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Subject: Disturbing thought - Fate Deck MAY be broken? rss

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Sean Shaw
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I had played this way, but hadn't thought over the ramifications until reading how a LOT of the people like counting cards and saying a strategy was to wait until the fate deck was low to make certain decisions...I had played the opposite, trying to consume cards to make the deck low for others...but now that I think about it, it MAY have been HIGHLY unfair to others that I did that...but I really didn't mean it, and if anyone from the game group is reading this and I'm right...I seriously am apologizing to you guys. Really, I didn't mean to hose anyone.

When looking at it, the odds of having all the good cards at the bottom of the deck are actually REALLY low. In fact, the lower the deck goes, the less of a chance of being able to draw a good card.

Let's say for Diplomacy, to get allies, you have a 1/10 chance of drawing a card. When you only have 6 cards left in the fate deck, the chances of all those cards being drawn is actually quite high, and the chance of you having ONLY cards requiring you to fight (hence no reason to spend anything to even try diplomacy) are quite high as well.

In fact, your chances of a bad draw increase as the deck gets lower, since you don't reshuffle the deck each time.

So, what do I do, when I see a player, especially if they are the last player, trying to convert units or do diplomacy, I hog cards...or try to run the deck.

Some would call this strategy, I call this unfair.

In a four player game it is a likely that the fourth player will be at the state where they have a low pile. That's a bad thing to be going for diplomacy, but knowing due to hogging, the only cards left will be to fight...leaving you NO CHANCE.

IN fact, that's actually a little unfair, since the ONLY reason this occurs is because of the player order. It's not a balanced issue at all, the player before the last player have a distinct advantage.

Now one could argue that the last player hence, should be the most experienced one, and it could balance it out. That's not always going to be possible however. It's actually really easy to hose the last player in line with the fate deck (and once again, I AM SORRY ABOUT THE LAST TWO GAMES, since this was my strategy) by doing card hogging, aka, running the deck.

Is this actually something you might consider broken? If so what would be your fix?

My only thought is to either ignore that strategy, OR make it so that there are shuffles more often, perhaps after the deck gets halfway depleted instead of fully depleted?

It seems unfair to the last player (seems to occur with four players, probably not as much a factor with two players, but that's an assumption on MY part) and possibly due to HOW YOU CAN COMPLETELY hose their strategy...perhaps broken?

The worst for them is at the beginning few rounds of the game when the deck gets under ten cards for them, many times a little before the reshuffle. It's AWFULLY easy to get them in that state as well.

I was just playing the odds even, not even counting cards specifically...but the more I think about it, the worse I am feeling about it.

If it does do that to the last player, I'm thinking it's probably is broken, and NOT a good thing to be doing. It gives an unfair advantage to those over the last player (s) as I can see it would be a lot harder, but MAYBE possible with three players too. As I said, I think it may not be a valid thing under two players though.

Once again, if I haven't made it known enough...I AM sorry to those that I did the running the deck strategy too, if it is broken and I HAD realized it at the time, I would NEVER have used it on you.
 
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Brandon
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I would say that this would fall under the category of "conscious design decisions by the developer". I don't see a problem.

The fix? Wait till fall!
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Antigonus Monophthalmus
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Neverfade wrote:
I would say that this would fall under the category of "conscious design decisions by the developer". I don't see a problem.


There can be problems with conscious design decisions by the developer.
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BagpipeDan wrote:
Neverfade wrote:
I would say that this would fall under the category of "conscious design decisions by the developer". I don't see a problem.


There can be problems with conscious design decisions by the developer.


I find it hard to believe that running the deck down would be considered one of them, especially considering the bevy of options available to you at any given time.

However, I don't think it would upset anything too much if you just wanted to shuffle the deck after every use. /shrug
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Cameron McKenzie
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You are way off on this. The last player doesn't have a disadvantage. The probability of the last 5 (or however many) cards being bad is exactly equal to the probability of ANY 5 cards in the deck being bad.

Yes, there are situations in which the good cards have all been drawn from the deck and there are very few or even none left for you -- but at least you know this fact and can just avoid attempting diplomacy.

On the other hand, there are situations in which all of the players before you have failed, and a higher than normal ratio of the remaining cards are successes.

It's not as if players can intentionally pick out all of the successes before they get a chance. The only way they can get every single one for sure is to exhaust the entire deck, in which case they are all replenished anyway.

The last player has different odds of success than the first player. They are sometimes better and sometimes worse, but the average is the same.

I wonder if you aren't doing something wrong, like returning the "rejected" fate cards to the deck. All of the cards drawn on a diplomacy deck are discarded, not just the one that the player chooses to resolve.
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Bill Gates
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Turn order is not a constant. It varies from season to season, determined by Order Card # and amount of influence on hand to break ties.

Quote:
when I see a player, especially if they are the last player, trying to convert units or do diplomacy, I hog cards...or try to run the deck.


Fate cards are drawn to determine diplomacy, combat and quests. How are you "running the deck" during someone else's turn? How are you "running the deck", period? Quests only happen during the summer. Only two order cards (Mobilize and Conquer) allow you to move units into areas occupied by neutral or hostile units (giving you the chance to draw fate cards for combat or diplomacy), and you may not use both of them every year if you have more pressing concerns (seeing as only four of the eight order cards can be used each year). So, at least two seasons out of every year you won't be able to draw fate cards for diplomacy or combat (exception: you will be able to draw fate cards when someone attacks you, but that's beyond your control). And then, the number of fate cards you can draw is limited by the amount of influence you have on hand, and the number of units you have to send into combat.
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Sean Shaw
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MasterDinadan wrote:
You are way off on this. The last player doesn't have a disadvantage. The probability of the last 5 (or however many) cards being bad is exactly equal to the probability of ANY 5 cards in the deck being bad.

Yes, there are situations in which the good cards have all been drawn from the deck and there are very few or even none left for you -- but at least you know this fact and can just avoid attempting diplomacy.

On the other hand, there are situations in which all of the players before you have failed, and a higher than normal ratio of the remaining cards are successes.

It's not as if players can intentionally pick out all of the successes before they get a chance. The only way they can get every single one for sure is to exhaust the entire deck, in which case they are all replenished anyway.

The last player has different odds of success than the first player. They are sometimes better and sometimes worse, but the average is the same.

I wonder if you aren't doing something wrong, like returning the "rejected" fate cards to the deck. All of the cards drawn on a diplomacy deck are discarded, not just the one that the player chooses to resolve.


Except you aren't running off the law of averages, that would ONLY apply if you were reshuffling EVERY time.

In this case you are using the rules of diminishing returns and chance, aka, every card drawn reduces the chances of other cards being drawn.

Hence, why it's impossible to have a 1/10 chance of drawing a card when only 9 cards remain. When only two cards remain, it's impossible to have three different cards. This is explained by rules that show the stats for how the reductions of chance occur...and seem to indicate that the lower you get in the deck, especially under 6, but under 10 as well...your chances for good cards start to REALLY go down quickly in comparison to a full deck.
 
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Maybe I read your post wrong, but there's nothing about six cards being at the bottom of the deck that makes them less likely to be good. If the cards are shuffled, then you could draw x number of cards from anywhere in the deck and they would be equally likely to be desirable cards.

If it was worse to draw from the bottom of the deck than from the top, then you could just reverse the order of the cards and make it better to draw from the bottom than the top, which doesn't make sense.

It's true that as the deck gets lower, there will be less good cards in it, but as cards are drawn, the number of good cards will decrease at a rate proportional to that of the bad cards. The only variable is the distribution of cards, which is just as likely to put more desirable cards at the top as the bottom.
Of course, there may be a point toward the bottom when there are no desirable fate cards left, but in the absence of card counting there's no way to know, and the number of consecutive bad cards isn't likely to be greater than what would occur in the beginning or middle of the deck. If this is a concern of yours, it could easily be fixed by a house rule that says you reshuffle once there are only 5 or 10 cards left in the deck.

The only benefit of waiting until the fate deck is low is if you're counting cards, because it will allow you to calculate your odds more accurately.

Edit: I was a bit lazy in typing this post and it looks like MasterDinadan covered most of these points above. Sorry about that!
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Sean Shaw
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milgate wrote:
Turn order is not a constant. It varies from season to season, determined by Order Card # and amount of influence on hand to break ties.

Quote:
when I see a player, especially if they are the last player, trying to convert units or do diplomacy, I hog cards...or try to run the deck.


Fate cards are drawn to determine diplomacy, combat and quests. How are you "running the deck" during someone else's turn? How are you "running the deck", period? Quests only happen during the summer. Only two order cards (Mobilize and Conquer) allow you to move units into areas occupied by neutral or hostile units (giving you the chance to draw fate cards for combat or diplomacy), and you may not use both of them every year if you have more pressing concerns (seeing as only four of the eight order cards can be used each year). So, at least two seasons out of every year you won't be able to draw fate cards for diplomacy or combat (exception: you will be able to draw fate cards when someone attacks you, but that's beyond your control). And then, the number of fate cards you can draw is limited by the amount of influence you have on hand, and the number of units you have to send into combat.


What normally seems to happen is several of us have similar ideas. You can many times figure out what others will do, especially if they are trying to do a lot of diplomacy. I have purposefully taken a less than advantageous move (though STILL normally advantageous) to move MORE units than needed simply so that I can attempt diplomacy, purposefully fail, and run through the deck with a battle if I can think the it will run the deck, for a later player. In fact, the past two games I did it constantly, and actually managed to piss someone off in the last game.

I may say his sportsmanship WAS lacking, but after reading some stuff today, and thinking about it further, perhaps he was right to be upset?

Especially considering how I kept on doing it...

Edit: for the person above...I wasn't counting the cards, just using stats on this one. The one who got upset, he WAS counting the cards, and got upset because I continually left him with nothing but bad results left in the deck, after running it low. I'd also purposefully try to be the one who drew cards first in the attack simply to run the cards down and hit him before he could draw, didn't have much effect on his hexagonal pieces, but seemed to ravage his rectangular pieces occasionally...but only because he'd have two of them, and there'd only be two to four cards left in the deck...
 
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Filip Lange
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MasterDinadan is correct, and your analysis is off. If anything, the last player has an advantage, since he knows when he has increased or decreased odds of success and can plan his actions accordingly.
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GreyLord wrote:
Hence, why it's impossible to have a 1/10 chance of drawing a card when only 9 cards remain. When only two cards remain, it's impossible to have three different cards. This is explained by rules that show the stats for how the reductions of chance occur...and seem to indicate that the lower you get in the deck, especially under 6, but under 10 as well...your chances for good cards start to REALLY go down quickly in comparison to a full deck.


You still have a 1/10 chance even when 9 cards remain.
Think about it this way: You have a full deck. At this point we can agree that the first 9 cards each have a 1/10 chance of being what you want. Now take those 9 cards off the top of the deck and put them in a new pile. Does this change their odds? Of course not. The same goes for if you took them off the top and put them on the bottom of the deck. There is a 1/10 chance because one tenth of all cards printed is good. This fact is not affected by how many of the cards are in the discard pile and how many are left in the deck.
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Sean Shaw
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dolan wrote:
GreyLord wrote:
Hence, why it's impossible to have a 1/10 chance of drawing a card when only 9 cards remain. When only two cards remain, it's impossible to have three different cards. This is explained by rules that show the stats for how the reductions of chance occur...and seem to indicate that the lower you get in the deck, especially under 6, but under 10 as well...your chances for good cards start to REALLY go down quickly in comparison to a full deck.


You still have a 1/10 chance even when 9 cards remain.
Think about it this way: You have a full deck. At this point we can agree that the first 9 cards each have a 1/10 chance of being what you want. Now take those 9 cards off the top of the deck and put them in a new pile. Does this change their odds? Of course not. The same goes for if you took them off the top and put them on the bottom of the deck. There is a 1/10 chance because one tenth of all cards printed is good. This fact is not affected by how many of the cards are in the discard pile and how many are left in the deck.


Not if I've drawn 4 of them at that point. I have a 1/10 chance of the first card being a good one, after that is drawn the majority of time it will be NOT a good draw, now making the chances better than a 1/10 chance to draw a good one. In fact, around card #20, you stand the best chances for drawing a good card. It's because of the reductions of the deck and basic stats. The deck is decreasing in size, increasing your chances for a good draw...up to a certain point when the chances of a good draw start to equalize out to those that are bad draws...and then they shoot your chances downwards consistently after that.

Basic stats. It's NOT a constant deck, you're assuming constant reshuffles after every draw, which is not the case. It's reduced cards, so you have to apply the additional formulas to the draws in regards to increasing and decreasing numbers in relation to chances.

AKA, that's why people actually can see whether the chances are better or not by going through the piles...because the chance is NOT constant when you are drawing the deck like that. Basically, when you are down to 3 cards, you with a 1/10 chance, 1/10 of the time, or 1/3 of the times the deck gets that low, there will be a good card in there.

The other two times...you're hosed at that point...no chance. So the best thing for the player before you to do is reduce it to that point, because he knows once you get to a certain level, the majority of the time you won't have any good cards (or two times out of three).

Second addendum...I suppose you could argue that you stand a 1/3 chance of a good card being there, but in truth, it's far worse than that, that's a 1/3 chance of 1/3 chance or 1/9 of drawing the card...but with 1/9 multiplied even further (too late/early in morning, math a little fuzzy here, is that a 2/3 multiplier to the 1/9, or another number...oh well, use the 2/3, or a 2/27th's chance of drawing a good card compared to the 1/10 on a draw. MUCH worse odds...since 2/3 of the time there is ZERO chance any more to actually draw the card at all).
 
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GreyLord wrote:
I have a 1/10 chance of the first card being a good one, after that is drawn the majority of time it will be NOT a good draw, now making the chances better than a 1/10 chance to draw a good one.

I get what you're saying here. I'm not arguing that the chance never varies, just that one portion of the deck does not yield better chances. It's true that there's a good chance that the last 3 cards will not be good, but that can be said about any selection of 3 cards anywhere in the deck. You're just as likely to have the top 3 or the middle 3 cards be bad as the bottom 3. If you decided to spend 3 influence and draw 3 cards, you have to draw the top 3 cards from the deck. In this way, it doesn't matter if there are 3 cards in the deck or 30, because the only ones you're concerned about is that top section of 3, which is unaffected by how many cards are beneath it.

At this point I'm not even sure why I'm arguing about this; I don't mind the fate deck even if you're right. I suppose I'd just like to know if I'm wrong. This reminds me of that mathematics illustration with the game show and the goat where it's somehow beneficial to change your door. I never did understand how that whole thing works.
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Rich S
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dolan wrote:
GreyLord wrote:
Hence, why it's impossible to have a 1/10 chance of drawing a card when only 9 cards remain. When only two cards remain, it's impossible to have three different cards. This is explained by rules that show the stats for how the reductions of chance occur...and seem to indicate that the lower you get in the deck, especially under 6, but under 10 as well...your chances for good cards start to REALLY go down quickly in comparison to a full deck.


You still have a 1/10 chance even when 9 cards remain.
Think about it this way: You have a full deck. At this point we can agree that the first 9 cards each have a 1/10 chance of being what you want. Now take those 9 cards off the top of the deck and put them in a new pile. Does this change their odds? Of course not. The same goes for if you took them off the top and put them on the bottom of the deck. There is a 1/10 chance because one tenth of all cards printed is good. This fact is not affected by how many of the cards are in the discard pile and how many are left in the deck.


Disagree on this point. Your analysis assumes that the contents of the discard pile is unknown. If there is one good card and 9 other bad cards in a deck and 5 are showing as bad on my turn, then I have a 1/5 shot of drawing a good card.

I believe that the OP is refering to the advantage someone has when the pile gets close to empty opposed to that of the player that has to deal with a full deck.
 
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phosrik wrote:
dolan wrote:
GreyLord wrote:
Hence, why it's impossible to have a 1/10 chance of drawing a card when only 9 cards remain. When only two cards remain, it's impossible to have three different cards. This is explained by rules that show the stats for how the reductions of chance occur...and seem to indicate that the lower you get in the deck, especially under 6, but under 10 as well...your chances for good cards start to REALLY go down quickly in comparison to a full deck.


You still have a 1/10 chance even when 9 cards remain.
Think about it this way: You have a full deck. At this point we can agree that the first 9 cards each have a 1/10 chance of being what you want. Now take those 9 cards off the top of the deck and put them in a new pile. Does this change their odds? Of course not. The same goes for if you took them off the top and put them on the bottom of the deck. There is a 1/10 chance because one tenth of all cards printed is good. This fact is not affected by how many of the cards are in the discard pile and how many are left in the deck.


Disagree on this point. Your analysis assumes that the contents of the discard pile is unknown. If there is one good card and 9 other bad cards in a deck and 5 are showing as bad on my turn, then I have a 1/5 shot of drawing a good card.

I believe that the OP is refering to the advantage someone has when the pile gets close to empty opposed to that of the player that has to deal with a full deck.


I was assuming that the contents of the discard pile is unknown. Sorry, I should have communicated that more clearly. If people are looking through the discard pile, there is definitely an advantage to drawing later in the deck in that you have more knowledge to base your decisions off of.
However, it is my impression that the OP believes that, in general, your chance of drawing a desirable card decreases as more cards and discarded and the deck gets thinner. It is this argument that I am disagreeing with.
 
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We have a house rule, "no card counting". Everyone in our group finds it really borring, causes lots of down time, and even a bit of a cheat (although we are all aware it's alowed technically in the rules).
 
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Cameron McKenzie
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Greylord, you don't really understand. Yes, a card that has been drawn can't be drawn again. However, in order for a disproportionately high number of remaining cards to be bad, it would require the other players to draw a disproportionately high number of good cards before you got to draw. If they happened to draw a low number of cards, you could actually end up with a MUCH higher chance of success. You can't assume the worst case scenario. The cards in the deck are randomly distributed, nobody can intentionally pull out a good card.

The card doesn't know whether it's good or bad. Instead of thinking of them as "good" and "bad" think of an example where the cards are red or blue in equal amounts. If someone draws half of the deck and ends up with more blue cards than red cards, anyone drawing now has a higher chance of drawing a red card. This is the point you are arguing, and it's a fine point, but it depends on the first player drawing more reds than blues.

If the player draws more reds than blues(note this is equally likely), then the player drawing next is more likely to draw blue cards. The point I'm making here is that no single card in the fate deck is more likely to be drawn "first" or before a certain point. Yes, it's possible for the successes to run out before you get your turn -- just don't attempt diplomacy in this case. But it's also possible for the failures to run out, in which case diplomacy is a sure thing.

You can't simply assume that the worst-case scenario, least probable thing is going to happen. If we are going to argue about inbalances based on the worst case scenario, I could easily argue that the first player to draw from the fate deck is at a severe disadvantage because he has no chance if the success cards are at the bottom. But why would I assume the success cards are at the bottom? You can't just assume that, and you can't assume that they won't be either.

I have a B.S. in Mathematics and one important lesson I've learned is that you can't assume that the "intuitive" solution is the correct one. Even if you can't intuitively understand why the last player isn't at a disadvantage, it can be mathematically proven that he is not. A lot of results in mathematics are not intuitive.

By the way, to those saying that the last player has an advantage because he has a better idea of the probability, that's kind of false. The first player is perfectly aware of the probability, it just isn't the same probability that the others players have once they get their turn. Other players may have a better or a worse probability based on the contents of the discard, but the probability is always known.
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Determining probabilities can be difficult, particularly as information is progressively revealed. It's easy to tie yourself in knots. If you're interested, check out the Monty Hall Problem on Wikipedia. My brothers and I have gone round and round about this and they still don't understand why it's better to change which door you pick.

For the sake of simplicity, let's suppose that we have ten identical cards and that we draw a star on one and shuffle the cards. Sean, your argument essentially seems to be this:
(1) There is a greater probability that the card with a star on it is in the first 2/3 of the deck.
(2) Therefore, those who draw from the first 2/3 of the deck each have a better chance of drawing the star.
(3) Therefore, those who draw from the last 1/3 of the deck each have a lower chance of drawing the star.

The claim made in (1) is true, and (3) follows from (2), but (2) doesn't follow from (1). For now, let's assume that there are only 5 of us drawing cards and everyone draws a card and reveals simultaneously. Suppose that each of us draws 1 card. What probability do each of us have of drawing the star? Each of us has a 1/10 chance of drawing the star (even though 5 cards were not drawn). Now let's suppose that you draw 6 cards instead of 1, and everyone else just draws 1. You have a 6/10 chance of drawing the star while the rest of us have a 1/10 chance. Notice that our odds remained the same, while yours increased. You drawing more cards did not decrease anyone's odds. Suppose that I am the last person to draw a card. My odds are still 1/10--the same as they were when we each only drew 1 card--even though you drew 6 cards.

Now let's complicate things by drawing the cards and revealing them one at a time. Does the last player to draw have a disadvantage? No, but he doesn't have an advantage either. However, once you add a betting mechanic (as Runewars does), he gains a decided advantage. He has more knowledge of the deck than any other player before him. If it's his turn and all of the cards are drawn except one and the star hasn't been drawn yet, he is guaranteed to draw the star and so he should go all in. But if it's his turn and the star has already been drawn, then it's stupid to bet--he's guaranteed to lose. Just imagine a similar kind of betting game in Las Vegas. If you could ensure that you always drew the last card and you didn't have to make a bet until it was your turn to draw, you would make millions.

Hopefully that helps clarify things.
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GreyLord wrote:


In fact, your chances of a bad draw increase as the deck gets lower, since you don't reshuffle the deck each time.


This is nonense. It's exactly the same chance for any card you draw of the deck.

The later you draw however the more knowledge you have and so you can assess better your chances of success or failure, therefore it's advantageous to draw from a diminshed deck.
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MasterDinadan wrote:
Greylord, you don't really understand. Yes, a card that has been drawn can't be drawn again. However, in order for a disproportionately high number of remaining cards to be bad, it would require the other players to draw a disproportionately high number of good cards before you got to draw. If they happened to draw a low number of cards, you could actually end up with a MUCH higher chance of success. You can't assume the worst case scenario. The cards in the deck are randomly distributed, nobody can intentionally pull out a good card.

The card doesn't know whether it's good or bad. Instead of thinking of them as "good" and "bad" think of an example where the cards are red or blue in equal amounts. If someone draws half of the deck and ends up with more blue cards than red cards, anyone drawing now has a higher chance of drawing a red card. This is the point you are arguing, and it's a fine point, but it depends on the first player drawing more reds than blues.

If the player draws more reds than blues(note this is equally likely), then the player drawing next is more likely to draw blue cards. The point I'm making here is that no single card in the fate deck is more likely to be drawn "first" or before a certain point. Yes, it's possible for the successes to run out before you get your turn -- just don't attempt diplomacy in this case. But it's also possible for the failures to run out, in which case diplomacy is a sure thing.

You can't simply assume that the worst-case scenario, least probable thing is going to happen. If we are going to argue about inbalances based on the worst case scenario, I could easily argue that the first player to draw from the fate deck is at a severe disadvantage because he has no chance if the success cards are at the bottom. But why would I assume the success cards are at the bottom? You can't just assume that, and you can't assume that they won't be either.

I have a B.S. in Mathematics and one important lesson I've learned is that you can't assume that the "intuitive" solution is the correct one. Even if you can't intuitively understand why the last player isn't at a disadvantage, it can be mathematically proven that he is not. A lot of results in mathematics are not intuitive.

By the way, to those saying that the last player has an advantage because he has a better idea of the probability, that's kind of false. The first player is perfectly aware of the probability, it just isn't the same probability that the others players have once they get their turn. Other players may have a better or a worse probability based on the contents of the discard, but the probability is always known.


You also realize that the chance is NOT STATIC in a changing deck then, Stats 101. Hence the problem, you are calculating for a FIXED deck, aka, shuffling every time...NOT for a changing non-static deck. Instead of figuring for a fixed deck (or die roll) you need to figure for a changing deck, the odds change every time a card is drawn for better or worse.

For example, with a full deck, with a 1/10 chance, that's 3 out of 30 that I'll draw. The chance of the good draw is 1/10. However, with the next, the chance is actually higher for the good draw, with it being 3/29, unless of course the good card is drawn, at which point the chance immediately drops to 2/29.

Once you get to 3/18 you stand a 1/6 chance of drawing a good card EVERY draw. At 3/12 you stand a 1/4 chance of drawing a good card Every draw if one hasn't been drawn yet. Hence those that are thinking that the odds actually get better...but they don't.

The actual chances (which I'd start having to do the math at and calculating percentages) are actually quite high for a card to be drawn prior to there being 10 cards left, and even pretty good for two cards being drawn, which still leaves the 1/10 chance we'll say for the last 10 cards.

Now here's the thing, there's a 1/10 chance that the card will be drawn each draw, and the instant it's drawn the chances to have it drawn again, result in 0%. Conversely, as my chances go up in drawing the card, the chances for there to be a zero chance for the person behind me to have a good draw go up equally.

So to make it simple, with ten cards, my first chance is a 1/10. There is a 1/10 chance that the person behind me is screwed.

The next one is a 1/9 chance, there is a 1/9 chance the person behind me is screwed. At this point I cannot have worse odds than what is left. If the good card is STILL in there, and there are ONLY 9 cards...the chance is then...1/9. 1/10 becomes the talk of fantasy land at that point. It's because the deck has changed that the odds change as well.

The next is a 1/8 chance, there is a 1/8 chance the person behind me is screwed.

Basically, if I can draw 5 cards, there's a HIGH probability I can screw the person after me, all those percentages ADD up.

Will it happen every time...no...but it will happen often enough.
 
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GreyLord wrote:

So to make it simple, with ten cards, my first chance is a 1/10. There is a 1/10 chance that the person behind me is screwed.

The next one is a 1/9 chance, there is a 1/9 chance the person behind me is screwed.

The next is a 1/8 chance, there is a 1/8 chance the person behind me is screwed.

Basically, if I can draw 5 cards, there's a HIGH probability I can screw the person after me, all those percentages ADD up.

Will it happen every time...no...but it will happen often enough.


And if you DON'T screw over the person after you, you are helping them, as you point out. So by drawing a card, I'm occasionally hurting them significantly, but I'm usually helping them slightly. The average effect is completely neutral. You said you haven't calculated the odds, so I don't know why you are trying to argue that the negative effect outweighs the positive. It doesn't.

I don't know you are assuming that I didn't account for the lack of replacement in the deck or that I have trouble understanding Stat 101 concepts. You provide one example of the later player being screwed, while ignoring countless examples of the later player actually being helped. That is not how statistics is done. Anecdotal evidence totally irrelevant.

I could take all of the arguments you made about the good player being less likely to draw a good card, replace the word "good" with "bad" and the arguments would be just as valid -- but we would arrive at a contradiction because the later can't be less likely to draw both good and bad cards. Therefore, the argument was not valid.
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MasterDinadan wrote:
GreyLord wrote:

So to make it simple, with ten cards, my first chance is a 1/10. There is a 1/10 chance that the person behind me is screwed.

The next one is a 1/9 chance, there is a 1/9 chance the person behind me is screwed.

The next is a 1/8 chance, there is a 1/8 chance the person behind me is screwed.

Basically, if I can draw 5 cards, there's a HIGH probability I can screw the person after me, all those percentages ADD up.

Will it happen every time...no...but it will happen often enough.


And if you DON'T screw over the person after you, you are helping them, as you point out. So by drawing a card, I'm occasionally hurting them significantly, but I'm usually helping them slightly. The average effect is completely neutral. You said you haven't calculated the odds, so I don't know why you are trying to argue that the negative effect outweighs the positive. It doesn't.


What I'm saying is statistically, you stand a better chance of running the deck and making it impossible for them to suceed, hence the last person to go is statistically forced into an unfair position.

In this case, I draw the one good card, their chances get reduced to ZERO as opposed to the chances I had to actually draw it. At that point, they know it, I know it, that they have no chance to suceed in their chosen action.

I do it to them three or four times in a game and they throw a fit and whine about it being unfair...which in truth...it is. And the thing is, statistically, I can arrange to do it pretty often to who comes after me.

PS: Actually I did the simplified math above for you. I reedited it for clarity so you understand the statistics of a changing deck (which according to you, you should understand) as opposed to the continuous roll of dice. Some forms of card counting actually depend on these changing ratios for success. The thing is normally they are determining chances of getting a good draw...but when there are so few cards (normally using the four aces idea in a 52 card deck), at the low point, statistically with even distribution, there is only going to be one card left, and when that happens, as the odds go up of it being drawn, the next person to draw has their chances of drawing it go down, simply because once it's drawn, it becomes a 0/5 or 0/9 (by the way, those are illegal numbers...they all are simply 0 to tell the truth) is impossible. They get zero chance at that point.

My odds of getting the good card with 3 to 4 cards are actually PRETTY darn good, if it's still there when there are 10 cards left, enough for a gamble to completely hose the person behind me so they have zero chance for a success.
 
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GreyLord wrote:
MasterDinadan wrote:
GreyLord wrote:

So to make it simple, with ten cards, my first chance is a 1/10. There is a 1/10 chance that the person behind me is screwed.

The next one is a 1/9 chance, there is a 1/9 chance the person behind me is screwed.

The next is a 1/8 chance, there is a 1/8 chance the person behind me is screwed.

Basically, if I can draw 5 cards, there's a HIGH probability I can screw the person after me, all those percentages ADD up.

Will it happen every time...no...but it will happen often enough.


And if you DON'T screw over the person after you, you are helping them, as you point out. So by drawing a card, I'm occasionally hurting them significantly, but I'm usually helping them slightly. The average effect is completely neutral. You said you haven't calculated the odds, so I don't know why you are trying to argue that the negative effect outweighs the positive. It doesn't.


What I'm saying is statistically, you stand a better chance of running the deck and making it impossible for them to suceed, hence the last person to go is statistically forced into an unfair position.


Suppose the chance of success is 20%. You take an action that either reduces their chance to 0% or increases it to 100%. Wouldn't you EXPECT the chance to be reduced to 0% more often? The original probability was a lot closer to 0% after all. If the only way to make it fair is to give them the same chance of the good result as the bad result, then you are essentially turning 20% into 50% and they are much better off.

Just because something happens more often doesn't mean it outweighs the alternative. If I roll a die, and gain a point on 1-4 but lose two points on 5-6, the positive result is more common than the negative result, but it's half as good, and the average result is 0.
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MasterDinadan wrote:
GreyLord wrote:
MasterDinadan wrote:
GreyLord wrote:

So to make it simple, with ten cards, my first chance is a 1/10. There is a 1/10 chance that the person behind me is screwed.

The next one is a 1/9 chance, there is a 1/9 chance the person behind me is screwed.

The next is a 1/8 chance, there is a 1/8 chance the person behind me is screwed.

Basically, if I can draw 5 cards, there's a HIGH probability I can screw the person after me, all those percentages ADD up.

Will it happen every time...no...but it will happen often enough.


And if you DON'T screw over the person after you, you are helping them, as you point out. So by drawing a card, I'm occasionally hurting them significantly, but I'm usually helping them slightly. The average effect is completely neutral. You said you haven't calculated the odds, so I don't know why you are trying to argue that the negative effect outweighs the positive. It doesn't.


What I'm saying is statistically, you stand a better chance of running the deck and making it impossible for them to suceed, hence the last person to go is statistically forced into an unfair position.


Suppose the chance of success is 20%. You take an action that either reduces their chance to 0% or increases it to 100%. Wouldn't you EXPECT the chance to be reduced to 0% more often? The original probability was a lot closer to 0% after all. If the only way to make it fair is to give them the same chance of the good result as the bad result, then you are essentially turning 20% into 50% and they are much better off.

Just because something happens more often doesn't mean it outweighs the alternative. If I roll a die, and gain a point on 1-4 but lose two points on 5-6, the positive result is more common than the negative result, but it's half as good, and the average result is 0.


That's the problem which I think you are having, and which I had until I started pondering about it this evening. You are calculating from a DICE roll perspective instead of a CARD reduction perspective.

The thing is, once you get to a limited number, Cards actually ARE very different then dice. With dice you are always guaranteed that chance percentage...with cards due to the changing odds, you are not.

At some point, the return is 0%. When you first draw that first card, odds are even at that 1/10, but as the cards change, so do the odds dependant on what is drawn. It becomes more and more likely for the cards to give a zero return with limited numbers than it is for dice, unless the number was low to begin with.

In this case I am reducing the person's chance to suceed with each card I draw. AT first their chance of losing is 10%, the next time it shoots up to around 11%, their chance of not being able to suceed goes up to 12.5% with 8 cards left...and with 3 cards left their chance of losing on that draw is a whooping 66% if they are fortunate not to have had it drawn yet for their one draw.

However, chances are better that I can draw that card collectively on a 3-4 card draw, and really good on a 5 card draw, to completely hose them to make their chance go from a 55% chance of losing...to a 100% chance of losing.
 
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Here is my example using actual numbers from the fate deck.
Deck of 30 cards, 4 are successes:

Suppose another player draws 15 cards out of the deck, and then I draw 5. Sorry I didn't simplify my fractions, but they are all correct.

The probability of the other player drawing 0 successes is 1365/27405. If this happens, the probability of me drawing at least one success is 1155/1365.

The probability of the other player drawing 1 successes is 6825/27405. If this happens, the probability of me drawing at least one success is 335/455.

The probability of the other player drawing 2 successes is 11025/27405. If this happens, the probability of me drawing at least one success is 60/105.

The probability of the other player drawing 3 successes is 6825/27405. If this happens, the probability of me drawing at least one success is
5/15.

The probability of the other player drawing 4 successes is 1365/27405. If this happens, the probability of me drawing at least one success is 0.

Multiply the probabilities together and add them up:
0.5384054

What is the probability of drawing a success if we simply draw the first 5 cards of the complete deck?
0.5384054

Exactly the same answer, using two different methods on two different problems, because from a probability standpoint, the two are the same.
You can talk all you want about how you screwed you friend over several times in a row, but that's anecdotal evidence and is utterly and completely useless for calculating probability and expected values.
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