal, cause stats of some players changed instantly (and PT can't catch this) and it takes time to find the players who really start taking shots/start to made too many folds against you.

So it's easier to change a table or take a break quitting the complicated analysis of players...

The poster advocates quitting when significantly winning or losing because the context generated by either position forces one to deviate from a more typical playing strategy: more extrapolation, less interpolation. As such our judgement is warped, decision-making is tougher. Undoubtedly every player has seen routine decisions transform into real quandaries under the climate of running at extremes.

However, even though our decision-making becomes less efficient, it can increase in effectiveness – even with a greater error-count [1]; despite acting less optimally, we might still expect to gain. Conditions change for everyone: success is to adapt quickly and advantageously, not to match or improve on performance metrics achieved under normal conditions. It’s a different game.

The presence of asymmetric information, the culprit of adverse selection, appears to hatch the belief, here, that winning or losing reference-states are penalised. It is common-place in, and to some degree particular to, on-line poker, it seems, to be largely unaware of an adversary's observations and thus ignorant (at least initially) of any factoring in of your reference-state into his strategy; however, he will be perfectly aware of any adjustments, or lack of them. A normal strategy would be deployed against one oblivious to your standing, to an opponent aware of it, an adapted one. Since we know not if our rival is fish or fowl, we must compromise or risk being compromised: not an issue, or at least less of one, under routine conditions. So, comparatively, we are likely to under-perform and execute more errors; your opponent appears to have you at a disadvantage. The solution, easily affordable on the internet, is to quit, reinitialise the variables and start elsewhere under the (likely) realisation we are observed as neither winning nor losing.

However, there is an oversight: the advantage of asymmetric information is not held solely by your opponent. Your foe, for example, isn’t aware if you are planning on his game to be normal, adaptive or some compromise: you are. We can reflect dilemmas to and fro indefinitely: has he presumed your response to be normal or adapted? You don’t know; he does. And so on. It seems reasonable to presume each dilemma (or item of information) is weighted and so in any given exchange summing these weighted advantages should determine who net gains from the context driving these imbalances.

On a more practical note, suppose against his veiled strategy you deliver your standard game; a player unaware of your reference-state is likely to adopt his typical playing style (for you) and so maintain the status quo. Were, though, he to be conscious of your winning or losing state and adopt, in his eyes, an appropriate adaptive-strategy then the chances are your strategy will be less efficient (or sub-optimal for you). However, he too is inappropriately applying a strategy - an adaptive game to a normal one. On this superficial evidence it is not apparent who has the upper-hand. Who gains: who knows? At a guess, whichever strategy is more robust, and, naturally, whoever adapts to their opponent’s true strategy the quickest, and most effectively[2].

Of course individual reasons exist to quit when winning or losing; however, increases in sub-optimal play typical in a change of climate, or indeed, the generation of additional asymmetric information, aren’t necessarily among them.

Next article: Friday Oct 27th: Sklansky's theorem: fundamentally flawed (i).

[1] Error count is a poor metric since errors vary with significance; however, the arguments hold even if we view ‘error-count’ as ‘weighted-error count’ or some measure of optimality.

[2] you'd certainly expect the guy playing less tables to to be advantaged.