M57 wrote:

Alpha wrote:

Toto wrote:

It would not solve your debate, but I think it would be very interesting to have a 'luck index' displayed for each player. As it was said, you always consider more the bad luck you had attacking than the good luck you had defending. Such an index would help you to better understand if you won/lost because of good/bad luck or because of good/bad strategy.

There is a luck index in the works, the mathematics and such for it has been worked out and it is in the large list of things on tom's plate. The index will have the following basic properties: unbounded in either direction (good - positive, bad - negative). defense luck: calculated by itself on all defensive rolls attack luck: calculated by itself on all attacking rolls overall luck: sum of attack and defense The sum of all of the luck in the game is 0. The luck is not based on dice rolls exactly, but on the expected values of winning/losing and attack/defense roll. I apologize for the formatting, using an old IE version and none of the formatting sticks.

If I understand correctly ad 0 is the sum of all luck, which is game adjusted away from the expected outcome.

So a luck index of -1 means something like:

..you had one worse roll than the average player on this board?

..you lost one more army than you should have if you had the same amount of luck as the average player in this game?

If I'm close, wouldn't there be a huge difference in meaning between a -10 rating over the course of a 2000 move game, and the same score over a 500 move game?  If not, I'm curious to understand how this number retains a kind of relevance between situations like these.

I would really like to see independent numbers for each player that represents a SD from the expected outcomes.  Maybe one each for offensive, defensive, and sum of rolls.

 

I think you have it correct, a luck score of a -1 would mean that you have lost one more army than is excepted bases on the expected values. These will be calculated per turn (taking modifiers into account) and than agrugated for a overall game luck as well. My understanding/request was for an addition tab containing this info, similar to one of the luck stat pages from the old world. It is true that the meaning of these stats will be different depending on the length of the game, hence the need for a per turn luck calculation. Using any type of pure standard deviation measure will converges to zero very quickly after say 100 attacks so I do not see any way to make this reasonable. If you have ideas, let me hear them and I will try to work it out.

Here are a couple of ideas.  The first one doesn’t really calculate pure SD but I’ll bet it’s pretty close.

Let’s say you are attacking a large stack of 100 defenders with 3 dice vs. 2 dice all the way.

For baseline sake we know that for every 100 rolls, you are expected to destroy both defending armies 37 times, kill one and lose one army 34 times, and lose two armies 29 times, for a total of 108 kills and 92 loses.

But lets say you win by losing only 84 armies to defender’s losses of 100.  Using a Risk Dice calculator I found that the probability of taking out 100 with 85 armies is about 43%.  Now it’s been a while since I have used SD so I may be way off here, but if I look for 17% away from 50 on a normal distribution SD table I come up with an implied SD of  .44

Idea #2. You’d probably have to tweak it, but using your “pure” number that converges on 0 (though I’m not sure why it would), multiply that number by some a variable like the # of dice thrown, perhaps with an additional multiplier like 0.5.

One last thought:  If we can come up with some kind of SD number (like with idea #1), to make it more palatable, we could multiply it by a number like 30, then create a friendly luck scale:

0-24 = marginally lucky

25-49 = lucky

50-74 = really lucky

75-99 = incredibly lucky

100+ implies divine intervention.

My example would come in with a luck stat of .44 * 30 = +13 using this method.

One more example: destroying 100 and losing only 60 in the process comes in at a less than 2% probability and therefore yields an implied SD of 2.88.     2.88 * 30 = +86

Who cares about how people run or how lucky one is? my guess is that people who will run under their expected value will take it as an excuse for bad ranking.

Useless stats imo.

ecko wrote:

Who cares about how people run or how lucky one is? 

Poker players for one, or just about anyone who plays games where chance is an element and are looking to evaluate their play on a comparative basis.

Useless stats imo.

iyo.  The next time I take you out, don't complain that you were unlucky.

ecko wrote:

Who cares about how people run or how lucky one is? my guess is that people who will run under their expected value will take it as an excuse for bad ranking.

Useless stats imo.

Good and bad I think. An individuals luck, in all games and in the long run, would balance out to zero (at least it should)... so this would silence the "I'm cursed" contingent. 

Game-to-game stats would vary greatly, and I'd like to know what goes into a win. This could fuel the "you won because you're lucky" dialogue.  It can't all be luck... as evidenced by folks with great rank (higher than averages) but a site-wide luck of roughly zero. Same goes for bad players.

Once we settle on a decent per-game luck stat, I'd actually like to go one further, and figure out the average luck of a winner for any particular map. This would be a great indication of just how much luck goes into a victory: also where I'd like to see a SD calculation. Since the proposed luck stat would vary based on games, some kind of normalization could happen, then those scores could be averaged.

Complaining about luck already happens. A lot. I don't see how a luck stat would dramatically change that. If you have a serious issue with it, go play chess.

Luck stats aren't just for players... they're for designers as well. When you make a board, there are plenty of "fun factors" and determining overall luck of the winner would be an additional piece of information one could use in evaluating their own design. This could be kept private between tom the board designer, if that amount of knowing would be too damaging.

Last bit of advice: have a Plan B. If you get crushed in one attack, you should have thought ahead in the event that happens. Sometimes you gotta go all in, but you should have some idea of the risks going into it. Your strategy should minimize the risks and maximize the payoff. Best you can do. If it doesn't work out, it doesn't work out.

You can also play five or seven.

If you feel that dice rolls and luck are such a HUGE factor in every game please explain to me people like BlackDog, Yertle, Hugh and the once and still Kobra Kai.  These players excel at almost every map and figure out a strategy very quickly and implement it.  I've almost never heard any of them complain about dice nor do I ever see them get totally ruined by 1 attack and I've played with all of them quite a bit (I think Yertle and I have close, if not more, than 1500 games played against each other between here and ToS).  It's part of the game and when a dice fail happens, it happens.  I won a 10 v 14 battle only losing 2 armies earlier today and in the same game I lost a 23 v 11 battle going down to 3.  There was a "Stoopid RiskyBack!" shouted at my computer and then I think the next sentence I said was "why do flamable and inflamable mean the same thing?"

Dice Happen

RiskyBack wrote:

Dice Happen

now THAT is a motto.

So are we saying that the mods that were suggested are bad ideas?

(A mod that gives a -/+ modifier for disproportionate attacks, like a 1-4:2 attack having  6v6 dice, but 5-8:2 gets 7v6 dice, and 9-12:2 gets 8v6...) so if I attack a 4 with 20, I get a +2 bonus. 

Heck, even a reverse of that could be a fun mod. attacking a 20 with 4 could earn a -/+ bonus. like a sneak attack award. If the 4 attack a 20 they get +2 for cohones.

The other mod was one that would simply reign in max losses for disproportionate rolls.

Remember, these mods are suggested options. Not changes to all maps. 

It would be interesting to play a few of those games out and see what happens. It could have an interesting effect on how borders work into the strategy.

The other problem with the mod idea is large numbers of dice. For example, using this rolling simulator, we find the following...

8 vs 2: 90% success rate
800 vs 794: 100% success rate (actually 99.99...%)

So, a six unit difference in a small unit scenario still has a 10% chance of a loss, but a six unit difference in a large unit scenario is almost a perfect hit. In fact, 735 attackers against 794 defenders has the exact same fail rate as an 8v2 (only 10%!). So, a simple "I think this attack should work because I have more units than you" mod, or, alternatively, a "I think you're attacking out of desperation" mod, will seriously break game play, especially on larger boards.

That is if you are using addition instead of multiplication.

 

800 vs 794 is pretty much 8:8, or 1:1

the 8:2 I described would get the same modifier if it was 4:1, 800:200, or 100:25.

A designer could get creative with a map and do what you are suggesting if they wanted or you could try and do it.  Seven and Five are examples and Toaster's Diplomacy is another.

What I don't like is trying to make this site something different than what it is.  It is a Risk Based site and I think that should be the basis of all else.  If you can modify the basic rules to make something different the first person to hail you will be RiskyBack (however I sometime hail by fling dung so watch out for that) but wanting to change the site into another type of gamming site is just not cool with me.  I've done a lot to morph the tools we have here to do something different but it's within the rules and that's what makes it fun for me.

When I play here I don't expect it to be World of Warcraft and when I play Adventure on my Atari 2600 I don't expect it to be Assasins Creed (I don't have an Atari).  I'm all for Luck Stats being available and I'm all for being pissed at the dice, but I'm not for giving options to either players or designers that greatly change the basic concept behind the site unless the designer can think of a way to be creative with the set rules to do it.

That's my 2 cents and you can keep the change!

P.S.  Yes, I will probably be working on an Adventure map in the near future.

Mongrel wrote:

ecko wrote:

Who cares about how people run or how lucky one is? my guess is that people who will run under their expected value will take it as an excuse for bad ranking.

Useless stats imo.

Good and bad I think. An individuals luck, in all games and in the long run, would balance out to zero (at least it should)... so this would silence the "I'm cursed" contingent. 

Game-to-game stats would vary greatly, and I'd like to know what goes into a win. This could fuel the "you won because you're lucky" dialogue.  It can't all be luck... as evidenced by folks with great rank (higher than averages) but a site-wide luck of roughly zero. Same goes for bad players.

Once we settle on a decent per-game luck stat, I'd actually like to go one further, and figure out the average luck of a winner for any particular map. This would be a great indication of just how much luck goes into a victory: also where I'd like to see a SD calculation. Since the proposed luck stat would vary based on games, some kind of normalization could happen, then those scores could be averaged.

Complaining about luck already happens. A lot. I don't see how a luck stat would dramatically change that. If you have a serious issue with it, go play chess.

Luck stats aren't just for players... they're for designers as well. When you make a board, there are plenty of "fun factors" and determining overall luck of the winner would be an additional piece of information one could use in evaluating their own design. This could be kept private between tom the board designer, if that amount of knowing would be too damaging.

Last bit of advice: have a Plan B. If you get crushed in one attack, you should have thought ahead in the event that happens. Sometimes you gotta go all in, but you should have some idea of the risks going into it. Your strategy should minimize the risks and maximize the payoff. Best you can do. If it doesn't work out, it doesn't work out.

You can also play five or seven.

Poker is my main hobby, I've played it for 4 years now. So I have a good idea of how luck weights on a particular victory. It is a game full of programs that bring you "luck stats" and while it's more useful in this game because money is involved, I don't think it brings any useful information in risk other than "I should have been up 3 more units after this attack" or "damn, this guy is lucky he shouldn't have won this fight". And it's already painful enough in poker because of the discreditation that follows. To make it simple, players win because they run good and not because they are that good. Believe it or not, that's really the kind of comments such stats bring and I really don't think wargear needs that.

Then, concerning map designers, I disagree with your argument. I don't see how determining overall luck of the winner will help map designers in their creation process. Luck is luck, losing a 11 vs 3 units match happens in every map, regardless of the design. Of course some have more border modifiers than others, but players are aware of that - or should be.

Concerning plan B I don't see why you are mentioning it, I deal with the consequences of a failed attack or plan. And I very rarely complain about bad rolls.

RiskyBack wrote:

What I don't like is trying to make this site something different than what it is.  

I identify with Risky's sentiment, but it's nigh well impossible not to note that there are quite a few modifications that we already have that go pretty far beyond the "standard" Risk paradigm.

Dice mods are an obvious example, but there are already a host of options here that permit designers to create very unRisk-like games ..such as Seven and Five as Risky mentioned.  Alternative engines such as SimulGear and Kjeld's proposal are extreme examples of rules changes that among other things deal with the workings of the dice, and clearly Tom thinks there is room for these types of alternatives here.

This discussion goes to the entire debate about how many/much options/variety designers want/need. Though I'm not fond of its specific mechanics, I think Epstein's sliding mod scale idea is intriguing.  It's advantages seem obvious enough.  Large forces overwhelm smaller forces, and the question we should be asking here is: "Are Risk dice with current mod options adequate to the task?"

I'm going over the list of "complaints" about the dice on this thread and I'm inclined to say that odds the way they are seem quite realistic to me. Take Epstein's initial 11 v 2 example.   I ran ~100,000 simulations of this and there looks to be a ~0.7% chance of a disaster.  Seems realistic to me.  Your troops get suckered by that old Trojan Horse tactic, or a General turns out to be a traitor, or there's an epidemic or earthquake, etc.   "Dice happen," and that's a good thing.  As someone pointed out before, this isn't chess.  Dice are meant to emulate the vagaries of war, and I have to say that the dice right out of the box do a pretty impressive job of this.  Throw standard mods on top of this and you can emulate terrain.

My initial opinion right now is that sliding mods based on stack size would take the "realism" out of the game.  I could be convinced otherwise, but I would need to see a concrete example where a sliding mod scale makes sense for a particular board design, is clear enough for the users to understand in the context of that design, and simple enough to implement in the designer section.

 

There are too many discussion here to really respond, but I'll try.

@Risky/M57 - I agree that part of the fun of designing boards is bending the rules that are already here. I like risk and that is why I am here playing risk games, but I also like pure strategy games which is why Five and Seven came into existense. I would say that SimultGear is very different from standard risk, but Risk has been reinvented several time in the last 20 years so there are lots of modification out there. I think it is hard to say for sure what Risk is, but easy to say what Risk isn't.

@M57 - I do like your luck stat idea, but I think it is hard to scale. When I click total attack, your luck stat is moderately easy to calculate (there is alot of calculation going on in the background to come up with the numbers, but I am sure it could be stream-lined). The scaling part that I am unsure of is if I make 15 3v2 attacks across 7 different borders, how will the luck be calculated? That is, if I lost 13 and killed 17, am I treating the turn as a 13 v 17 luck stat calculation?

@ecko - Without a luck stat analyzer, players already complain that the only reason why the lost was because of bad luck and the only reason why someone else won was because of good luck. Every roll and every attack is in the history so this analysis can already be done and is how this thread and many like came into existence.
How the average winning luck stat could help a board designer is this. If the average winner has say 55 (using M57 scale above), this says that the board is really won by luck, whereas if the average winner has say a 5, then there must be some strategy to the board since luck is not the only thing winning games. Since I am interested in making boards with several strategies, I want to see how much strategy over luck wins games (a stat would help analyse this).
As a player, I want to know my luck stats for the following reason; I don't want to complain about bad luck. On complicated boards, where there are many winning strategies, I want to know if my strategy was good and I lost do to rolling so I should keep the strategy, or I won because of divine intervention and the strategy was crap. I should try something different next time. A perfect example of this is with Spy vs. Spy. As we were trying to decide optimal strategies, it is very hard to decide whether or not a win/lose came from good/bad strategy or from good/bad luck.

I am sure I missed something and maybe these threads should be split. Later if I have time I will create a luck stat thread recaping.

All this aside....just give me MORE DICE

ecko wrote:

Mongrel wrote:

ecko wrote:

Who cares about how people run or how lucky one is? my guess is that people who will run under their expected value will take it as an excuse for bad ranking.

Useless stats imo.

Good and bad I think. An individuals luck, in all games and in the long run, would balance out to zero (at least it should)... so this would silence the "I'm cursed" contingent. 

Game-to-game stats would vary greatly, and I'd like to know what goes into a win. This could fuel the "you won because you're lucky" dialogue.  It can't all be luck... as evidenced by folks with great rank (higher than averages) but a site-wide luck of roughly zero. Same goes for bad players.

Once we settle on a decent per-game luck stat, I'd actually like to go one further, and figure out the average luck of a winner for any particular map. This would be a great indication of just how much luck goes into a victory: also where I'd like to see a SD calculation. Since the proposed luck stat would vary based on games, some kind of normalization could happen, then those scores could be averaged.

Complaining about luck already happens. A lot. I don't see how a luck stat would dramatically change that. If you have a serious issue with it, go play chess.

Luck stats aren't just for players... they're for designers as well. When you make a board, there are plenty of "fun factors" and determining overall luck of the winner would be an additional piece of information one could use in evaluating their own design. This could be kept private between tom the board designer, if that amount of knowing would be too damaging.

Last bit of advice: have a Plan B. If you get crushed in one attack, you should have thought ahead in the event that happens. Sometimes you gotta go all in, but you should have some idea of the risks going into it. Your strategy should minimize the risks and maximize the payoff. Best you can do. If it doesn't work out, it doesn't work out.

You can also play five or seven.

Poker is my main hobby, I've played it for 4 years now. So I have a good idea of how luck weights on a particular victory. It is a game full of programs that bring you "luck stats" and while it's more useful in this game because money is involved, I don't think it brings any useful information in risk other than "I should have been up 3 more units after this attack" or "damn, this guy is lucky he shouldn't have won this fight". And it's already painful enough in poker because of the discreditation that follows. To make it simple, players win because they run good and not because they are that good. Believe it or not, that's really the kind of comments such stats bring and I really don't think wargear needs that.

Then, concerning map designers, I disagree with your argument. I don't see how determining overall luck of the winner will help map designers in their creation process. Luck is luck, losing a 11 vs 3 units match happens in every map, regardless of the design. Of course some have more border modifiers than others, but players are aware of that - or should be.

Concerning plan B I don't see why you are mentioning it, I deal with the consequences of a failed attack or plan. And I very rarely complain about bad rolls.Understood,And I'm not singling you out. Just saying luck stats have merit.

Understood. And I'm not singling you out, just saying luck stats have merit.

Games can amplify luck or can control it. Spy vs spy being the essential example here. There's some luck in attacking but setting those attacks up before contact, in open space where there's a guaranteed victory, controls the luck factor. Essentially, position games can control the luck.

On the other hand, leaving a field or neutrals to bash through means each advance is questionable- more luck. An extreme example would be two territories w/50 in each. First to go has a good chance at winning.

Is there any game that has an average luck of winner equal to zero (or slightly positive)? I don't know, but I'd like to.

Perhaps all the tricks to control luck have been figured out. But the 'avg luck of winner' stat might also tell us something we dont know yet.

Alpha wrote: 

The scaling part that I am unsure of is if I make 15 3v2 attacks across 7 different borders, how will the luck be calculated? That is, if I lost 13 and killed 17, am I treating the turn as a 13 v 17 luck stat calculation?

That is what I had in mind.  It keeps it as simple as possible while still permitting the possibility of sampling and analyzing a historical range of play, I have no idea how that scales.   If over the course of a game a player runs 5000-10,000 3v2 attacks, will it bring the system to its knees?  If so, might there be a way to estimate the luck without calculating the sum of all possibilities and then backing out the solution?  For instance, using a roll simulator I created a table of what 50% looks like for a range of outcomes and I'm not great at linear regression, but I think I figured it out:

 25 v 25
 46 v 50
 89 v 100
174 v 200
260 v 300
346 v 400
430 v 500
515 v 600

857 v 1000

2564 v 3000

5126 v 6000

Given:  a = # of attackers, d = # of defenders:

a = 0.853d + 4

Note: I used a on-line calc that keeps the minimum number of attackers to 3, so I might be off a hair, but once you find the number and tease that coefficient out 2 more decimal places you're good to 1,000,000 attacks.

Granted you'll need to figure out 99 of these for each of the six different categories of battle (3v2, 3v1..), but I'll bet there's a pattern.

I was also thinking that one of the tricky parts might involve how to weight the six categories of battle, but maybe that wouldn't be so hard. If each destroyed unit counts as an event, then 3v2 numbers should influence the aggregate twice as much 3v1 attacks.

 

The constant should be .853414373 and I do believe that this fails to be exactly linear, but an approximate linearization would work so okay (I haven't really thought this part all the way to the end).  I also have slightly different numbers than you, but don't want to argue about them since I might be wrong.  There is also the issue of whether or not you are allowing a 2 v 1 attack at the end or not.

The only correction I want to make is that you are using standard scores from the normal distribution, not using standard deviation (related, but different, blah blah blah).  I like your idea and it has an instantly palettable interpretation with your proposed scale.

I do think that the background calculations that would have to be done to compute the expected relative frequency of successfully killing a 100 with 75 would bring the site to it's knees, at least how I am thinking about this.  If these calculations were happening after every attack, there are 1000 of calculations being done for a single turn.  However, if you were only using this as a overall luck stat calculated at the conclusion of a game, then I think it could work.
Additionally, there is the problem of modifiers and non-3v2 attacks that would need to integrated and this make it all more complicated.

 I also have slightly different numbers than you, but don't want to argue about them since I might be wrong.

No argument from me.  Mine was a very rough estimate based on running a few thousand simulations for each set with guess and check methodology.  Hey, I teach fifth grade math ..what do you expect? 

I was looking a little deeper into the problem and it appears as if 50% was a bit of a tease.  There doesn't appear to be a fixed constant for 25%, so my intuition says you're wrong about it not being linear at 50%.   I conjecture that at 51% it should be very close to linear, but at 75% that extra coefficient starts kicking in harder.  I may not be explaining this clearly, but I'm thinking it might be necessary to alter the equation in a manner that takes into account the slope of the standard curve at each given percentage point.

However, if you were only using this as a overall luck stat calculated at the conclusion of a game, then I think it could work.

Yes, a set of game-end numbers would be great.  One set of calculations and done.  But unless the number of calculations are significant, I see no reason that the "history" page couldn't be outfitted with a calc that computes the stats "to the present", and also lets the user input a turn range.  I'm guessing the history page doesn't get a lot of hits; this, and Tom should make it a Premium feature.

Additionally, there is the problem of modifiers and non-3v2 attacks that would need to integrated and this make it all more complicated.

One problem at a time.