Role of Fencers?

[Pentarctagon]

Let's say there's this game. It costs nothing to play. There's a 97% chance you'll win $10 and a 3% chance you'll have to pay $200. Would you play?

im not sure. i guess first off is how can it cost nothing to play if i have a 3% chance of paying $200 ? hm. i would have to say no. while the 97% chance is extremely high, the 3% chance would mean i lose 20x more than i would have won. so while there is a high chance that i would win, the chance of such a huge loss in comparison would make it seem like too large a risk because there's always that tiny chance that it might happen...

[jmegner]

Let's say there's this game. It costs nothing to play. There's a 97% chance you'll win $10 and a 3% chance you'll have to pay $200. Would you play?

im not sure. i guess first off is how can it cost nothing to play if i have a 3% chance of paying $200 ? hm. i would have to say no. while the 97% chance is extremely high, the 3% chance would mean i lose 20x more than i would have won. so while there is a high chance that i would win, the chance of such a huge loss in comparison would make it seem like too large a risk because there's always that tiny chance that it might happen...

As far as I'm concerned, the answer to "do you properly weight the effects of a 3% chance event?" is no. 0.97 * $10 - 0.03 * $200 = $3.70. You would expect to win on average $3.70 for every time you play this game.

edit: just to make it clear, I would play this game as often as possible. Even if I could only play once, I would.

[Araja]

I had 98.5% chance of killing a target in an SX match and it levelled up, this sort of thing has happened several times over my Wesnoth career in general, giving me a constant fear of attacking any "boss-like" unit.

So I agree with Pentarctagon in saying that yes, RNG paranoia is very real.
Every time I see a high defence unit in combat I watch it like a hawk...

[dragontamer]

im not sure. i guess first off is how can it cost nothing to play if i have a 3% chance of paying $200 ? hm. i would have to say no. while the 97% chance is extremely high, the 3% chance would mean i lose 20x more than i would have won. so while there is a high chance that i would win, the chance of such a huge loss in comparison would make it seem like too large a risk because there's always that tiny chance that it might happen...

As far as I'm concerned, the answer to "do you properly weight the effects of a 3% chance event?" is no. 0.97 * $10 - 0.03 * $200 = $3.70. You would expect to win on average $3.70 for every time you play this game.

edit: just to make it clear, I would play this game as often as possible. Even if I could only play once, I would.

I disagree. Averages are not everything. If I could play this game 10,000 times, I would. However, if I could only play once, I wouldn't. Why? If I play 10,000 times, then the probability of me losing money is practically zero (erm, z-score of ~160 by my calculations. Practically, I have a better chance of dying in an asteroid crash in the next 2 minutes than losing money after 10,000 games). If I could only play once, then I have a 3% chance of losing $200. 3% is still a rather large percent.

Lets change the numbers up a bit for example. Would you play the game if you had a 97% chance to gain $1,000,000, and a 3% chance to lose $20,000,000. Unless you have the ability to pay that $20,000,000, I wouldn't care about the "on average" compensation of $370,000.

[Skrim]

The thing with the RNG Paranoia Shield is that people remember when something went wrong or failed. The successes are generally forgotten. If someone had a 97% chance of killing a target and leveling, and a 3% chance of getting killed and leveling the enemy, they won't remember it if they got the 97% probable outcome. They would remember it if they got the 3% outcome. It's like rolling a natural 1 when anything but 1 could have done the trick. The better the odds of success, the more memorable is the failure.

[uzytkownik]

I disagree. Averages are not everything. If I could play this game 10,000 times, I would. However, if I could only play once, I wouldn't. Why? If I play 10,000 times, then the probability of me losing money is practically zero (erm, z-score of ~160 by my calculations. I'll gain money one google / 100 of the time). If I could only play once, then I have a 3% chance of losing $200. 3% is still a rather large percent.

Lets change the numbers up a bit for example. Would you play the game if you had a 97% chance to gain $1,000,000, and a 3% chance to lose $20,000,000. Unless you have the ability to pay that $20,000,000, I wouldn't care about the "on average" compensation of $370,000.

The average is more correct - but the question is average of what. IMHO value is the correct variabl. We usually assumes that the money have linear value and we can use it as a unit of value. However it is not as marginalism (an theory in economics explaing value) shows. Real value of a dollar for a given person is valued less. So with first $10 I can do many things - for example buy a sandwitch to not be hungry. However next $10 are spend on less important needs so it have lower utility hence less value. If I have $21,000,000 (I don't ) the difference in utility between that and $1,000,000 is much highier then between that and $22,000,000. Is it worth playing - it depends o many circumstances and is very personal dependend (how much I value different spendings).

How to apply it to game? It is very hard to state. On average such gambling would have a netto effect. However if you have for example winning situation and you can attack enymy leader with 97% chances of kill him and 3% of killing yourself it is worth it. If your enymy left you with no gold, no units, no villages (etc. - he have near 100% chance of killing you in following turn - for example he have sufficient number of bersek units) and you can attack his leader with your leader with 97% chance of suicide and 3% of success - it is probably worth it. Many of those odds depends on exact situation on the board.

However in most cases the fight is widely spread. Probably you success or failer should not depend on single success. Therefore it is relativly safe that in neiberhood the value function is flat (i.e. linear - similar situation is with mass in physics: it is generally safe to assume that dm/dt = 0 despite it not being true with relativity effects taken into account).
In some cases it is not - for example if you have 3 liches lost of one allowing you to win a game (when opponent have not many high level function) is much less lost of value then loosing the only one.

PS. Sorry if I'm being technical. I think that so-called pure mathematica reasoning is incorrect and need the valuation theory from economics.
If it very easy to assume that money have linear value function - but they have not. Similar is with everything. Marginal value of anything is decreasing (appling to game - marginal value is decreasing the more units you have).

[Pentarctagon]

As far as I'm concerned, the answer to "do you properly weight the effects of a 3% chance event?" is no. 0.97 * $10 - 0.03 * $200 = $3.70. You would expect to win on average $3.70 for every time you play this game.

i would just like to point out that expected value doesnt really work to well with events that occur one time. sure, the expected value is $3.7, but in reality you dont win $3.7. you either win $10 or lose $200. since that is the case, the potential loss outwieghs the potential gain so much that i dont really want to risk it. i agree with dragontamer though, if i could player the game 10,000 times i would play it.

[manored]

...in some situations estimated damage is not everthing...
...it might be worth to trust luck...

@manored:

You're, right, expected value isn't everything, but it sure is important. I play the game with a very statistical mindset. I would say I try to make every decision based on expected utility. Be aware that expected value is not the same as expected value.

Trust luck? Is that believing things will go better than you should statistically expect? Or do you mean something else?

I mean: not merely suming up all damage you can cause and reducing it based on the chances of hitting. Thats a nice way to predict damage accurately and fast, but thats not how the game works What I mean its this: Dont forget to take in account attacks are composed of only a few tries, so there are large fluctuations between the estimated damage and the actual damage caused: If I have 5 attacks with 50% chances of hitting and 10 damage each, the estimated damage is 25 but the real damage will be most likely 20, 30 or 40. That has to be taken in account then deciding how to move, because, for example, maybe causing 30 damage or more would give you a chance to kill with another unit, and considering it will be 25 could make you lose an opportunity.

Personally I think I have learned to acknowledge good luck as well as bad luck. If you can do that, you will realize that just like a disaster can happen something wonderfull may also happen... that way, you can escape the paranoia

[Eskon]

If I have 80% chance to kill on an enemy leader versus 20% of losing, I'll risk it. Why? Because if the game is close enough that I lose if the leader attack fails then obviously my chances to win in the long run are much worse than 80%. If it fails, I don't feel bad. Why? Because I know that if I play more games things such as this will even out. You win some, you lose some.

[dragontamer]

If I have 80% chance to kill on an enemy leader versus 20% of losing, I'll risk it. Why? Because if the game is close enough that I lose if the leader attack fails then obviously my chances to win in the long run are much worse than 80%. If it fails, I don't feel bad. Why? Because I know that if I play more games things such as this will even out. You win some, you lose some.

That is true. However, if you look at how ranking systems are done (I think the Wesnoth Ladder uses the "Elo" system?), then you have to perform better than your expected skill to climb the ladder. If you're say, 300 points above your opponent, you have to win 85% of the time to keep you're ranking. So in this case, if you overall go for 80% chances vs the opponent, you will lose your ranking over the long term.

Basically, for a high-ranking player to be ranked even higher, they have to win even more games on the average to continue to climb the ranks (in the Elo system). Other Elo based systems follow this metric as well. (although, Microsoft's "TrueSkill" has different constants. IIRC, to climb like 10 points above someone you need to win 80% of the time or something like that. Smaller numbers, but the same idea)

[jmegner]

@manored: thanks for the clarification. I completely agree that attacks should not be analyzed in isolation.

@eskon: Everything you said on the 80%-20% scenario was wise and just.

@pentarctagon: I still believe in expected value for one-time events for two reasons. 1) During your life you get to partake in many one-time events. 2) You would still expect to come out ahead.

@uzytkownik: Your quote block is wrong. You're quoting someone other than me. Nested quotes get complicated. Also, thanks for covering what expected utility is. I mentioned it briefly but didn't want to get into it. You cover a lot of the reasons that I say I make decisions based on expected utility, not value. However, while you would say that the valuation theory is not mathematical, I consider it very mathematical. So I'll stand by my stance of making decisions in a very mathematical way, but I hope you interpret my stance differently now.

@everybody: Thanks for answering my "do people really have RNG paranoia?" question.

Let's not get confused. Just because something has a positive expected utility, that doesn't mean I would do it. I might have another mutually exclusive option that has a greater expected utility. So, would I attack the opposing leader if I had a 99% chance of killing him? Only if the expected utility of attacking was greater than not attacking.

[Elvish Scientist]

I think this discussion about chances is a little beside the point in a discussion on the role of fencers. Fencers should avoid confrontation with more then one unit. If you want a unit to hold one particular village, use spearman or HI. The fencer should move to a next village if he is attacked. If he does, he is very annoying. Either the opponent is going after him, or he reoccupies the village. In both cases the fencer can take one village after the other, doing great economical damage. The only way to prevent this is to kill the fencer before he breaks through the lines. This will often require several units which will pay time for the loyalist army to retreat at dusk and will help them through the night.
The only units which can prevent this fencer tactics are those who can really kill him quickly: mages, adepts, horsemen and the like.

[manored]

I think this discussion about chances is a little beside the point in a discussion on the role of fencers. Fencers should avoid confrontation with more then one unit. If you want a unit to hold one particular village, use spearman or HI. The fencer should move to a next village if he is attacked. If he does, he is very annoying. Either the opponent is going after him, or he reoccupies the village. In both cases the fencer can take one village after the other, doing great economical damage. The only way to prevent this is to kill the fencer before he breaks through the lines. This will often require several units which will pay time for the loyalist army to retreat at dusk and will help them through the night.
The only units which can prevent this fencer tactics are those who can really kill him quickly: mages, adepts, horsemen and the like.

I believe you are right both on the off-topicness and in the role of fencers... getting back on topic

I think globins placed on your villages are also nice to prevent fencers from dancing on top of then, if you have globins, that is.

[Pentarctagon]

though if your using goblins to take a village to keep a fencer from taking it, you had better have some harder hitting units pretty close behind. the goblin has much less hp than the fencer and the fencer would probably be on equal or better terrain than the goblin.

[Skrim]

Goblins or Walking Corpses can prevent Fencers from taking a village, but they:

A. Cost you gold which could be used for making more front-line units.

B. Make nice targets for the Fencers if not backed up.

They also exert no ZoC whatsoever, and can't stop happy Gryphon-raiders and other marauding scouts from escaping. Fencers in particular are skirmishers and can't be ZoCed by anything, without being completely surrounded.