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Here's why I think tilt is hard to quantify: it's about human motivations. As opposed to something like heat, which is a measure of energy.
As people, we are bundles of conflicting motivations, and I think tilt is a prototypical instance of conflicting motives.
In poker, there are tons of motives: the profit motive, the fun motive, the need to win motive, the need for risk motive, the need to socialize motive, the need for acceptance motive, the need for control motive, just to name a few.
I believe what most of us mean by tilt is when any of these other motives supercedes the profit motive. Put another way, any motive that in any way prevents you from maximizing EV is tilt.
We tend to identify tilt with frustration and rage, because that is what we feel when the 'winning motive' and/or the 'fairness motive' is not satisfied properly. Our emotions overwhelm us, and we start making decisions to try and restore the equilibrium we feel has been upset instead of trying to maximize EV. Because our memories are tied strongly to our emotions, we associate tilt with that anger, or with that frustration - but correlation does not imply causation.
There is also that tilt that comes from the other end of the emotional spectrum. To use an extreme example, consider the bipolar player who's in a manic phase. These are often characterized by complete disregard for money. He's likely to play in games that are too big and push edges that he may not even have. He's satisfying some of his motivations, but just not that profit one. He's not maximizing his EV.
People who tilt seem to consider it a problem yet don't seem to realize that their actions are perfectly valid in context of their immediate desires. People may SAY they want to maximize EV, but when they chase losses and jump levels, they're very clearly NOT doing that. What they are doing is satisfying some other urge, it's just not the profit one. The stated motivation is different from the actual motivation.
I've strayed a little, but here are my conclusions:
1. Tilt is nearly impossible to measure quantitatively (because it's very difficult to calculate what our EV "should" have been - Tickner's post above puts this very concisely)
2. It is however possible to 'measure' it qualitatively, by examining what our actions revealed about our true motivations as we were playing
3. Tilt can be "cured" by self-awareness. The better a person is able to understand his own motivations, whatever they be, the better he is able to control them.
4. The first step to doing this is actually committing to having the profit motive be your fundamental poker motive while also trying to identify your true motivations in the moment and not be subservient to them.
Note that according to my definitions a valid "cure" for tilt would be just accepting that you're a ragemonkey who flies off the handle and plays poorly when sucked out on. This is only a true problem if you actually consider (or want) the profit motive to be your fundamental one.
Another note: this framework also explains why things external to poker can be detrimental to EV: if you're upset about something in your non-poker life, you can very easily be distracted and unfocused - perhaps even uncaring - in your approach to poker that day. In that case, you're tilting, because you've let something distract from the profit motive.
Apologies for the tl-ness of this post, it's just something I've been thinking a lot about lately.
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