On 19/01/2012 16:23, Don Dailey wrote:
On Thu, Jan 19, 2012 at 10:27 AM, John Tromp <[email protected] <mailto:[email protected]>> wrote: On Thu, Jan 19, 2012 at 9:59 AM, "Ingo Althöfer" <[email protected] <mailto:[email protected]>> wrote: > What I mean is the following: > The human player (in 19x19) determines how many handicap stones he gives > to the bot (either 2 or 3 or 4 or 5). > > When he selects a difficult task (=giving high handicap) he gets high > reward in case of a win. When he selects a more easy task (= giving low > handicap) he gets only small reward in case of success. So, the list > from the original posting (300 Euro bonus in case of a win at 5 handicap > stones) is what I mean. > > By giving him this choice under the reward system, I want to learn > what this special person thinks about his/her chances. Considering that the smallest handicap at which computers have beaten pros is 5 or 6, few pros would want the embarrassment of choosing less. Being the first pro to lose a 4 handicap game is not a particularly attractive prospect:-( I expect they will blindly go with the 6 handicap option, mostly due to professional pride, but also because of the higher reward and because there is less embarrassment (even if a higher chance of) losing at the higher handicap. Of course this can be influenced by the incentive, right? I think if a pro were offered a million dollars to beat the computer with a handicap that only gives him a 10% chance of winning he would take it over a sure win that only returned $50. The expectation of winning for each stone handicap should be computed and the incentive for the human should be chosen to make it more attractive to play the higher handicap matches. This should be clearly explained to the pro before proceeding so that he understands that the higher stone handicap is a better bargain but the lower handicap is a more certain payoff. Unfortunately I think you point still holds unless the pro thinks like a scientist or mathematician. There is a factor called "risk aversion" which is a psychological concept and is different for each person. It says that people tend to reject a clear bargain if it has a less certain likelihood of payoff. In this case their investment is not monetary but in the form of embarrassment and pain, thus they are likely to be extremely "risk averse" as you intuit here. But I have a solution that should change the players thinking significantly and cause him to make a slightly better decision. The first step of course is to make it a bargain to play higher handicap matches. The SECOND stage of the solution is to offer him different incentives for losing. You can make this a "game" in which his risk aversiveness (is that word?) is a minor factor if he always comes away with something. He should get more money for losing a high handicap match but still not enough that it is better to lose a high handicap match than win a low handicap match. Here is an example which may say something about your own risk averseness for anyone who has not heard of this concept. You could also add an additional zero the monetary amounts in this example to see if you would change as this increases the risk: Which would you pay $10 for - if given only these 2 choices? : 1. 1 out 2 chance of getting $100.00 2. 1 out of 2000 chance of getting $100,000 Both would be a bargain, because each are worth exactly $50 and you are asked only to pay $10. Some people are so risk averse they would not pay $10 for a 50/50 chance of winning $100.00 simply because they fear losing $10. However most people would immediately see this a bargain or opportunity. If you choose option 1 you have an excellent chance (50/50) of going home $90 richer. If you choose option 2 you will almost certainly go home $10 poorer, but if you win you win really big. Many people don't like the idea of taking a chance and losing $10 (this depends of course on their personality and their income) and are likely to choose option 1. Many would see option 2 as stupidity, a way to give away $10 even though it's actually a bargain. The fact is however that both these options have equal value, an expectancy of $50. In other words if you played this game every day of your life you could expect to average about $40 per day on average to have a $40 a day extra income on average or about 1 million dollars over a 70 year lifetime. The second option is more granular and you might end up with substantially more than 1 million dollars or substantially less than 1 million after your 70 years. Which would you choose if you had to play this game every day? Would you go for the very steady stream of income or the big 100,000 payday which you might only see a few times in your lifetime? The second choice gives you a chance to do much better but risks doing much worse over a lifetime.
You write of risk aversion as something "psychological" and irrational. But, if the sums involved are comparable to one's total disposable wealth, it is perfectly rational. A rational person tries to maximise, not expected wealth, but the expected value of his utility function for wealth.
Admittedly, many people get these sums wrong, because they they are bad at sums, or don't know how to do them, or for "psychological" reasons. But professional Go players are brighter than that.
Nick -- Nick Wedd [email protected] _______________________________________________ Computer-go mailing list [email protected] http://dvandva.org/cgi-bin/mailman/listinfo/computer-go
