Tuesday, March 14, 2017

This is the seventh installment of our strategy blog written by game historian Shannon Appelcline. You can read all the installments here.

The heart of PACG is attempting checks to acquire boons and defeat banes. And every check starts with dice that need to be rolled.

Checks are all about rolling dice, so the heart of managing a check is knowing your dice. Obviously, if the results of a check aren't that important, you should just throw your dice and see what happens. However, if you really want to gain a boon or defeat a bane, then you should understand your odds.

You can calculate the odds of your dice in a number of ways. This listing goes from least conservative (you might lose!) to most conservative (you won't lose!):

• Count dice + sides then divide. Add up the number of dice and all their sides, then divide by 2, then add the modifiers. For example, if you're rolling 1d8 + 1d6+2, add 2 (the number of dice) + 8 (the number of sides on the first die) + 6 (the number of sides on the second die) to get 16. Divide that by 2 to get 8 (that's the expected value of your roll), then add 2 (the modifier) to get your expected result: 10. If the difficulty of your check is also 10, your odds of succeeding are a bit better than 50%. (The example given has 48 possible die combinations. 21 of them give a result less than 10, 6 equal to 10, and 21 higher than 10, so the odds of succeeding are 27 in 48, or just over 56%.) So if your expected result is the same as the difficulty of the check, you will succeed more often than not, but you will still lose often. This method of calculation is also a bit cumbersome for quick counting.
• Count half the sides. This author's preferred technique is to just count half the sides on each of the dice, then add the modifiers. For the 1d8 + 1d6+2 example, add 4 (half the sides on the first die) + 3 (half the sides on the second die) + 2 (the modifier) to get an expected result of 9. Not only is this quicker to count than the dice + sides technique, but it also underestimates a little bit: You'll be under the average by half of the number of dice, so it's a bit more conservative. (Using the example above, you'll want to look for a way to add a +1 to reach the difficulty of 10, which would increase your odds to 33 in 48, or nearly 69%.)
• Count every die as a 2. It may have been Obsidian's Nathan Davis who suggested that you should assume every die you roll comes up a 2. With this method, our 1d8 + 1d6+2 example gets you an expected result of 6 (2+2+2), so if the difficulty you're looking for is 10, you'll want to add 2 dice (of any size) to make up the difference. (Adding even 2d4 improves your odds to above 95% in the example.) This is a very conservative method, but if you use it for the most important stuff, you're rarely going to fail.
• Count every die as a 1. There's only one way to be 100% sure of success: your number of dice plus your modifiers must be equal to the target you're shooting for. Yes, this is ridiculously conservative, but you might want to use this criteria occasionally, particularly at the end of a game.

It's easy to use these methods as a basis for an even more conservative estimate without requiring much more work. Just look at the results in a more ad hoc manner: "I estimate these dice will get me a result of 12 and I need 11 to succeed, so if someone could throw in one more blessing, I'd feel a lot better about it" or "I need an 11 and I expect that from 3 dice, so an extra 2d4 will probably push me over.")

Corollary #1: More dice move things toward the average. If you're rolling just one die, the odds are spread evenly across all the possibilities, but if you throw a whole bunch, the odds will cluster toward the middle. For example, trying to get 5 or more on 1d12 has an 8-in-12 chance of succeeding (almost 67%). But trying to get that on the seemingly similar 2d6 results in a 30-in-36 chance, or just over 83%, while 3d4 gives you a 60-in-64 chance, or almost 94%. So if your expected result is a just a little bit above the difficulty, but you're using a lot of dice, you're more likely to be okay.

Corollary #2: Rerolling dice changes the average. Some monsters, like the Giant Hermit Crab, force you to reroll on success, while some weapons, like those that have the Polearm trait, allow you to reroll on failure. The math is tricky, but if you're going to have to reroll on a success, you want to be sure you can succeed twice in a row. In such a case, an average only a teeny bit over your target probably isn't going to cut it. On the other hand, when you get to reroll failures, you can be more comfortable with marginal averages.

"So... best 2 out of 3 then?"

Know What Blessings Can Do

Checks involve not just the dice that the cards say to roll, but also the benefits applied by various players, which often come in the form of blessings. Some checks are hard, so blessings can be the difference between having a poor chance of success and a decent chance.

The trick is that blessings also usually represent a potential extra exploration. Don't be afraid of using them, because you don't necessarily need a lot of extra explorations to succeed. But do ask yourself, "Is using this blessing to improve the odds on this check more valuable than having an extra exploration?" Often losing a card, losing a hand of cards, or losing out on a chance to gain a boon turns out to be less valuable than an extra exploration, in which case it's not worth spending a blessing for that check.

Corollary #1: Keep an eye on the blessings deck. Many blessings recharge if the same blessing is atop the blessing deck. Keep an eye on that and the blessings in your hand. If they match, be much more willing to use your blessing. It defers your extra exploration, as you usually have to go through your deck to get it into your hand again, but if you're playing aggressively, it's not lost to you.

The exception is, of course, late in the game. If you're not going to cycle through your deck and you're not going to get your deck shuffled by healing or some other means, then you should treat discarding and recharging the same (and burying too, for that matter).

Corollary #2: Don't bless low skills. Don't waste your blessings on d4 skills unless things seem quite dire. A blessing just doesn't add much to a bad skill. (To be precise, it adds an average of 2.5 to a roll, where spending that blessing on a d12 skill can be over twice as good, adding an average of 6.5 to the roll.) Heck, it can feel wasteful to spend a blessing on a d6 skill.

If a low skill needs help, look instead to powers and spells. If you need to help someone with a bad skill, it's more effective to use certain spells and abilities. Lem can often add up to 1d4+3, while an Aid spell can add a d6 and a Strength spell might add a +3.

Corollary #3: Don't bless excessively (or otherwise overcommit). Whether you're playing blessings, spells, ranged weapons, allies, or some other boon, you don't want to overdo it, yet there's a tendency for players to put too many dice into a pool. When you roll two or three times your target number, and the check wasn't to close a location or defeat a villain, you probably wasted resources that could have been used to take extra explorations or to give a player better odds on another check.

If you count your expected value and you're over your target by more than half, or you've got more than a few extra dice, consider if you really need everything that's in the pool, especially if getting there required discarding or burying cards.

Shannon Appelcline
Game Historian

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Gaby Weidling frequently embraces the "Count every die as a 1" strategy.

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(The date says February 14 but I don't think that's correct)

I like throwing everything onto the very last check of the scenario, whether it be a close or combat check. It's fun rolling 8 dice with a plus 7 when you only need a 15. ;-)

 RPG Superstar 2011 Top 32

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I'm pretty good with probabilities in my head (I've been a math teacher), so I'm usually the one advising my table on odds. I tend to use something like method 1.

Of course, this comes back to bite me when my friends are asking if I need a blessing and I'm like, "Nah, I've got a 96% chance to make this roll," and then it fails.

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Rebel Song wrote:

(The date says February 14 but I don't think that's correct)

I like throwing everything onto the very last check of the scenario, whether it be a close or combat check. It's fun rolling 8 dice with a plus 7 when you only need a 15. ;-)

Over on the Obsidian forums, I referred to this as Alpha-striking (Battletech term), which caught on. I created a thread for screen-shots of epic Alpha-strikes.

http://forums.obsidian.net/topic/86610-alpha-strike-screen-shots/

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Pathfinder Card Game, Class Deck Subscriber

I prefer using method 2 on my table. However, when we're temp-closing for the final villain showdown - we're going Method 4. Basically, we throw everything and the kitchen sink on the villain (and sometimes that even means some characters will die if we fail), so if a character has a 1/12 chance to blow his temp-close check - they still get a full blessing (assuming we lack another resource to bump him one point).

Pathfinder Card Game, Class Deck Subscriber

Is it just me, or is the math off in Know Your Dice Results Corollary #1? 26 in 36 is just over 72%, if I'm using this calculator correctly.

 Chief Technical Officer

Rebel Song wrote:
(The date says February 14 but I don't think that's correct)

Fixed. Thanks.

 Chief Technical Officer

James McKendrew wrote:
Is it just me, or is the math off in Know Your Dice Results Corollary #1? 26 in 36 is just over 72%, if I'm using this calculator correctly.

The percentage was correct, but the fraction was wrong: It should read 30 in 36. Fixed.

 Chief Technical Officer

If this blog interests you, you may want to check out the dice calculator at anydice.com. (To see what the odds of our primary example—1d8 + 1d6+2 with a difficulty of 10—are, you'd enter "output 1d8 + 1d6+2" at the top, click the buttons "Table" and "At Least", then hit the "Calculate" button. Find the result "10" in the table, and you'll see the odds of getting at least 10 on that roll are 56.25%.)

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Do Bless Low Skills

Supporting isn't about how large a die you add to the check, it's about attaining the desired result. Getting rid of a particularly annoying card, avoiding a hand flush or other very bad thing, (temp) closing a location, and occasionally even acquiring a desired boon are all times that you may want to use whatever means you have available. Sometimes your party members have other cards or abilities that can help, but usually it means Blessings. Don't be afraid to use them when the result is worth it.

Also, in Guild play, don't forget your reroll item! :)

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Gaby Weidling frequently embraces the "Count every die as a 1" strategy.

A friend of mine's dice also frequently embrace the "count every die as a 1" strategy, much to the table's chagrin. I remember the time where he managed to roll a 1 on every single die (there were like 8 of them), when success was just 3 more than that roll. It was the final roll against the villain, so we threw everything we had at it to "make sure" it was successful.

I played with a guy at a con once who had a probability calculator app and would not roll if he didn't have a 95+% chance of succeeding. This was pretty annoying in terms of the amount of blessings it ate up.

I follow the "Count every die as a 2" strategy, which seems to work fairly well. It gets you high enough probability wise without expending too many resources.

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Thinking of it, we tend to follow a non written metamathrule that looks like:

- If you don't care (like you encounter a boon that is not great and you aren't short in cards left in your deck), don't waste ressource, throw your basic di(c)e

- If it's a standard bane (not a big deal if you lose), we somehow use the "Count dice + sides then divide" version (which gives by definition more than 50% chances

- If it's a important boon or bane (someone in the group will really benefit of the bane, the bane has a very nasty outcome if undefeated, or you really need one more card in your hand), count dice as 2 (or 3 for d10 and above)

- It it closes (defeating the henchman that will give you the opportunity to close, the closing itself, a not to nasty villain that is not cornered but has limited locations to escape and we still have time), count dice as 2 and roll at least 3 dice

- It it a must win, except final fight (cost on the blessing deck too high if failure...), count every d4 and Dd6 as 1 and all other dice as 2and roll at least 4 dice

- Final fight, throw all you have (we managed to roll 22 dice once with 6 players)

Maybe it's a little tricky, but we take 1/2 the first die + 1/2 the second die + 1 + 1/2 the third die + 1/2 the fourth die + 1 etc + bonuses.

 Chief Technical Officer

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elcoderdude wrote:
Maybe it's a little tricky, but we take 1/2 the first die + 1/2 the second die + 1 + 1/2 the third die + 1/2 the fourth die + 1 etc + bonuses.

That's one of several different expressions that get you to the same result as "Add up the number of dice and all their sides, then divide by 2". I personally do that with a method that falls in between the one Shannon described and the one you described: I add half of the max value of each die, then add 1 for every 2 dice. So my "1d8 + 1d6+2" math is 4 (half of the d8) + 3 (half of the d6) + 1 (for two dice in the roll) + 2 (for the modifier).

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I was reminded in the Pathfinder Adventures app today how these all fail during Scaling Mhar Massif in all those Death Zones.

Hawkmoon269 wrote:
I was reminded in the Pathfinder Adventures app today how these all fail during Scaling Mhar Massif in all those Death Zones.

Yeah that one really screws with my head math. I keep failing checks I thought would be easy, or beating them by a lot after spending way too many resources.

Addressing the question of what dice-counting methods we actually use:

My table tends to count dice with method #2 (half the number of sides), but then if it's important we try to throw in an extra dice or two past when the expected value matches the target. It's an easy to count ad-hoc method.

For the important stuff, we try to get close to method #3 (count each die as a "2"), though on one our recent games I was throwing seven or eight dice ... and missed with that method. Doh! Our villain did _not_ get beat on that encounter as a result.

I dunno, things seem "quite dire" for me all the time. I've lost track of the number of times when I've run up against an obstacle that's going to keep pounding me for insane damage unless I succeed on a check using one of two skills that I just don't freaking have. So I toss a Blessing, roll 2d4, and hope for the best. Surprisingly, it's worked a fair number of times!

Hawkmoon269 wrote:
I was reminded in the Pathfinder Adventures app today how these all fail during Scaling Mhar Massif in all those Death Zones.

Ambushed by a Warlord in the Death Zone?