If you lower the size of the bets you're better off taking a long series of them, but otherwise, you're raising the risk of bankruptcy.

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Occupy Babel!

If you lose the first bet, then the prospect of losing the second bet hurts worse, but the prospect of winning the second bet seems more attractive by the same amount. If you like the nth bet you should like the n+1th bet just about as much, whether you win or lose the nth bet (unless you're literally unable to take the next bet due to liquidity constraints).

This is not accurate. In most experiments dealing with these things, they do it quite differently. In the case you describe, you get a board for the 20 you spend, so it is not a loss, it is a transaction. If you think the board is worth 5 it is a loss, but it gets too complicated. In actual experimental research they do things like this:
Case 1) Give someone two tickets to the movies for free. When you get to the movies, the person finds out that the tickets are not valid. Although they got the tickets for free, a majority of people actually see this as a loss. From the starting point, nothing was gained or lost. People change their status-quo to a point where they have the tickets, so they see it as a loss. In these types of cases, the loss is perceived to be quite high in comparison with the gain in receiving the tickets.
Case 2) You are gambling over a period of time, starting with 100$, you continue to lose 10$ each hand. At 50$, you win 20$. In most cases, people see this as a "gain" not a "loss." Despite the fact that you are still 30$ down, people get a "high" about their win and continue to gamble. This is how gambling works for most people who play casino games.



I think there is a place for the status quo frame in terms of one's rank in go and losses. If someone is placing the status quo frame at their current rank, then a loss is painful. If they place their status quo frame at where they started playing (e.g. 20k), then they are probably still doing quite well (at like 5K) and the loss is not painful.

Prospect theory does not apply completely, because the theory involves the choice between two lotteries with different frames/status quo bias. In the case of go, you either win or lose a single game. There is no choice between lotteries.
Perhaps it might fit better if you were considering which of two players you wanted to play (where each game represents some form of lottery, with different odds of winning/losing). In that case, the frame might matter. I would have to think about it more, though.


Strictly speaking, risk aversion and diminishing marginal utility are not at all the same thing. Risk aversion does not necessarily apply to any nth number of items. If you talk to smart financial advisors, they understand the concept of risk aversion quite well, and it has nothing to do with how many times you invest or how many nth stocks you own. Actually, the solution for risk averse individuals is to own many stocks and diversify to minimize risk.

when this discussion turned from go to gambling (and the "real" loss aversion), it instantly reminded me of the anime Kaiji. it revolves around series of interesting and twisted gambles, which can also be perceived as thought experiments

sample: you are deep in debt, which will take, let say 20 years of hard work to pay off. you get a chance to erase the debt and even earn something more for a fresh start - but it requires crossing a long steel beam, so high above the ground that falling down means sure death. how safe does the crossing have to look in order for one to accept? and would you estimate your chances of successful passing to be the same if the beam was just above the ground?

while the previous paragraph is a bit off-topical, i think the last question is well relevant - different possible loss tends to change your estimate of its probability even if the gamble's nature remains the same. similar to travel insurance - research has shown that insured people estimate the chance of something bad happening to them lower than uninsured ones.

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Spilling gasoline feels good.

I might be wrong, but probably not.

GoJapan, I think Jts is describing the same thing as you are--an initial transaction that then turns into a loss (losing the board/finding out the tickets are invalid).

You often hear about misplacing something you just bought in expositions of prospect theory.

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Occupy Babel!

OK. Fair enough. I probably just read quickly and didn't pay close enough attention to what the poster said.

Okay, perhaps the research has evolved since I last read it, but this is quite different from both the results and the interpretations of the results that I came across as an undergraduate.

At that time, if you just gave someone some tickets for free, those tickets were in the gain domain. If they subsequently lost those tickets or found out they were invalid, that would not take them into the loss domain (the tickets were a windfall), and they would likely be willing to buy a new pair of tickets if the price was affordable for them. However, if you sold someone a pair of discounted tickets and then the tickets were lost or invalidated, they would generally be unwilling to buy a new pair because (despite the nominal price they paid for the original tickets) losing the tickets pushed them in the loss domain and paying more for a new pair of tickets pushed them further into the loss domain.

Further, the normal interpretation of gambling behavior is that people get really excited about winning when they're losing to the house on net precisely because they're in the loss domain. Movements within the loss domain count approximately double, whether it's a positive or a negative change, and the slope is sharpest as you get closer to the dividing line between the loss domain and the gain domain, so people are happy to engage in risky behavior to get themselves out of the loss domain. (This, connected to breathtakingly stupid ideas about probability and luck, creates the gambling personality.)




This isn't really relevant to Go and we're getting into "wrong on the internet territory" but... okay. The reason that you want to diversify your stock portfolio is to lower the volatility of returns. In an ideally diversified portfolio, the returns of every item in the investment basket are uncorrelated with the returns of every other item. You can mimic this by comparing the returns from one portfolio to rolling a die and multiplying by three, and comparing the returns from the other portfolio to rolling three dice. Now, the average of the returns is the same in either case, and your lower chance of getting a three is balanced out by your lower chance of getting an 18, so why would you prefer the balanced portfolio to the volatile one? Well, obviously because of diminishing marginal utility; the 7 units of consumption between 3 and 11 are way more valuable to you than the 7 units between 11 and 18.

So I don't see how I could claim anything more banal than "risk aversion is related to diminishing marginal utility". Indeed, it might be more accurate to say "risk aversion is diminishing marginal utility."

I don't want to increase the size of this post, so I am not quoting our posts.

I think I will just make two comments to clarify my point, and then I am going to leave this alone because it is not totally relevant to go.
First, in terms of your comments about the domains and people being in a particular frame,
frames are about perceptions. They perceive themselves as in one or the other for a particular decision. The anchor can change and does change over time. So, someone who starts in a gains frame because they won some money can update their anchor point and any loss is perceived as a loss, even if it is less than what they gained. The multi-round games/experiments are very complicated in regards to frames and anchoring.
When K&T did research developing Prospect Theory, they presented fictional scenarios to individuals in text form as a one-shot game. They gave texts that presented the "gains" frame to one group, and "losses" to another group. This in effect, manipulated the perceived frames through rhetoric. It is important to note that within this research, the results varied. In different studies, anywhere between just over 50% to about 80% conducted their behavior as prospect theory hypothesized. (In truth, we should not even call this a theory. K&T did not have a theory when they started. They simply drew the graph based on their empirical results. They actually did not have a theory about why people acted that way until later scholars understood the evolutionary origins of this behavior.) The other people acted as predicted based on theories of utility maximization and rationality. What this means is that in aggregate, people have a propensity to act according to Prospect Theory (Risk seeking in losses and risk averse in gains), but not all people act this way all the time. Actually, it means anywhere between 50-80% are "prospectors." In addition, some other scholars have suggested that prospect behavior is context dependent and K&T's experiments were limited by the use of text based experiments.
There have been subsequent studies done on Chimps to see if they demonstrate the same behavior. These studies have shown that Chimps exhibit similar behavior at similar rates. There are also theories on the evolutionary origin of such propensities based on foraging and sex. One of my colleagues published such a paper documenting these evolutionary origins using agent-based modeling.
Second, risk aversion acts whether one has one investment or many investments. Whether one plays one game or many. It is not the same as diminishing marginal utility. Diminishing marginal utility suggests that every added item provides less benefit than the previously consumed item. Just as you said, eating the 5th slice of pizza does not feel as good as eating the first slice of pizza. In go, it would be like winning 20 games in a row. Each time you win, it doesn't feel as good as the win before it. Because of our ranking systems, your chance of winning the next game actually go down (subsequent games get harder), so you may not experience a diminishing marginal return.
Risk aversion or risk acceptance is about the perceived sensitivity to loss. For example, if someone is risk averse, the expected value of a bet must be quit high before accepting such a bet. If someone is risk acceptant, then they are willing to accept bets with lower expected values. Some people are also risk seeking, where they accept bets that have a negative expected value because the thrill of the bet adds to the value. (Usually, we calculated expected value based on money/points, but actual utility is subjective.)
Risk aversion can be made less of a problem by diversification, for example, but that does not make them the same thing. What this means is that diversification of portfolio reduces the real risk of the investment. This makes a risk averse person feel better about the investment because the actual risk is lower.

In terms of go, I am not sure how it applies, as I said. If you play a game and lose perhaps you are in a domain of losses. In that case, you are more risk seeking for the next game perhaps? Maybe you will play riskier moves? I am not sure. Perhaps you are more likely to accept a challenge from a stronger player? That is, all else equal, but in Go it is not. If your rank changes, then your chances of winning the next game go up (game gets easier).

I guess I would also answer that last question. Why would you prefer a volatile portfolio to a non-volatile one? Usually, with volatile portfolios, the average return is higher. So, if you can withstand greater risk (risk acceptant), you have a chance at a higher rate of return. This is not related to diminishing marginal utility as far as I can see. It does have a lot to do with someone's risk propensity because if they are risk acceptant, they will go for the higher rate of return for increased volatility and risk for loss.

Anyway, I am going to leave it here. All of this information is from the perspective of psychology and economics. I am not a finance person, so I could be wrong about that part.

Thanks to the above discussion between JTS and Go_Japan, I've become a bit more familiar with a few psychological and economic terms, and I find it interesting to view my own emotional reactions to winning and losing through this new framework. I'm not sure whether I should feel relieved that my feelings are normal, or irritated that my personal reaction can be so predictable.

The ranks of my several accounts have been somewhere near the 6k/5k border for quite some time. Several accounts? Yeah, thats me using diversification to reduce my risk aversion. So, if the rank of an account wanders close to the border, my frame suddenly becomes narrow, and losses feel all the more awful. Losses are falling off the cliff, whereas wins leave me still close to the precipice. I guess this is the loss domain. If however, one of my accounts either climbs to the mid 5k's or sinks to the mid 6'ks, my frame widens, I feel in the win domain: losses are easier to shrug off and wins increase my confidence.

Regarding Palapiku's original question about why people with a stable rank keep playing, the theory seems to explain at least my behavior well. When I'm in the win domain, games are generally enjoyable, often interesting, and sometimes downright relaxing. When I'm in the loss domain, games tend to be intense, and both the joy and pain of the outcome offer an nice artificial infusion of drama into my daily routine. That, and the feeling that I'm doing something cool that helps to keep my brain malleable, are what keep me going.

Like I said, I'm not sure if I should find this enlightening or unsettling. Who likes being all figured out? How to use this newfound information to my benefit? Well, if things continue in this manner, the border frame will widen with time, I'll enter the "who cares?" domain, and games will lose their intensity. The lack of drama could lead to getting bored with the game altogether. Solution: keep trying to improve. ON TO 4K!!!

Edit: Funny thing. After having not played on my cs account for a while (liking it at 5k) I played 2 games on it this morning - lost to a 6k, demoted to 6k, beat a 5k, promoted to 4k.

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Patience, grasshopper.