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.