Some more thoughts on T&K loss aversion.

[peterbirks]

Tversky and Kahneman uncovered one of the most fascinating aspects of the human psyche by asking people two simple questions. In the first the respondents were asked to choose between a certain gain of $3,000, or an 80% chance of getting $4,000 and a 20% chance of getting nothing. A large majority of respondents chose the certainty of a $3,000 profit, even though the EV of taking the gamble was $3,200. In the second question they were asked to choose between a certain loss of $3,000, or an 80% chance of losing $4,000 and a 20% chance of losing nothing. In this case, most people (the SAME people) took the gamble, even though taking the certain loss had a better EV.

We might consider ourselves above such peasants, but, let's be honest, if it was a real situation, what would YOU do? And look at Nick Leeson, look at the companies (Independent Insurance, HIH, Mayflower) that struggled on even though it would be far better for them to have given up earlier.

It probably goes right into our hard wiring, back to the prehistoric days where two dead deer weren't that much better than one (because you could only eat so much before it went off), but losing that one dead deer might result in you going very hungry indeed.

Time and again I have to fight against this tendency when I am playing at higher stakes. When I am up, say $200, I want to protect the gain that I have, so I become risk averse, even when I should be taking on a +EV risk. But when I am down, I am willing to take these risks. This is bad play. It is playing "scared money". But psychological barriers are hard to overcome. We have to play tricks on ourselves.

I've found one way to do this (at least at the beginning of the month). If I am playing $15-$30, I am now setting myself a win target of $3,000 for the month. That way it doesn't matter if I go from $1,000 to $1,200, because I am still $2,800 short of my target. In other words, I am down rather than up. This, hopefully, prevents fatally hesitant or tentative play. Unfortunately, this doesn't get rid of the problem at the END of the month, when the desire to "protect" your certain gain becomes even stronger.

Unless through sheer force of will I can make myself play properly, the best solution I can see to this is to drop down a level or two and to multi-table. The hourly rate is pretty similar (in theory) and the volatility is much less. And the relatively lower stakes make me less "scared" because a lower proportion of my monthly profit is at risk.

I know that there are players out there who appear utterly invulnerable to the T&K psychological flaw, and good on 'em. But they are rarities (as T&K showed in their research!). For the humble, ordinary human beings among us, who suffer from prehistoric man's "what we have, we hold" desire, self-trickery may be the best solution.

Comments

[andy-ward-uk.livejournal.com]

I think it's very useful to take a similar mindset into tournaments. If I enter tournaments with a total buyin of $10K this year, then I need to accumulate $15K in winnings to have a good year, or $20K for an excellent one.

Obviously hanging on to make 18th place for $60 isn't going to do much to help me towards $15K+ over the year, so I can go for the win without any regrets. In theory !

Andy.

[(Anonymous)]

Hi Peter,

Not surprising I sniffed this one out.

The examples of K&T that I prefer are those which offer the same utility, but with different reference points since these seem the most ‘irrational’. These instances don’t offer the same utility, because the different dilemmas will involve different states of wealth. The more interesting examples for are those where the dilemma appears identical, but differs only in reference point. Say you are £500 up and faced with an all-in scenario with marginal value, which will leave you down £500 if you lose, with reference points of having been up 2k 10 minutes earlier or down 2k 10 minutes earlier. How do poker-playyers respond?

The second of your two dilemmas presents quandry the following to me:

Choice A: You’re f*cked

Choice B: probably a bit more f*cked (i.e. your still f*cked) or a lowish chance you’re not f*cked.

No wonder the chose B.

I’m not keen on the prehistoric man/ deer example to illustrate/explain K&Ts findings. Describing, as you’ve done, the second redundant deer as redundant, you’re talking purely utility and is more appropriate for highlighting Bernoulli’s or Von Neumann’s perspective. It may serves to illustrate why, at times, we behave in a risk-averse way. K&T concluded, as your example illustrated, that people are (more) loss-averse than risk averse. Even though the two dilemmas might be identical, if one outcome feels like winning in one dilemma but losing in the other, then responses may well change in light of these reference points.

Imo, a more appropriate pre-historic hunting man (!) K&T example would be this:

Four cavemen go out hunting: chase deer; catch nothing; achieve a high state of ‘knackeredness’ and decide to return to the caves.

The same four cavemen go out hunting: chase deer; catch deer; kill deer and then are forced to abandon deer to sabre-toothed tigers. They have reached the same state of knackeredness as before and, as before, they have nothing. They carry on hunting.

In the second example the caveman would have to return to the caves having ‘lost a deer’, in the first case they never had it to lose and, of course, are in a completely different frame of mind.

For me this has applications to poker, particularly in tournaments, as I wrote on BDD’s blog last year some time.

regards

chaos

The sabre-tooth tiger

[peterbirks.livejournal.com]

Yes, I like this analogy. This can definitely be applied to cash games (but more so to tournaments). You go nowhere for an hour, building up gradually from 1,500 to 2,000, when a potential gamble with a very marginal positive EV comes up just before the break. You decide that you have done ok, you still have average chips, there is no need for you to gamble.

Alternatively, you shoot off like a rocket, zoom up to 4,500 chips, get someone else all-in when you have Aces and he has Jacks, and he spikes a Jack on the river, bringing you back to 2,000 chips. The next hand, a potential gamble with a very marginal positive EV appears. This time you take the gamble, so you can get back to your "rightful" position of 4,500 chips.

Interesting. I smell an article.

THere's a flaw in this argument.

[iadams.livejournal.com]

You (and presumably T&K, although I haven't read the source) assume that the utility value of money is linear, but it's not. Your example of the caveman and his two deer is much nearer the mark: two deer are worth much less than twice one deer. Suppose I owe a loan-shark $2,500, and am offered $3,000 or an 80% shot at $4,000: which makes logical sense for me to take?

Re: There's a flaw in this argument.

[peterbirks.livejournal.com]

I'm aware of the non-linear point here (and I'm sure that T&K were as well). I could have used another example, where exactly the same situation was posited, but it was phrased differently. This also gained a similar non-rational response. This second hypothesis had a situation where you were told that you were a battle commander with 600 troops, in a desperate situation. You had one option under which 200 could certainly be saved, while the other option had a one in three chance of them all being saved. Which do you choose? Most chose to take the "200 certainly saved" option.

However, when the question was phrased in the mannner "you have one option under which 400 will certainly die, while under the other option there is a 33% chance that none will die", most chose to take the 33% chance.

I chose the "money question" because it has a direct corollary in Mike Caro's essay in SS2, whereby $800 is $800 whether you go from $7,200 down to $8,000 down or from $800 up to level. Clearly if people were on the "margin" of total wealth here, then an extra $800 would not be of proportional satisfaction, but, surely, in this case, they should select the "certain" loss of $3,000, rather than take a gamble for $4,000? That extra $1,000 that they might lose would be worth proportionally more EVEN IF the value of money were non-linear. And yet, people usually choose to gamble. Hence the "loss averse" rather than "risk averse" point.

Re: There's a flaw in this argument.

[iadams.livejournal.com]

The battle commander question, where different phrasing of the same outcome gets different results is much better. It is my (purely anecdotal) observation that most (almost all) people are indeed loss averse: but the origianl cash question doesn't properly adress this, because the assumption of money's linear utility-value confounds the result.

Re: There's a flaw in this argument.

[(Anonymous)]

iadams: Agree that the cash example doesn't highlight K&Ts findings well because of the linearity issue, but they (and Peter) understood appreciate the non-linear way we value money.

Peter: I managed to dig the post up from Dave's blog, which I've yet to turn into anything...(Daves titles are a real help!)

http://internetpokerpro.blogspot.com/2004/11/best-of-bronski.html#comments

chaos

The value of winning

[geoffchall.livejournal.com]

An interesting example of the value people set upon winning a chance thing. We were helping to run a Christmas disco a while back at the girls' school. We were trying to get rid of some of the tat that was left over from the Christmas fair and failing to sell this rubbish at 10p/item.

However we revamped the thing as a raffle/tombola and sold tickets for 5p that had a 1 in 5 chance of winning. The prize was a crap toy from the heap and even though they knew this, the kids were happy to pay, on average, 25p for exactly what they'd been refusing to pay 10p for. The only difference is the value that they set on winning games of chance. Got rid of the crap in about 20 minutes.