[Computer-go] Computer Go and EGC 2012
Don Dailey
dailey.don at gmail.com
Thu Jan 19 10:27:49 PST 2012
On Thu, Jan 19, 2012 at 12:33 PM, steve uurtamo <uurtamo at gmail.com> wrote:
> Moreover, we are not generally offered the opportunity to repeat such an
> experiment infinitely many times, nor do we generally have infinite
> bankrolls to survive an unlucky sequence. Variance is as important as
> expected value.
>
Understood. The only reason I mention repeating such an experiment a
large number of times is that it makes it easy to understand what the
expectancy is.
Where I worked years ago they would have a game pool for football games.
A 10x10 grid for 100 different bets and you would pay someone $5 per bet
for a chance to win $500. Sometimes they had $1 bets or $10 or $20 bets.
The winning square was based on the least signficant digit of the score
0 - 9 of course. It's easy to see that this is an even game. A $5
bet was worth exactly $5 (at least in principle if not in practice.)
However, there were some people that didn't understand this - much to my
surprise that actually thought it was a good deal - after all $500 is a LOT
of money to them and they only had to risk $5 !!!! These people often
bought up several squares and I think they believed it improved their
expectancy, even though all it did was improve their chances of winning
but at a compensating cost.
This was always a losing game in practice for a couple of reasons.
Usually the guy collecting the money took a small percentage which
immediately makes this game a negative expectancy proposition. And
there was always the chance that the "banker" would take off with the
money, lose it, or just fail to pay off. That was actually very rare
but it is in fact part of the risk which by itself tips the balance into
negative expectancy territory. More often they would let you take a
slot without paying right away with an IOU or promise to pay. They were
not always able to collect from every person once the game was over and the
winner declared or collecting was like pulling teeth for them and the task
of collecting went to the winner, which also makes this negative
expectancy even if you do collect since your time is worth something. Of
course they solved this problem by insisting that you cannot buy a square
with an IOU but had to pay immediately upon purchase and signing your name
on the square.
I never participated because I am not a gambler, but it was fun to watch
as a study in human behavior and greed.
Don
> s.
> On Jan 19, 2012 9:19 AM, "Nick Wedd" <nick at maproom.co.uk> wrote:
>
>> On 19/01/2012 16:23, Don Dailey wrote:
>>
>>>
>>> On Thu, Jan 19, 2012 at 10:27 AM, John Tromp <john.tromp at gmail.com
>>> <mailto:john.tromp at gmail.com>> wrote:
>>>
>>> On Thu, Jan 19, 2012 at 9:59 AM, "Ingo Althöfer"
>>> <3-Hirn-Verlag at gmx.de <mailto:3-Hirn-Verlag at gmx.de>> 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
>> nick at maproom.co.uk
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>
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