Talking extended contests here - rough answers are OK. (I already know the answers for simple contests, they're easy to analyze, and weird - I think I'd come extended or not at all for anything except a simple yes/no between conflicting non-GM players).

Does anyone have a good sense of what your odds to win are up 10 points? 1 mastery? 1 mastery and 10 points? 2 masteries? etc.

Or alternately, how many points edge do you need to have a 2-1 chance of victory? 75%? 90%? 99%?

I realize that the answers are highly complex because you can have variable augment sizes. (For example, getting the drop on someone's bad ability who generally outclasses you - you have a good chance to waste him fast, but if the extended contest goes on his double-size augments are going to catch up to you.) For simplicity's sake, let's assume that the ability to augment on each side is about equal, though if someone has detailed info for un-equal augments that's cool too.

Also, assume that AP bidding is roughly equal on both sides, even though that's even more abstract.

Or don't make these assumptions and just tell me what you know about particular cases. Thanks for the help.

(The core book says 1 mastery edge means you've got about a 75% chance to win - I have no reason to think that's wrong but I'm wondering if anyone has more information. That number's got to be for extended contests because it's wrong for simple.)

I'm not sure that you can give a meaningful answer to this in the abstract, since there are too many variables at play that can make a big difference to the outcome of an extended contest - not least of which is the size of the bids you are making relative to the number of AP's both parties start the contest with.  Take in to consideration that a Critical success will result in an AP transfer, further complicating the issue.

eg. Skill of 30 vs Skill of 10 (1 mastery difference) - starting AP are 30/10
                                                Bid of 3AP  Bid of 5 AP  Bid of 10AP
Complete Victory 4.75%                39/1            40/-5          40/-20
Major Victory    24.75                    30/4            30/0          30/-10
Minor Victory    41.00                    30/7            30/5          30/0

so merely by varying your opening bid, you can vary your chance of ending this contest in one round from 0-70% (which is another reason for only using Extended contests when it is dramatically appropriate to do so - it is always possible for the party with the higher AP total to (try and) end it in one round anyway).  ((Actually this table is not completly acurate - while a complete victory will always result in a transfer, it is possible for a lesser victory to do so to if you roll a critical success, but the principle holds true)

If you wanted to try and build some sort of model you could try this
Find the %age chance of each possible outcome, and multiply this by the multiplier for that outcome (so x2 for a Major victory, x1 for a minor, x.5 for a minor, -.5 for a minor defeat etc) - Add up the totals and (excluding transfers) you get the average return for a 1AP bid - the higher this numbewr, the more likely you are to win...

The other thing this doesn't take into account is the option of trading AP victories for wounds.  I find this quite a useful tool as a GM. particularly erith new players,  as it allows you to keep a contest going to give the PC's a chance to win (or to choose an alternative strategy for losing...) without necessarily shutting them out of the contest - since the effects of the wounds carry forwards they can see the benefit of ending the contest before they get ground down

[Note that I cross-posted this with Tim, and haven't bothered to update it to reflect his post].

Complex question, yes. And I don't want to seem to be avoiding it, but if you could tell me why you're interested, I might be able to answer more coherently.

First, the 75% actually does apply to simple contests as an aproximation. With a one mastery advantage, the odds actually range from a low of 70.5% at TN 10, to 90.75% for TN of 1 or 20. Generally the closer you are to the ends of the spectrum, the more the mastery advantage pays off. But 75% works as an approximate average.

(It's also interesting to note that while the odds of the higher guy winning go down in the middle of the mastery range, the odds of him getting a better victory go up. I call this the Kung Fu master effect. Basically when near a mastery (high or low TN), think of it as the character getting very practiced, but very predictable. He's finishing up a cycle of learning to perfection. As they approach the middle of the range, the character is incorporating more new knowledge - like new kung fu techniques for a new "level" - which open up the possibility of doing far better more often, but also make him a bit more erratic as they're new. This cycle of development is one of my very favorite effects of the HQ resolution curve.)

Second, any aporoximation of an extended contest is heavily based on what sort of bidding goes on. But here's a generall rule to remember, assuming each roll has the same TN and mastery advantage, then more rolls means that the higher side's advantage increases as compares the same contest done as a simple contest. Basically, it's always the lower side's optimal strategy to make as close to a simple contest out of it by bidding as much as possible - the text even points this out. In effect, this means likely two rounds will happen if you're calculating best odds (since the lower side can't bid enough to win in one go even if they do go first). So take the simple odds of success, and then adjust them slightly towards the higher side.

Now, the interesting thing is that often times players will actually drag out extended contests, even if they don't have the advantage. Why? Well, because it's interesting to do so. You get to see more action. Because winning isn't as important in HQ as playing interestingly is. So with lower bidding, and more rounds, you get even more slanted advantage to the character with the higher rating. But this is ameliorated by the fact that less is being gambled each time. So the effect doesn't tend to be horribly pronounced. For example, it's nothing like the math that says that if a character has a 90% chance to win that two rounds give him a 99% chance to win (multiplying the failure odds with each other). Losing either may put the character out of range of a win, and require yet another win.

Complicating this all horribly are two things. First, HP obviously change all of this. Think of them as disposable masteries, essentially (but ones that can only be used if you don't get a critical success to start). Again, they're less effective overall in an extended contest, and a player may have to use several of them to win. But they do change the odds substantially depending on player willingness to use them.

Even more complex is the fact that often a player will come up with a tactic on his round that gives him the advantage. For instance, we have a duel, and the player's hero is being attacked by somebody looking to do him bodily harm with a sword, and the player decides his goal is to avoid that harm while making the attacker look like a fool. On the attacker's round, he has his mastery in swordfighting, and we make the player roll for his character to defend with that, to represent him having to at least fend off his opponent. On his turn, he makes verbal attacks, which gives him a mastery over his opponent. This, of course, evens the odds a lot, though the character to go first has somewhat of an advantage depending on how much he bids.

In fact this situation really incentivizes players to bid high on their round. To avoid "falling behind" in the race to reduce AP. Anyhow, basically after players discover these facts about how extended contests work, they will either:
A. Ask never to do extended contests if what they care about is winning. Or, more likely
B. Understand that extended contests are about drama, and ask for them without worrying what the odds are precisely.

Here are some other simple contest odds:
6 vs 14 - you see this a lot, the player using a non-existant ability at default against the default difficulty of the world to resist. So, navigating a city you've never been to before, for instance, by asking directions to get somewhere in time, for instance.
Player chance of victory: 40.5% (3% Tie). Not bad.
Lesson: HQ doesn't discourage trying mundane things, even if untrained.

13 vs 6 - Novice Trained vs default difficulty - again, really common. Finding your way through a forest that you've been introduced to a little.
Player chance of victory: 54.5% (3.25% Tie)
Lesson: a little training is enough to be dangerous to yourself.

13 vs 14 - Casting a spell you just learned to find your way to the next town.
Player chance of victory: 47.75% (4.75% Tie)
Lesson: May as well flip a coin when it's this close. But novices have a reasonable chance to accomplish standard tasks.

17 vs 14 - casting same spell a few years later, in same situation, but you don't really practice this spell ever (you're only better because your general knowledge is slightly better, represented by a keyword of 17).
Player chance of victory: 49% (4.25% Tie)
Lesson: Broad knowledge is no substitute for expertise. But it doesn't hurt.

1W vs 6 - Knowing the lay of the land with a bit more experience or practice.
Player chance of victory: 70.75% (1.25% Tie)
Lesson: Once you're a journeyman, default is relatively easy. But note that HQ is a dramatic system, so the chance to fail (or win against the odds if you're the underdog) is always substantial as long as the task is within a wide range of potentially interesting resistances. This is a feature of the system that the GM can largely guess on Resistances without worrying too much, and it'll likely produce fun results.

1W vs 14 - A bit more general experience with the spell to find the town, or you've practiced it a little.
Player chance of victory: 51.75% (3.25% Tie)
Lesson: The basic default level for magic makes it likely to bite you in the ass occasionally, even when practiced a little. Don't use magic unless you need to do so, or

10W vs 14 - Very high level of general experience, or some significant expertise with the spell.
Player chance of victory: 63% (1% Tie)
Lesson: OK, now you're getting safer (to say nothing of the better results overall), but, again, magic is never really "safe" until...

5W2 vs 14 - Probably not from keyword, this is an ability that's been honed to a level of mastery.
Player chance of victory: 93% (No ties, and you can't even get a marginal victory, only better)
Lesson: Mastery does what it advertises. Remember that one mastery is "Journeyman" level. True mastery comes with the second one and...

10W3 vs 14 - Definitely not from keyword unless you're some sort of demigod. This is an ability for which the character is known far and wide. You can probably use the ability rating just to scare people.
Player chance of victory: 99.75% (61.5% Complete Victory)
Lesson: HQ does allow mastery of a level where failure becomes remote. You probably don't need to roll at this point, but you can if you like mostly to see how well the character did. Keep in mind that when complete victory occurs, the character should never have to roll that contest again. His spell just always works now to find this town.

10W4 vs 14 - The character is known as a hero, because of this ability. If it's the finding your way spell, he's probably known as "The Pathfinder" or something.
Player chance of victory: 100% (94.25% Complete victory)
Lesson: Heroes of legend do not fail at basic tasks. Period.

I got all of these results using my Simple Contest Outcome odds calculator that you can get from the files section of the HQ-Rules Yahoo group. It's fun to play around with it, and see what trends occur.

Note that for all of the above calculations, augments could, of course, substitute for actual ability to bring the level of ability up. Or, more precisely, the above success ratings are what the character experiences at the levels indicated if the contest in no other way "fits" the character. If the character has related abilities, a personality that lends itself to this task, or, better yet, has a reason to care about succeeding like a relationship or three, then he's going to do substantially better. That is, a couple of points of augment probably only mean a percent or less difference. But 15 points of augment are something entirely different, because of the curve.

In conclusion, I think that all a player really needs to understand in terms of the odds are only a few things anyone needs to know:
1) Higher rating has a better chance to win than the opponent does. Not neccessarily better than 50% to win, however, considering ties.
2) More is better, in all cases. Peole say to me, but Mike, you say above that a character with a 10W2 has less chance to win against someone a mastery lower than he than does a character with a 1W2. So doesn't that mean that it's a bad idea to increase your ability? Do I have to explain the fallacy here? 10W2 has a better chance against 10W than does 1W2. Higher is always better.
3) Everything is pretty dangerous until you have at least a full mastery advantage, and you can't be really confident until you have two.

But the most important thing of all to understand is that failure is a fun and regular part of HQ. So even if you have less ability than the opponent, go for it anyhow. If you fail, it's fun. If you win against the odds (which the system makes pretty likely), it's even more fun. Which, again, means that the narrator should feel free to set resistances at just about any level. It's hard to go wrong.

Mike

Mike wrote:
2) More is better, in all cases. Peole say to me, but Mike, you say above that a character with a 10W2 has less chance to win against someone a mastery lower than he than does a character with a 1W2. So doesn't that mean that it's a bad idea to increase your ability? Do I have to explain the fallacy here? 10W2 has a better chance against 10W than does 1W2. Higher is always better.

Excellent question. 

If you look at the increase in effectiveness of raising an ability by one vs spending a HP to bump, what you generally find is that bumping is about equal to raising that ability up by one mastery, or 20 points for the one contest. So based on that simple analysis, spending on raising abilities at any point seems pointless. Forget about the marginal differences in how much an ability is raised, these are minuscule, generally - who cares if you're getting a 0.25% increase or a 0.5% increase in chance of success? But there are several mitigating factors that make the marginal rate of increase less important.

First, obviously, there is the fact that, long term, you might use the ability 20 times or more, making the investment worthwhile in an expected value sort of way. Not likely, I'll admit, but depending on the ability, and the length of the campaign, it could happen. More likely, you'll use the ability to augment quite a bit. So you tend to see lots of jumps from 13 to 15 and the like, to get the breakpoint bonus. The climb from 15 to 25, however, is pretty steep.

Second, I'm betting you're looking mostly at the pure win/loss ratio. What's interesting is that, while the overall chances of victory don't change much, the types of victory or loss do change, sometimes so dramatically that you lose entire categories of win or loss. So, even if the success margin doesn't change much, the type margin does change more substantially in those cases. So you actually are getting something in return for your lower absolute victory margin shift.

Third, you can't get to 25 without going through all the ranks below first...so part of your purchase, marginal as it may be, is an interest payment on your way to paying off the mortgage. Yeah it might not be worth very much to start, but you have to start, or you'll get nowhere.

And you do want to get somewhere...at least my players do. That is, they do increase abilities with great regularity, even if they're at very marginal points. Because, though you can bump, your ability, including that likely available single HP to bump with, is capped by the ability level. For instance, you simply can't win against a foe that's around 3 full masteries above you or a bit higher (the only question is how badly you lose), 4 with the HP to bump. Raising your ability level means that you raise the level of opponent you can compete against.

And...finall, that's not even it, really. It's not really about who you can compete against, because the HQ system isn't about competition or anything. It's about pointing to what's important to your character, and making them look cool. It's like bragging rights. My character has the highest level of fighting ability. This is not the same as bragging about it in D&D or somesuch. In that sort of game, you are, as a player, bragging about your own ability in getting the character to that level of ability. In HQ, there's no skill involved, simply player decision about what to spend the HP on. So the "bragging" is simply saying, "I've got the character who's coolest in this particular way." You're bragging about how you've crafted the character to be interesting. Or just about how cool you think they are. Like talking about how strong Superman is or something.

The point is that players do spend HP. I think they just do not care about the marginal level of effect that the expenditure has. Consider also in the balance of the equation, that, while it can be fun to bump to win or mitigate some failure, it's also fun to fail in HQ. So neither side of the equation is balanced towards hoarding points for one or the other, as you're not really concerned about whether or not the character wins. It's more about getting to control whether or not the character wins or loses in certain circumstances, or what to feature on the character. All about directing the character's dramatic life as he develops.

Also, a HP that's sitting unused is...useless. That is, I find that players almost always spend down to a certain level of HP that they keep around as their "safety net." That is, they keep around just enough HP that equals most of what they think they ever might want to spend in a session. And then spend the rest. In fact, I find that some players let them pile up and then realize that having 18 HP in reserve is quite pointless, at which point they spend 15 of them on various abilities. When you're spending that many HP, too, you tend to really not worry about the relative level of value of each increment of ability.

One more thing...I think that players really don't know about the curve. That is, while I have played a lot of HQ, and done the research, and understand and appreciate the curve, I think that most players are oblivious to it.

Even though I do know about it, however, I still spend on whatever tickles me at the moment. I simply can't imagine trying to tweak my character to some optimal level in HQ. It simply doesn't make any sense. What's the advantage to doing so? If the narrator wants to, he can always come up with a more potent enemy, or hit my character with a contest that shows up where he's weak - I'm never going to get to the point where my character is "safe" (not that I'd want that). It's not impressive as a player to have a particularly powerful character. So why would I bother trying to do some rigorous min-maxing here?

Lastly let's say that I did only spend on the abilities that were most valuable at the moment to spend on in terms of pure odds. Well, eventually things will come around to where I'll have to purchase everything, or everything is at the same level of marginal gain. So when I have that absurd pile of 18 HP...why not spend them on something?

Now, all this said, if your a GM who gives out scant HP, such that players do not tend to accumulate piles of them, and tend to want even more to bump with than they have...well, then all the above is out the window. But I'd say that at that point, you're giving out too few HP. Or, rather, you're running what I'll call an "austere" game. Meaning one in which players are forced to make really difficult decisions on what to spend their meagre resources on. Which is fine, really, but then it's no surprise if players save all their HP to bump with, and make few to zero purchases. There's actually nothing particularly wrong with this, either, lots of stories don't involve characters getting any better at anything.

I've noted that I have players who have received upwards of 200 HP for a single character. What's fascinating is that they do not end up "lopsided" meaning having lots of low abilities, and a few very high abilities. Oh, they still have lots of low abilities, but they have lots of medium abilities as well. All-in-all, they are not significantly more powerful than when they started. That's after 200 HP, mind you. And it's not because they don't spend HP - I have players who hardly ever bump. It's simply because they purchase levels in the abilities that most interest them at the moment. Because they're not trying to min-max the character, they're trying to make the character more and more interesting to play. Interestingly sometimes that does mean having some high level in some single ability. But in that case, it's again because the player is showcasing that in the character.

OTOH, Fred's character started with Strong 2W5, which has not grown one iota in play in 50 sessions or so, and which has been surpassed by his "Loves Isadora" ability a while back, IIRC. Which is a huge statement in and of itself about what the player found interesting about the character in play. Who knew?

I wish more players did understand the curves like I do, because I think it's interesting. Because then I think players could look at the whole mastery cycle and consider its effects in play. I think that understanding how it's interesting could make them want to progress more through the cycles, and comment as they go on how this is changing their characters' types of victory and such.

Anyhow, I stand by all of this as the practice seems to match my theory. Now, that's just for me, of course, others may have other experiences. But at least in this one case, it all works fine.

Mike

<quote>OTOH, Fred's character started with Strong 2W5, which has not grown one iota in play in 50 sessions or so, and which has been surpassed by his "Loves Isadora" ability a while back, IIRC. Which is a huge statement in and of itself about what the player found interesting about the character in play. Who knew?</quote>

Actually... I did.

From the first scene where Okhfels completely misunderstood why Isadora was interested in him, I knew that ability would eventually become the relationship it is...

...and now I'm contemplating where it goes from there.

First, thanks Mike, for your thorough response.  It was very helpful, and I am going to direct my current game group to it.

Mike wrote:
Second, I'm betting you're looking mostly at the pure win/loss ratio. What's interesting is that, while the overall chances of victory don't change much, the types of victory or loss do change, sometimes so dramatically that you lose entire categories of win or loss. So, even if the success margin doesn't change much, the type margin does change more substantially in those cases. So you actually are getting something in return for your lower absolute victory margin shift.

Now, all this said, if your a GM who gives out scant HP, such that players do not tend to accumulate piles of them, and tend to want even more to bump with than they have...well, then all the above is out the window. But I'd say that at that point, you're giving out too few HP. Or, rather, you're running what I'll call an "austere" game. Meaning one in which players are forced to make really difficult decisions on what to spend their meagre resources on. Which is fine, really, but then it's no surprise if players save all their HP to bump with, and make few to zero purchases. There's actually nothing particularly wrong with this, either, lots of stories don't involve characters getting any better at anything.

I wish more players did understand the curves like I do, because I think it's interesting. Because then I think players could look at the whole mastery cycle and consider its effects in play. I think that understanding how it's interesting could make them want to progress more through the cycles, and comment as they go on how this is changing their characters' types of victory and such.

Fred, I get what you're saying, but what I was getting at is that I don't think that any of us predicted that he'd fall in love with her from the start. Basically that as play develops what interests players about their characters can change a lot.

Hans, that's another good point, that not understanding the mechanics can disappoint players. Players can learn the hard way, but you're right that it should be explicit up front. Especially for players who are used to systems where the character wins almost all the time. The thing for players to understand with HQ is that you're character is going to fail, and fail a lot of the time. Unless the narrator throws contests at the players that are really simple, like two masteries below their ability level, their characters are going to fail at something every single session.

This is a huge advantage that HQ has over other games. That is, failure is a normal part of the dramatic cycle. Playing D&D, if you fail, you lose your character likely, and you're out of the game. So you can't have a lot of dramatic failure (usually only one, and the game is over). In HQ, you can fail all you like, and keep coming back for more. Because the stakes for contests are set at things other than character death and removal from the game, even in "combat". I'd argue that failure makes characters more interesting to play in HQ - it gives you something to do with the character, fixing the problem that the failure caused (be that a wound, or wounded pride or whatever).

So this is hard to get players of more "traditional" games to overcome. That is, they expect that failure is a rarity, and feel that somehow failure means that they have failed as a player. If you look at the rules, however, this is simply not true - there's really no way as a player to affect your chances of victory or defeat, it's all in the narrator's hands, and the whim of the dice.

The resolution system in HQ isn't about player victory, it's about giving the player an opportunity to try to show off the character, by finding how the character's abilities augment in the contest, and thus how the character fits into the contest. How it all relates together. So that when the resolution does come down, everyone has that much more context from which to build further actions. "He was partly relying on his faith to see him through, but now that he's failed, I think he's starting to doubt his god." I've heard that at least three times in play, and it's fantastic fun each time it happens.

So embrace failure. As a player this is so freeing, I don't have words enough to describe the effect. It basically means that I'm free to have my character do stupid things. That's an extreme way of putting it, but the point is that I don't have to worry about "playing well" in terms of winning or losing, I only have to worry about what's important to the character, and making the situation more and more interesting.

Best of all, I can have my character be heroic. I can have him charge headlong into battle, or over the precipice, heedless of the danger, not because I know that the system will save my character; but instead because I know that if I fail, it's still interesting. And if I win, then my character has striven against the odds, and come out ahead. Players in D&D can't take that sort of risk - they don't want to lose their characters. So they play it safe, including the DM taking it easy on them. Heroism is rare in such games. In HQ it happens every single session of play.

If you look at the curve, there's one more thing that I love about it. It's realistic. Yep, consider how many times you fail at things in your life. I mean, if it's really a reasonable challenge, you fail at times. Look at descriptions of combat - why are well trained people afraid when they go into combat? Is it because there's a slim chance that they'll die? No, combat is a chaotic situation where the combatant is only in slight control of events, and the chances of their death are significant at each and every encounter. This is why nobody ever tries to get into a "pitched battle" situation. You always look for a way to cheat, and alter the odds dramatically in your favor.

Most RPG systems slant character effectiveness such that they are simply capable of consistently dealing with any opponent that's not as effective as they are. Bell curves and stacking of effectiveness and such are used to ensure this sort of thing. Leveling up means not just more HP, but more ability to hit, maybe more ability to do damage, and more other special abilities. Making level an exponential rating of effectiveness, not linear.

In HQ, the opposite is true. Unless you're way, way, way better than your opponent - so much that it's probably not a dramatic contest anyhow - if you're anywhere in the same neighborhood of ability as the opponent, as you say, Hans, it's almost as though you might as well flip a coin to see who wins. That's realistic, and that's dramatic because it's realistic. We know that the character has a good chance of losing something, and that means that the tension on each and every contest is high.

I mean, when Indiana Jones gets into a scrape, we're not concerned that he's going to die, we know that he's going to make it to the end of the movie. But there's tension anyhow, because there's something on the line that Indy cares about, and there's every chance that he's going to lose this fight. Indiana Jones is not a cool character because he wins every fight, he's cool because he loses repeatedly, and still fights back despite the indignities he suffers.

So I hope your group gets that, Hans, and enjoys this sort of play. Dive headlong into adventure, show off your character, forget about tactics, and just have fun. HQ's system makes this all possible.

Mike

Hans wrote:
First, thanks Mike, for your thorough response.  It was very helpful, and I am going to direct my current game group to it.

Mike wrote:
Second, I'm betting you're looking mostly at the pure win/loss ratio. What's interesting is that, while the overall chances of victory don't change much, the types of victory or loss do change, sometimes so dramatically that you lose entire categories of win or loss. So, even if the success margin doesn't change much, the type margin does change more substantially in those cases. So you actually are getting something in return for your lower absolute victory margin shift.

This is a good point.  I had noticed that while the win/loss is very flat in the +/-5 range around the resistance, the relative proportion of the victories changes pretty rapidly in the same range. 

I do think (no offense Erik, if you are reading this) that I have been playing in an "austere" game.  However, after forwarding this thread to my game group on our own meeting board, and talking over it there a bit, I think that might change.

On our campaign's message board (http://roleplayers.meetup.com/261/boards/view/viewthread?thread=1587394&pager.offset=100#3676530) I have been posting about the ways in which heroquests can dramatically improve old abilities or add powerful abilities at 1 stroke.  So, discussions of character improvement should consist not only of the factors mentioned so far (hero points, the relative benefits of using bumps or making permanent changes),  Players should always be thinking bumps, permanent ability changes, and heroquests when thinking of the long-term growth of their characters.

Erik Weissengruber