I took lessons from a Korean pro, Myungwan Kim; one of which was an analysis of
choices made in yose, which was solidly based upon a probabilistic model of
expected gains. Don't underestimate the mathematical skills of Go
professionals.
Terry McIntyre <[email protected]>
Unix/Linux Systems Administration
Taking time to do it right saves having to do it twice.
>________________________________
> From: Don Dailey <[email protected]>
>To: [email protected]
>Sent: Thursday, January 19, 2012 11:23 AM
>Subject: Re: [Computer-go] Computer Go and EGC 2012
>
>
>
>
>On Thu, Jan 19, 2012 at 10:27 AM, John Tromp <[email protected]> wrote:
>
>On Thu, Jan 19, 2012 at 9:59 AM, "Ingo Althöfer" <[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.
>
>
>Don
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>
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