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Friday, May 3, 2013

Divine Favor prayers: the odds

I use GURPS Powers: Divine Favor in my Circus Sophia campaign. If you are not familiar with it, it allows a character to pray to the gods to grant some sort of miracle. There are three sorts of prayers: general, specific, and learned. Learned prayers are automatically successful, but the others require you to roll some dice to see if you god hears you and is favorably inclined to your request.

It's those die rolls that I want to explore a little. General and specific prayers work nearly the same. First, you GM makes a roll against your Divine Favor level, with suitable modifiers. On a success, your god hears you. Then the GM makes a reaction roll to see how your god feels about you at that moment, again with suitable modifiers. If this succeeds, your prayer is answered. With a general prayer (a simple "help me, my lord!"), the better the reaction, the better the result, but the GM decides how the god wants to help you. With a specific prayer ("lord, please heal this fool of a meatshield"), you get what you asked for if the result is good enough, or nothing if you don't.

The Petition Roll

The first roll, the petition roll, is based on your Divine Favor level, the advantage that lets you (semi)reliably call upon the power of a god. It ranges in level from 4 to 16. Modifiers can push this down below 3, in which case you have no chance of contacting your god, or up above 20, in which case it's guaranteed. If you fail, repeated attempts are at -1 for each attempt in the next five minutes. This is explicitly not a success roll, so there are no critical successes or failures.

Given that Divine Favor starts at 15 points for level 4, and is 70 points for level 10, this seems a bit harsh. You must pray for 1d seconds, and even after spending 70 points, you only have a 50/50 chance of being heard. It's not going to be a very good idea to try to rely on this in combat.

Out of combat, though, it's not as bad as it seems at first. In basketball, they say, you get four fouls, so that must mean they want you to use them. With Divine Favor, you can make repeated prayers at a cumulative -1, so the rules must want you to try. This means that at Divine Favor 10, you get to roll at 10, at 9, at 8, at 7, and so on down to 3. At 1d seconds per try, this will take you a maximum of 48 seconds, and the odds of success are much better than 50/50.

Is there any downside repeated attempts to get your god's attention? No, not that I see in the rules. You do take a -1 penalty for every successful prayer your god has granted to you that day, but there's no effect on the reaction roll for repeated but answered prayers. So if you get a divine busy signal, you just hang up and redial. Given that, your odds of contacting your god with a given modified Divine Favor are listed below.

Initial target Probability
3 0.46%
4 2.31%
5 6.83%
6 15.46%
7 29.16%
8 47.52%
9 67.20%
10 83.60%
11 93.85%
12 98.41%
13 99.74%
14 99.98%
15 100.00%
16 100.00%
17 100.00%
18 100.00%

Table 1: Probability of a successful Petition Roll on repeated tries

That seems like a lot of die-rolling for a spread of probabilities that's not a lot different from a one-minute prayer that give you a one-try roll at Divine Favor+1 or +2. And in fact one of the modifiers for this roll is +1 for a five-minute prayer. This is only a better probability if you are starting from a roll of 6 or less.

And if your god still doesn't answer, you can try again in five minutes. That being the case, the only reason to take the +2 bonus for a two-hour prayer is if your target number for the roll would otherwise be a 1. In any other situation, you're better off with repeated shorter prayers.

I don't much see the benefit of all this die-rolling. It hasn't come up in my game so far, because none of the PCs have Divine Favor and NPCs have only been using learned prayers, but I'd be tempted to say that outside of combat, petition rolls are at +1 and take 1d6*10 seconds. If you fail, you can't try again for five minutes.

The Reaction Roll

But getting heard is only half the battle. Even if your prayer gets through, your god may or may not feel like helping you. For a general prayer, you need a Neutral or better reaction, which is a minimum 10. Again, that's a 50/50 shot. In this case, repeated tries may not be such a good idea. There's no penalty on a Poor result, but a Bad result or worse means your god punishes you in some way.

You get modifiers to this roll depending on what the stakes are, how faithful to your religious beliefs you've been lately, the sanctity of the area, and how many successful prayers you've had so far that day. This can put your reaction roll modifier anywhere from +10 to -10 or even lower. So, at a given modifier, if you make repeated prayers, what are your chances of getting a Neutral or better before you get a Poor or worse? That's given by the second column of the chart below.

Reaction Neutral Good Very Good Excellent
Modifier or better or better or better
+4 or more 100.00% 100.00% 100.00% 100.00%
+3 99.49% 99.26% 98.25% 90.91%
+2 97.84% 96.43% 89.74% 50.00%
+1 94.12% 89.01% 66.67% 9.09%
0 87.10% 73.68% 33.33% 0.00%
-1 75.52% 50.00% 10.26% 0.00%
-2 59.12% 26.32% 1.75% 0.00%
-3 40.88% 10.99% 0.00% 0.00%
-4 24.48% 3.57% 0.00% 0.00%
-5 12.90% 0.74% 0.00% 0.00%
-6 5.88% 0.00% 0.00% 0.00%
-7 2.16% 0.00% 0.00% 0.00%
-8 0.51% 0.00% 0.00% 0.00%
-9 or less 0.00% 0.00% 0.00% 0.00%

Table 2: Probability of getting a given reaction or better before getting a Bad or worse reaction on repeated tries

It's not so bad, as it turns out. Even with a -2, you're more likely than not to eventually get a positive outcome. If you can get a +1, which is not that hard, you can get a positive result almost 19 times out of 20.

But that's for general prayers. With a specific prayer, you may be asking for something fairly minor, such as the ability to withstand pain, or something huge, such as bringing the dead back to life. The smallest blessings require only a Neutral reaction or better, with more powerful effects requiring better results, all the way up to Excellent.

Before calculating Table 2, I figured you might need some pretty high modifiers to pull off the best miracles. And indeed you do, if you're in a hurry about it. If not, a bonus of only +4 guarantees you a minimum result of 7 on your reaction roll, which is Poor. Since you will never get a Bad reaction, you just need to keep praying, and eventually you'll get there. A +4 is not exactly easy to get, but it's far from impossible.

So, does this mean the system is broken? Is all this die-rolling unnecessary? Well, let's look at an example. Joshua, a priest of the god Yahweh, is leading his people into battle. The battle stretches out all day, and his enemies are in danger of escaping if the sun goes down. Joshua prays to Yahweh to cause the sun and the moon to stand still, so that there will be light enough to finish the battle.

This is a specific prayer for a very powerful miracle, and it requires an Excellent reaction. Assuming Joshua has made his petition roll, it takes a 19 to get an Excellent reaction, which means he's going to need some bonuses.

He can get a +4 from the fact that many people's lives are at stake. Nothing but a miracle is going to provide enough light to fight by. That would require him to roll a 15 or better, which he has only about a 9% chance of doing. If he fails, he can try again as many times as he likes, but it's going to take time. He's going to have to make several tries at it to even have a 50% chance of success, and he could still be praying in an hour. If that's the hour it takes for the sun to go down, it will be too late.

But wait! Joshua can also get a bonus from his faithfulness to his religion. If he has led a particularly saintly life and inspired people to work in the cause of Yahweh, he could get another +4. That would put him at +8, meaning that if he rolls 11 or higher, he gets an excellent result. That's 50% odds. It's very likely that his prayer will succeed within 4 tries, and he will probably save the day. If he hasn't been that saintly or inspiring, but still has scrupulously adhered to the tenets of his religion, he can get a +2 bonus for behavior, taking him to +6 overall. Now he's got about a 1 in 4 chance to succeed with his prayer, and things get a bit dicier.

So this is where the extra die-rolling counts for something. If you have all day, a +4 pretty much guarantees you a success. But if time is a factor, much might happen while you're trying to get that success. Your enemies might catch you, your people might lose faith and desert you, the volcano might erupt and kill you all. That's when the difference between any old priest and a saint shows.

And if you're Moses, and you need to be sure the sea is going to part, no question about it? That's what learned prayers are for. It will cost you, though. You'll need Divine Favor 15 just to qualify for Part the Sea, which is 170 points, and then it's another 32 points for the learned prayer. Being that powerful doesn't come cheap.


Wednesday, May 1, 2013

Game Session 2013/04/07


The Circus Sophia:

Sophie O'Griffin, human, the leader and ringmaster. Played by Echo.
Esmond Gellert, human, trick-shot archer and dog trainer. Played by Mike.
Ganz, elf, stage magician and wizard. Played by Jessica.
Quexechetl, lizard man, strongman and wrestler. Played by Karl.
Talman, half-elf, acrobat. Played by Joe.
Fiorio, human, a peasant with a knack for playing to the crowd that the circus picked up along the way. Played as an NPC.

July 1, 850, very early in the morning, in the Bekel

When we last saw our heroes, they had just found and killed the orc that they believed was controlling the army of undead orcs, and the dead orcs had then attacked the living ones. Three living orcs survived and ran away into the darkness. Talman recovered the staff from the body of the orc priest or wizard or whatever he was.

After backing off to a safe distance from the eight or so remaining dead orcs, the circus decided to follow the living survivors. Esmond, with his amulet of night-seeing, tracked them easily, with the rest stumbling along by the light of Sophie's lantern. They followed the orcs around the edge of a rise on the right side of the valley, down into the ravine that cut off the route to the north, where they found a ford. Climbing up the other side of the ravine, Esmond was just in time to see the fleeing orcs enter the forest on the far side.

He pursued, while the rest of the circus followed at a distance behind him. Not far into the forest, he saw first one light, then more. Small groups of orcs were gathered together, some carrying torches. The three survivors of the recent battle approached one group and spoke with them, pointing frequently back the way they had come, and also off toward King Miklo's army. The orcs dispatched a goblin messenger, who returned in about ten minutes. All the orcs then withdrew.

Esmond watched until he was certain all the groups of orcs were leaving, then withdrew. He reported what he had seen, and then the whole circus crossed the ravine again and returned to the king's army. They passed a handful of dead orcs who were stumbling around blindly at the bottom of the ravine. When they reached the army's encampment, they found that it had nearly finished off the undead horde, with only a little mopping up left to do.

At the center of the encampment, they found King Miklo with his principal advisors, including Count Anelmo and the Archmagus Tor. They began an explanation of what they had seen and done, but the Archmage interrupted, and asked Ganz if he would be so kind as to lay the staff they had found on the ground and step away from it. Ganz did so, and everyone gave it more room.

When the performers finished their tale, Archmagus Tor sent a squire to inform High Priest Eddicollo, the King's personal priest and another member of the regency council about these events. The square returned in the company of the High Priest, and the whole story had to be repeated again. Then, with many exchanges of "Your Grace" between them, the Archmage and the High Priest debated about who should take custody of the mysterious staff. In the end, the High Priest decided that if it were unholy, it might desecrate the holy objects in his care, and so that Archmage took it.

Than done, and with no enemies to be fought, everyone headed for bed.

In the morning, the army scouted about to make sure there were no more dead orcs around. Lord Fels took a group of knights with him to investigate the outcrop where the circus had fought the orcs and killed what might have been their leader. The men-at-arms and laborers were put to work dragging the bodies of the orcs into a pile and burning them. The dwarven engineers finally began constructing the bridge that would let the army pass over the ravine.

Meanwhile, the Circus Sophia had some free time, and so they decided to return to the ruined wizard's tower and investigate that cabinet they had found there. The cabinet was decorated with square panels crossed by X-shapes, each arm of each X being a separate piece of joinery. There were three panels on each side and six in the front. On their earlier visit, they had discovered that by depressing each arm of the top X-shapes on the sides and then rotating them, they could release the catches that held it to the wall. By fiddling around with some of the other panels, they found that the cabinet had a number of other interesting properties:

When the middle panels on the sides were rotated, the top third of the cabinet drew inward and then collapsed into the middle section, leaving a much shorter cabinet. Opening the doors, they found it had two shelves. A slim, leather-bound book lay on the top shelf. It was filled with sketches of the surrounding countryside and the tower itself, from long ago when it was intact. Each drawing was labeled dwarven writing. There was no sign of the bottles and crumbling cloth that the cabinet had contained when it was full-size.

Rotating the bottom side panels, the performers found that the cabinet collapsed again, down to the size of a large chest or trunk for clothing. It now opened from the top instead of the front, and was empty.

Returning it to full size by rotating the panels the other way, they then discovered even stranger properties. By rotating the top panels on the front, the doors opened to show not a wardrobe, but a multitude of small, deep drawers, like an apothecary's cabinet. Most were empty, but some contained musty bits of herbs or lumps of wax.

After rotating the middle panels on the front, the cabinet drawers opened to reveal dozens of wide, low shelves, only a few inches high. Most were empty, but a few held yellowed pieces of paper with dwarven writing on them.

Rotating the bottom front panels revealed the strangest transformation of all: the interior of the cabinet was more or less like a wardrobe again, but with a wide door at the back. Opening this door led into a short, wood-lined space, about six feet deep, with cubbyholes for storage on each side. The cubbyholes held a collection of mostly mundane-looking rocks, but there were some examples of quartz and lapis lazuli. Altogether, the rocks probably weighted a couple hundred pounds.

Talman volunteered to step inside the cabinet while Sophie transformed it into another configuration, to see what happened. She collapsed it to its two-thirds height, opened in, and Talman was gone! And yet he could hear his companions talking, and they could hear him, muffled as if he had been stuffed into any mundane closet.

At its smallest size, when collapsed to a chest, it weighed about thirty pounds, which Quexechetl could easily carry. He, more than anyone, was bothered by the question of where the extra space that the cabinet seemed to hold really was, but the others vetoed his suggestion that they go inside and start knocking out walls to see where they led to.

They all decided that they would tell no one about their amazing find. The took it back to camp, kept it chest-sized, and threw a few circus costumes into it. Sophie kept the key.

July 2, 850

The next day, the army finally broke camp. They ventured carefully into the forest on the far side of the ravine, but saw no sign of orcs. The marched until they found a large clearing, then stopped for the night.

July 3, 850

The army reached the ruined dwarven city of Norogon. A couple hundred orcs were observed fleeing, but nothing like the large numbers the army had been hoping to catch.

The foreign knights in the army were rather disappointed at this, since they more than anyone hoped to prove their gallantry in a fight. The king's counsellors decided that they had achieved what they wanted from a short campaign, and it would be a good time to return to Lodea and face the Gondans. That night, the circus decided to put on a show, and the dogs were particularly good.

July 4 to July 14, 850

The king's army marched back to civilization, without meeting any more groups of orcs large enough to care about. Drums were sometimes heard at night, but never very many, or very near. The army reached the northern Lodean town of Gorno on July 14, 850.

With King Miklo now safely back in his own country, Sophie called upon Lord Fels and raised the delicate issue of their payment. He said he figured they had performed valuable service by keeping the king away from trouble and killing the orc who seemed to control the horde of dead orcs. He paid 21 gold crowns altogether, to be split amongst the circus performers as Sophie saw fit. He also warned them off of trying to get paid twice by going to the Archmage. The less they talked to him, the better, he said, but he didn't elaborate on his reasons.

But when he heard that she intended to lead the circus back into the Bekel, on some quest by Quexechetl to find some ancient dwarven stronghold, he tried to convince her not to go. When she would not be dissuaded, he urged great caution, but also made another offer: if they could find out how the orcs managed to raise that horde from the dead, he would pay them another 21 crowns -- but only for tangible evidence. Sophie said she could make no promises, but would keep her eyes open.

June 14 to June 17, 850

The majority of the king's army marched south the next day, while King Miklo and his advisors took a boat downstream.

The circus performers hit the local shops to load up on supplies. They decided not to take horses, because they might not be capable of handling all the terrain. Instead, they decided to rely upon the magic cabinet for most of their storage. Talman and Quexechetl together fixed up a leather harness that would let Quexechetl carry the cabinet on his back after it was collapsed down to its smallest state.

They also found an old dwarf who could read the papers they had found in the cabinet. These turned out to be letters written to a dwarven wizard named Zabar, concerning everyday matters such as orders for supplies, inquiries about an apprenticeship, and payment for services. This told them nothing about the cabinet, but at least they could put a name to the owner.

With the shopping done, asked around for a local dwarf who might know some of the geography of the Bekel. They found a young farmer's son named Matto who said he knew the Bekel as well as any dwarf might claim to -- that is, only from stories. But he could at least translate a little. That was good enough for Sophie, and they planned to leave the next morning.