??????
You are not logged in.
Oh... but the main point of the amulet contest was the actual AMULETS themselves.
As in, 36 physical pieces of metal that would be mailed out at the end. 6 of them from 99.99% pure gold, 12 in 99.99% pure silver, and 18 in copper. I.e., I'd buy some Canadian Maple Leaf coins and lost-wax-cast the metal into hand-carved occult amulets that are one-of-a-kind. At the end of the contest, there would be 36 winners.
Ah, I wasn't sure how important that part was to you, it makes it a lot harder to prevent collusion/other weird incentives. e.g. this is guaranteed to get an edge: Have x colluding accounts, if two accounts ever meet in an amulet game have the game thrown to the one with the highest probability of winning that amulet (usually the one with the higher score unless that player has a higher score on another amulet). Also if you're a couple of points away from the lead you can offer pretty good money to players to throw games to you (the anonymity in the game makes it harder, but there's these forums and there's the chatrooms [and anyone following these gets an edge because of the chance of offering or being offered money to throw games]). I'm pretty sure these edges can't be eliminated in this structure, except with hard-to-police rules against the behvaiour. So the question is what size edgte does this sort of thing give you? Supposing colluding accounts can't do anything to increase the probability of facing each other then one has the amulet then the cahnces that they get to face a colluder will be the number of colluder/number of players. 10% seems like a doable amount of colluders to get, which means you get a 10% chance of winning for nothing, which is a 5% edge for someone who normally wins 50% per game, or 3% edge if you're winning 70% of normal games. That 3% edge for the 70% player increases their chances of getting 5 wins in a row from 16.8% to 20.7%, or of winning 10 games in a row from 2.8% to 4.3%, so colluding isn't going to guarantee a win but does seem worth doing if you want an amulet, (plus don't forget colluders have a time advantage because they can win really quickly if the face a colluder). Or if we look at it per game between colluders: Let's suppose for simplicity and because I think it's true that each player is only likely to get their hands on a particular amulet once so it's all about getting winning streaks. Let's further suppose that the score needed to win this particular amulet is 8 points. Two colluding players are playing, A with a score of 2 and B with a score of 0 and both with 60% chance of winning a game against a random opponent. Then if A wins they only need to win 5 more games which they do with 7.8% chance while if B wins they only have a 2.8% of getting to 8. Without colluding A and B collectively have a chance 5.3% of get the amulet, whereas with colluding they have a 7.8% chance so one they meet colluding is 2.5% of the value of the winner's prize. If A has a higher score then they stand to gain even more by colluding (the maximum is ~49% if A is on 7 points and the minimum is ~1% if A is on 1 point). If those edges are within the rules they seem worth taking to me.
You really have to change the structure of the thing quite a bit to avoid this while keeping the amulets: e.g. every point you win gets you 100 coins to play with in a mini-tournament for the amulet at the end of the promotion, or you only play people with the same number of amulet points as you (there are few different ways of doing this e.g. Each amulet has rounds in which games a played: each round for each amulet two new players are chosen to play an amulet game, and if any two players are on the same score they play an amulet game with every game worth one amulet point, and whoever has the most point holding the amulet [so the first round 2 people play for 1 amulet point and the amulet, the second round 2 new people play for just 1 amulet point, in the 3rd round the winners of the 1st 2 have an amulet point each so play each and two new players are chosen to play a game to get to 1 point etc., not really the structure you're looking for but it does prevent game throwing]). Another thing you could do is hide who has the amulets from everyone including the amulet holders, and then limit the number of games someone can play against the same opponent - actually maybe not as bad as it sounds if you could work it into the them of the game somehow and maybe drop some hints occaissionally about what is happening with the amulets. Otherwise you have to live with the edges or just ban them even if you can't easily police them.
Last edited by storeroom leaflet (2015-03-04 23:45:49)
Offline
An edge through collusion is impossible to avoid in any scenario where we don't verify the identity of each participant. Well, except in the main game, where we're lucky that collusion doesn't help you win more money. I'm talking about tournaments of any kind, etc. Someone with 2 accounts always has an edge over someone with 1 account, because there will always be some chance that those two accounts will play each other.
What I want to avoid is an obvious way for someone to GUARANTEE a win through collusion.
For example, if we didn't stop players from controlling who they played against, a colluding player would pick matches against only their collusion partners and thus rack up an unbounded number of wins in a single streak. A colluding player could easily beat any non-colluding player this way.
In The Castle Doctrine contest, there were methods like this available, sadly. Where a player could say, "If I just do THIS with two accounts, I will be sure to win."
Offline
An edge through collusion is impossible to avoid in any scenario where we don't verify the identity of each participant. Well, except in the main game, where we're lucky that collusion doesn't help you win more money. I'm talking about tournaments of any kind, etc. Someone with 2 accounts always has an edge over someone with 1 account, because there will always be some chance that those two accounts will play each other.
Not so! All my suggestions either provably avoided any number of colluding accounts from getting any edge by playing each other or left the potential small (e.g. with amulets losing points in game colluding players have an incentive to finish the game quickly).
But maybe we mean something slightly different by getting an edge from collusion? In all my suggestions 2 colluding accounts have more chance than 1 account of winning, but no more chance than 2 non-colluding accounts, and they do not increase that chance by playing each other. As a result in nearly all my suggestions two, ten or a hundred friends have no incentive to team up, and in the normal course of events someone doesn't get any benefit to having multiple accounts, even when tournaments are run (in the sense that their rate of return for the tournament doesn't change, they double their expected share of teh prize pool by doubling their entry cost). A promotion rewards a player having multiple accounts because it rewards every account upon creation with free entry into a contest with real prizes, under my suggestions for the most part that was the *only* reward someone got from creating multiple accounts. The collusion I mention above increases the expected payout *per account* and this is preventable.
Offline
No, I meant getting an edge somehow through the chance of two colluding accounts playing each other and thereby giving one account a free win.
One of your suggestions here (amulet players only matched with other amulet players who have the same points so far for that amulet), having two accounts playing through for that same amulet still helps you, because there's still a chance those two accounts, that have both built up points on the amulet, will play each other later. This is like a normal tournament tree. If you have two horses in the race, and both are playing well, they are likely to meet each other near the end, where one can throw the game. Better meet your accomplice near the end then some stranger.
An unskilled player cannot guarantee a win this way, but they would have an edge over someone who wasn't doing this. That's okay.
Same with earning points toward a final amulet tournament. If you get two colluding accounts into that tournament, you have an edge there too.
Essentially, in any structure where WINNING counts, having two accounts in the game will give you some edge.
Offline
No, I meant getting an edge somehow through the chance of two colluding accounts playing each other and thereby giving one account a free win.
Ok sounds like we have a genuine substantive disagreement here. You can make a structure such that if you have two colluding accounts of equal skill they have no edge over two non-colluding accounts of the same skill. All the structures I suggested had this property or were close to having this property.
One of your suggestions here (amulet players only matched with other amulet players who have the same points so far for that amulet), having two accounts playing through for that same amulet still helps you, because there's still a chance those two accounts, that have both built up points on the amulet, will play each other later.
Yes two colluding accounts might meet each other, and one could throw the game to the other but that only benefits one account at the expense of the other, and crucially the benefit the winner gets is exactly equal to the cost the loser pays. For colluders to get an advantage by throwing games they have to prefer that one account wins over the other, but in this structure both accounts have the same position in the tournament, so it won't matter to the colluders which account wins.
I think it will help to think about about friends with existing accounts colluding here rather than people creating multiple accounts. So suppose my friend and I are playing in the promotion with a structure like the one just mentioned where people only play other people with the same number of points for a given amulet. My friend and I realise that we have the same score, n, and are going to play each other next round, we've agreed to split any winnings from the promotion. What can we do to increase our combined chances of winning the tournament now that we're playing each other? Nothing, whatever we do we'll end up we'll end up with one of us on n point and one on n+1 points. (If one of us was significantly more skilled than the other it is better for us if they win the game, but if we play honestly then the significantly more skilled player is very likely to win anyway). As a result we have no incentive to play any differently to non-colluding players, and if we don't play any differently to non-colluding players we can't have an advantage over them. So colluding players get no advantage in this structure over non-colluding players. QED
This is different from the structure currently proposed for the promotion. If me and my friend meet while they're on 4 points and I'm on 0 points, it is much better for us if my friend wins, because it is much more likely that someone on 5 points with the amulet will win than that *either* of us will win if one has 4 points but no amulet and one has 1 point and the amulet. So I will throw the game to my friend and they'll get to 5 points with the amulet. Two non-colluding players in the same situation would only half of the time end up with one player with 5 points and an amulet, the other half of the time they will end up with one player with 1 point and the amulet and one with 4 points but no amulet. Making the assumptions I did in my previous post me and my colluding friend have a 60% cubed = 21.6% chance of one of us winning the amulet from this position, two non-colluding players in the same situation would only have 50*60%^3+50%*60%^7 = 11.6% chance.
If you have two horses in the race, and both are playing well, they are likely to meet each other near the end, where one can throw the game. Better meet your accomplice near the end then some stranger.
Well of course if you've got two horses in a race of course you have more chances to win but the possibility of one of your horses deliberately losing to the other doesn't necessarily help. For example suppose that it's a knockout structure, and both your horses are in the semi-finals and racing well (so they each win against the other horses 75% time), then if they get paired against each other you have 75% chance of one winning (guaranteed to get to the final and 75% chance of winning that). This is actually UNLUCKY for you, if they weren't paired against each other the chances of winning would be ~84%: in that case you have 3/4*3/4= 9/16 chance that both make it to the grand final (when one is sure to win). You also have 2*3/4*1/4=3/8 chance that only one makes it to the final when you have 75% chance of winning, giving you 3/8*3/4=9/32 chance of winning. 9/32+9/16=27/32 which is about 84% chance of winning. So you prefer it if your horses DON'T meet each other (for the simple reason that it's better to be paired with weaker opponents).
Essentially, in any structure where WINNING counts, having two accounts in the game will give you some edge.
Yes it will double your chances of winning, but the accounts don't need to collude, and by the same token your entry fees have also doubled; entering two tournaments also doubles your chances of winning one of them in a similar fashion. In the current working rule set for this promotion your chances more than double if the accounts collude, but in the structures I suggested they don't (and this is mathematically provable). As I say in this promotion your likely giving away more in prizes than the entry fees (card processing fees and tribute in the games) so doubling the entry fee and doubling your share of the prizes would still be worth it, but that really is unavoidable without changing the sign up process, if you reward account creation you motivate someone to create multiple accounts!
Last edited by storeroom leaflet (2015-03-06 00:10:05)
Offline
I'm still not sure about your QED. I buy the proof, but it doesn't feel intuitively right to me.
Say A and AA are colluding. They each have 4 points on the amulet by beating weaker players. Now they're at the point where both will lose against the stronger players at the 4-point level.
If we're randomly pairing them up, in a pool of N players, they do have 1/(N-2) chance of getting paired together. Say there are 9 other players, so they have a 10% chance of getting paired together.
If they DON'T get paired together, assume they lose. So each account, operating alone, has a 90% chance of losing. If they get paired together, one will throw the match to the other. Let's say AA is the one who will throw. So AA has a 100% chance of never making it to 5 points (will lose to all others and throw to A), while A has a 10% chance of making it to 5 points.
If they weren't colluding, they'd still have a 10% chance of playing each other, in which case one would win, the better one, let's say AA. So then AA would have a 10% chance of getting to 5 points, and A would have a 100% chance of not getting to 5 points.
I see that colluding doesn't help them, in the case of friends who would both be playing anyway.
HOWEVER, compare the cases for player A where AA does and does not exist. This isn't the friend case, but the case of whether or not to create an alt account. If A has scored 4 points but has no chance of scoring 5, having a second account AA with 4 points would give A a 10% chance of getting to 5 points, where without the alt account, A will have a 0% chance of getting to 5 points.
Your horses example is a good one.
Offline
OWEVER, compare the cases for player A where AA does and does not exist. This isn't the friend case, but the case of whether or not to create an alt account. If A has scored 4 points but has no chance of scoring 5, having a second account AA with 4 points would give A a 10% chance of getting to 5 points, where without the alt account, A will have a 0% chance of getting to 5 points.
In this example having the extra account play is increasing everyone's chances of getting a higher score, AA is sort of just one of 9 players getting an advantage. In a tournament setting , with an entry fee A will be paying into a prize pool which will then be shared out by the other players including AA (if 5 points is enough to get a share of the prize pool), so if you're AA you get something for having A in the tournament but not as much as A loses for being there in the first place (because most of that goes to the other players in the tournament), so there's no reason to make the alt account. BUT If there is no entry fee then of course there's no reason not to make the alt account, and it can be beneficial to do so.
There's a bit more to your example though. It showed me this rather unintuitive fact: that with no entry fees you can have a motive to create accounts which has no chance of winning the event and which doesn't collude with you (if your alt loses to everyone it can't really be considered colluding if it loses to you as well and can't control who it's paired with), which you can't ensure you're paired with and which doesn't change the size of the prize pool. That is you can benefit from having a bad player in a tournament even if that doesn't increase the prize pool and they're no more likely to lose to you as anyone else: Suppose a knockout structure where the winnings are split between 1st and 2nd (this structure does not incentivise any sort of collusion). Now suppose there are 3 other players, all of equal skill but much better than me, so I have a no chance of beating any of the other 3. If I add 4 accounts that are guaranteed to lose to any other account (except themselves), then I still have no chance of winning the tournament (I'm always going to have to play at least 1 genuine account), but now I have a chance of playing fake accounts in the first two rounds and so getting into 2nd. In fact I will benefit from those fake accounts so long as my chances of beating a genuine opponent are less than 50%. Surprising but true! What is going on here is that the fake accounts essentially add a random element to a skill-game in which I was outclassed, and adding random elements benefits the player with less skill, so by the same token if I have more than 50% chance of winnning against a genuine opponent, having a bad player enter the tournament is actually bad for me if they don't increase the prize pool, even if they have 0 chance of winning.
Question: Are there situations where a *skilled* player (>50% chance of winning against a random opponent) benefits from adding an account that plays no better than them, and plays no worse against them than anyone else? What do these situations look like, and what bounds, if any, can we put on the incentives here? (the effect above is not so worrying as benefit comes to a player who isn't getting much of the prize pool either way, but if you had something similar with a skilled player that could be a concern).
Note that these effects don't go against what I said before as they don't involve collusion just manipulating the composition of the player pool.
Offline
Well, in this case, there is no second place prize for a given amulet contest.
I was aware of what you are describing for knock-out tournaments with multi-place prizes, though. If I can't be Jere, ever, then I want to avoid playing him in a knock-out tournament as long as possible. Having alt accounts will help me with this. I will eventually face Jere, but having alt accounts will make it more likely that I face him for second place instead of for 5th place.
And yes, the problem we face here is essentially created by having no entry fee. The normal tournament structure in the game (when I run a tournament) involves entry fees and limits on pair-wise rematches, which makes alt accounts not worth using.
Entry fees are out of the question here because they won't make sense for brand new players.
Your point-tier structure is better in terms of collusion, but it changes the feel too much. I really like the idea of holding something that no one else holds at the moment... a hot potato, a golden ticket.
I'm fine with collusion lurking in there for a slight edge as long as there's no guaranteed win with it.
If people could play whoever they wanted while holding an amulet, the amulets WOULD be won by colluders, because they could easily rack more wins per amulet than any non-colluder.
But once that problem is solved, it becomes frustrating enough to collude, and colluding gives you no guarantee of winning. I need to balance a cool, simple, exciting contest against preventing any kind of collusion edge.
HOLY CRAP I'VE GOT THE AMULET.
I need to preserve that moment.
Offline
But once that problem is solved, it becomes frustrating enough to collude, and colluding gives you no guarantee of winning. I need to balance a cool, simple, exciting contest against preventing any kind of collusion edge.
HOLY CRAP I'VE GOT THE AMULET.
I need to preserve that moment.
Well my other suggestion of having the points represent starting amounts for a tournament to played at the end of the promotion does preserve that moment, and keeps the feel of the promotion generally intact I think. I remember you saying you didn't want a tournament because you didn't want to have a structure that would just go to one of the top players without the other gettting a look in. Well now you've got 36 amulets, there's no way Jere is going to get his hands on every one in the promotion week, and even if he did he's bound to lose *some* games and so could find himself in a tournament having only won 1 point, so really having his work cut out for him to win a tournament with players start with 5-10x what he has, where losing one or two games could see him out. You could also limit everyone to only playing in one tournament each, then Jere could only play in one tournament anyway. This would create some non-zero sum interaction again, but there would be much less potential for collusion here than in the current system.
Offline
http://techcrunch.com/2015/03/11/rose_gold/
I haven't looked too deeply into this, but I thought it might be semi-relevant:
I’m a mechanical watch collector and self admitted Apple fanboy. I wanted to love the Apple Watch Edition (Edition = marketing speak for “gold”). But I don’t understand the value here outside of the literal 1-2 troy ounces of 18k gold ($900-$1,800).
Sounds like you are giving away more/purer gold than is in Apple's $10,000 watch.
Canto Delirium: a Twitter bot for CM. Also check out my strategy guide!
Offline