- No re-rolls. This is in an attempt to place all the tension at the moment of the roll itself, rather than a negotiation afterward. I'm also not a huge fan of the re-roll option in Fate - it's sort of another hoop to jump through.
- Player driven compels. One thing I like about Cortex+ is the simplicity of player driven compels, where there is a mechanism for players to generate their own currency (fate points, plot points, etc). I'm not against GM-driven compels, but I *really* like a mechanism for players to bring in currency without the GM's guidance. The way I handled that in WotA was just to let players take a Fate point anytime they could narrate how an aspect they had caused problems on a failed roll.
- Start with d6 - d6.
- Spend a Fate point to:
- Step up a die in the first pool, or add a new d6 to the pool. For instance, with two fate points, you could roll d10 - d6 (incrementing d6 to d8, then to d10). Or you could roll 3d6 (taking the highest) - d6.
- Add a d6 to the second pool, taking the lowest of the results. So, with two fate points, you could roll 2d6 (taking the highest) - 2d6 (taking the lowest).
- Rolling d4 - d6 counts as a compel, granting a Fate point. Of course, an aspect is needed for this, and it must make narrative sense.
This system does fulfill the no re-rolls and player driven compels features. However, it also compromises much of the player agency that Fate provides. Anyway, it was interesting to explore the probabilities of such a system.
The first metric to look at is expected value. For expected value, the best way to use Fate points is just to bump the first dice up. Adding extra dice doesn't help expected value as much. In the last entries below, the parentheses indicate rolling a set of dice and taking the highest (if before the subtraction) or the lowest (if after). As can be seen from expected values, a Fate point in this system is worth much less than in regular Fate (it's roughly +1 instead of +2).
That said, expected value is only one way to look at probability. It doesn't take into account the distribution of results. For that, rolling a set of dice and taking the highest naturally makes the lowest results even less likely, while simultaneously making the highest results less likely (or impossible). For instance, the graph at right shows cumulative probability density functions for when three Fate points are available. In that case, the first dice can be bumped up three times from a d6 to a d12, or two extra dice could be added to the first pool (taking the highest) and one to the last pool (taking the lowest). Thus, if you really need to get above a two, more than you care about rolling really high, it's better to go the pool route. Because rolling a -5, -4, or -3 is very unlikely.
So, there are some real trade-offs in this approach, and risk can be involved. Interestingly, if the pools are removed and traditional Fate re-rolls are used with the stepped up dice (d8 - d6, etc), it's worth a re-roll if the expected value or less is rolled. So, if a +2 is rolled on d10 - d6, it merits a re-roll. This is another possibility that could be interesting: allow re-rolls, but the first dice must be stepped up and locked down before any re-rolls take place.
Anyway, after thinking about how this might work in WotA, I think I'm going to stick with the standard Fate model. However, I am considering using d6 - d6 for Fate rolls and allowing certain Stronghold developments to bump up the first dice. There's something very visceral about rolling d12 - d6 and nailing a +11. But I would keep Fate points the same (add +2 or allow a re-roll).
The first metric to look at is expected value. For expected value, the best way to use Fate points is just to bump the first dice up. Adding extra dice doesn't help expected value as much. In the last entries below, the parentheses indicate rolling a set of dice and taking the highest (if before the subtraction) or the lowest (if after). As can be seen from expected values, a Fate point in this system is worth much less than in regular Fate (it's roughly +1 instead of +2).
- d6 - d6 : 0
- d8 - d6: +1
- d10 - d6: +2
- d12 - d6: +3.0
- d12 - (d6, d6): +3.97
- (d6, d12) - (d6, d6): +4.46
That said, expected value is only one way to look at probability. It doesn't take into account the distribution of results. For that, rolling a set of dice and taking the highest naturally makes the lowest results even less likely, while simultaneously making the highest results less likely (or impossible). For instance, the graph at right shows cumulative probability density functions for when three Fate points are available. In that case, the first dice can be bumped up three times from a d6 to a d12, or two extra dice could be added to the first pool (taking the highest) and one to the last pool (taking the lowest). Thus, if you really need to get above a two, more than you care about rolling really high, it's better to go the pool route. Because rolling a -5, -4, or -3 is very unlikely.So, there are some real trade-offs in this approach, and risk can be involved. Interestingly, if the pools are removed and traditional Fate re-rolls are used with the stepped up dice (d8 - d6, etc), it's worth a re-roll if the expected value or less is rolled. So, if a +2 is rolled on d10 - d6, it merits a re-roll. This is another possibility that could be interesting: allow re-rolls, but the first dice must be stepped up and locked down before any re-rolls take place.
Anyway, after thinking about how this might work in WotA, I think I'm going to stick with the standard Fate model. However, I am considering using d6 - d6 for Fate rolls and allowing certain Stronghold developments to bump up the first dice. There's something very visceral about rolling d12 - d6 and nailing a +11. But I would keep Fate points the same (add +2 or allow a re-roll).
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