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[UmbrageOfSnow]

And anyway, I'm not even arguing that it's always correct to choose two targets, I'm arguing that it's not always better to choose one.

I believe there are some circumstances where choosing one might be better, like when there is an obvious NK target that you think should be protected, or when you suspect your reads are better than the rest of the town at the moment and you want to have some chance of protecting someone you don't think will be targetted otherwise, where picking two would increase the chances of your second choice overlapping.

People keep saying "the math does not work" and not backing that up.

[silverspawn]

faust... did back it up. in his last post. and he's 100% right.

picking 1 is always >= than picking 2 because 1 increases the influence you have on your decision. If you assign a value to every player based on how good of a target he is, you could list all players descending by there number. One has to be the first. Another one has to be the second. Targeting just the first has to always yield to a higher result, or at worst an identical result if your #1 and #2 have identical numbers, i.e. if your two biggest scum/town/whatever reads are equally strong.

and in practise, #1 always has the benfit of more information when it comes to claiming.

therefore, every PR should always pick 1 target in this setup.

[silverspawn]

*their  number

( I also don't have a spellcheck here, I hope it doesn't look too bad )

[UmbrageOfSnow]

Successful protection is more important than information, since the vast majority of the time significant information will be impossible to get.

I am not convinced your #1 pick is always superior to 50% #1 and 50% #2.

[UmbrageOfSnow]

Additionally, there's the aggregate read effect that XP pointed out.  All PRs are town, and all town know their own alignment.  Especially for the Roleblocker that seems significant, at least slightly.

And again, I think any slight improvement in targeting is far better than any slight improvement in information.

[pacovf]

I am inclined to agree with UoS, but I haven't given it much thought. It's true that it seems difficult to glean any information from a successful nightkill block.

[silverspawn]

but it is. Let's say protecting X is 60G (G is an arbitrary and undefined measurement for how good protecting it is which is of course impossible to measure. But it still is so and so good, so it has a theretical value). Y is 57G. Everyone else is lower.

If I submit X, then X is protected, and I get 60G. If I submit X and Y, then either one is proteced, and I get (57+60)/2 = 58,5G (on average).

Again, these numbers are arbirary, but they do serve to make a point here. You can also do it without numbers, and just say that protecting the best target is a little bit better than protecting the second best. You rather have the best protected than either the best or the second best.

Or look at it like this: suppose you wanted to pick 2 targets. You should never want that, but let's suppose so anyway. Instead of submitting both names, you could randomize for yourself, and submit whichever one you randomed. That is strictly better, since the results are the same except that you have more information later. Now suppose that, instead of randomzing it, you pick the one which you like more. That has to be at least as good, since a prefence pick is at worst as good as a randomized pick. So, once again, picking one for yourself is always preferable (or at worst identical).

Dunno, I just rephrased what I said in my last paragraph in 3 different ways. Protecting your favorite target is the optimal choice, everything else is either the same or worse. it's really that simple

[UmbrageOfSnow]

How fun would a part-time Vig be?  I think it would be lots of fun.

[UmbrageOfSnow]

If you submit X, X is not necessarily protected most of the time though.  Because there are probably other players with your PR.

And it's not all about the "best" target.  You guys really don't think Doctor protection ever comes down to a game theory type situation where it's all about guessing between two targets for both town and scum and optimal play becomes a random choice between the two?  Because I think that happens reasonably often.

[UmbrageOfSnow]

And again, no one's reads are perfect.  What about the situation in this game where I wanted to protect SS and Faust.  If I thought Faust was the best target, I'd have always protected scum if I targetted once.  But I had a lot of doubt about SS and Faust, so by choosing both, I figured they probably weren't scum together and was more likely to not be protecting scum.

i.e. MY EVALUATION of G-units was significantly off from the ACTUAL G-VALUE.  By choosing two, you get the average of the two values, which may be better than your own reads.  Especially if other PRs are in the game and also have good reads.

[silverspawn]

nono, the fact that your reads are inaccurate doesn't change anything. G is how good you expect it to be. You still want to maximize it. The degreei of accuracy doesn't change the principle, it just makes it less important. Like, if your reads are super good, then choosing 1 is much better than choosing 2, whereas if they're really bad (i.e. almost random), then choosing 1 is only a teeny tiny bit better than 2. But it's always better.

The only way it can get worse is if your reads are below random - like, if the player you believe to be towny has a higher chance to be scum. An assumption I made is that this is never the case, and it is one you will always make for any decision in mafiascum - having reads while not believing that they are better than complete random is logically impossible.

[UmbrageOfSnow]

You are much more likely to be wrong on one read than on two reads.  It's insurance.

[chairs]

Picking 2 targets is the equivalent of hedging in investment strategies - you make a bet, but you hedge that bet by saying "if I'm wrong, here's an alternative that might help me salvage some value".  http://www.investopedia.com/terms/h/hedge.asp

[ashersky]

You aren't factoring in scum thinking into your equations, by the way.

[silverspawn]

Picking 2 targets is the equivalent of hedging in investment strategies - you make a bet, but you hedge that bet by saying "if I'm wrong, here's an alternative that might help me salvage some value".  http://www.investopedia.com/terms/h/hedge.asp

no. it's not.

[skip wooznum]

UoS, unless you're claiming that statistically speaking, doctors would block more NKs if they're second target choice ended up being targeted rather than their first, (which I doubt is true), it is obvious that the doc should always target his first choice. And if you are claiming that statistic, then he should target his second choice all the time. There is no scenario, where randomizing a target is better than choosing one. There is one very specific scenario where randomizing is equal to choosing, and that is if the doctor has two potential targets that he prefers equally.
This might repeat some of faust's and ss's points, I didn't read them too carefully.

[UmbrageOfSnow]

The doctor does not know the scumteam and does not know their killing priorities in several instances.

I'm saying the doctor can't accurately predict who is the first priority and who is the second 100% of the time.  Or even most of the time.

[UmbrageOfSnow]

And bet hedging really is a good comparison.

[skip wooznum]

And bet hedging really is a good comparison.

it's not bet hedging though. Because there's a chance your first choice is correct and your second is wrong, hopefully greater than the chance the opposite is true. Why is this bet hedging?

Bet hedging is if instead of betting $100 dollars on horse A, I bet $70 on horse A and $30 on horse B, thereby lessening the risk of losing $100. You're describing a situation where instead of betting $100 on horse A, you flip a coin. If heads, bet $100 on horse A, if tails bet $100 on horse B. You're not lessening the risk of losing $100, you're increasing that risk by playing suboptimally.

[UmbrageOfSnow]

That analogy misses the whole central dynamic where 2 of the horses are evil and the mob is trying to figure which one you are betting on so they can injure it's leg... or something.

I'm tired.

And anyway, this doesn't feel like as much of a conversation as I was hoping for.  I don't know how to explain what I mean, I'll try again in the morning.

[skip wooznum]

WIFOM doesn't change the equation. At the end of the day, taking into account WIFOM, a doctor has to make a decision.  His best choice overall is better than the average of his best and second best overall, taking into account WIFOM. So if a doctor narrows it down to two and flips a coin instead of deciding, he's doing something that's at best equal to deciding himself, and most of the time worse than deciding himself. WIFOM isn't some magical wrench that gets thrown in the works, it's just something to think about prior to making a decision for who the best target is.

[UmbrageOfSnow]

I'm not claiming it's magic, I'm saying that you guys are undervaluing the coin flip.

And anyway this ignores the point that you can use other players reads better by choosing two.

[skip wooznum]

I'm not claiming it's magic, I'm saying that you guys are undervaluing the coin flip.

And anyway this ignores the point that you can use other players reads better by choosing two.

In general when you're a doctor, do you flip a coin?

[UmbrageOfSnow]

There are situations where I believe that's optimal, yes.

[pacovf]

...because it never gets old.