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Subject: The powers of the gods - Odin awfully unmighty? Frey the best of all? rss

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Brian Modreski
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We're up to 15 plays now, and getting a pretty sold hand on the mechanics and flow of Yggdrasil. We've also developed some opinions on the relative power level of the gods, and I'm wondering what other people think of Odin.

Frey seems like the best. One extra action is awesome. Having a spare action to get vikings or an elf or an upgraded weapon means he can be just as good as Thor's +1 bonus.

Tyr comes in second. Getting to roll twice is about as good as Thor's +1, but with the added benefit of getting roll twice for enemy effects.

Thor seems third best. The extra +1 to combat is very handy, letting him hold off enemies and defeat frost giants more readily.

Freya and Frigg are close to Thor. Frigg really ups the handiness of recruiting vikings early. Freya may not seem very exciting, but being able to upgrade weapons twice can let her push back foes quickly, keeping them low and weak on the track. And she can push a foe back twice in one turn, or kill two frost giants - very handy tricks!

Heimdall is pretty meh. One extra draw at best gets you 1 extra viking, worth a +1, so not as good as Thor or Tyr. You can potentially save up vikings over multiple turns atleast.

Odin...well, I think Odins is the first time with a co-op we've had a character we actively dislike getting dealt. Looking at two enemy cards is helpful on rare occasions, but...you've got to deal with them all anyway eventually. He seems very, very weak to us. Every game we've lost has had Odin in it.

Has anyone else found better uses for Odin? Does he need an upgrade to be worthwhile and more fun to play? Opinions?
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Patrik Eden
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I only have solo games under my belt, but I really like Oden.

My basic strategy is to put Nidhögg, Angry cards and Ragnarök cars at the bottom, leaving everything else on top. This radically reduces the risk of a mid-game loss. Sometimes, of course, if another enemy is just about to pass a power-line, it is nice to put that enemy at the bottom as well.

Not to mention the synergy if Tyr comes after Oden in turn sequence. Then you can give Tyr some extra Fenrirs and Jörmungands, which he can handle with his extra roll.
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Joel Eddy
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I think Odin's power diminishes the more players are in the game. If you are playing solo, I think he is the strongest choice. If you have 6 or 7 players, he's borderline pointless.
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Andrew MacLeod
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Generally speaking, Brian, I think you're spot on. With four actions, Frey is definitely the superstar. Odin? Well, his ability reminds of the line from the classic Looney Tunes film, Rabbit Seasoning: "Do you want to shoot me now, or shoot me at home?" Definitely at the bottom of the Norse pantheon, for me.
oldshortsnout wrote:
My basic strategy is to put Nidhögg, Angry cards and Ragnarök cars at the bottom, leaving everything else on top. This radically reduces the risk of a mid-game loss.

I've tried that very thing: and have lost miserably. Certainly, it reduces the risk of a mid game loss, but it leaves this horrible powerhouse of evil awaiting you at game end. By that point, I'm in pretty bad shape from all the other combats during the game. I do agree with Patrik, though, that Odin can best be used if Tyr is playing right after him. Otherwise, it's the choice of shooting me now or shooting me at home. And if you're playing solitaire with only one deity and that god is Odin? I think you've basically lost the game.
I would rank Freyja ahead of Thor. With his +1 strength, Thor is great to have around; but that alone is not enough to defeat either a frost giant or an enemy, so I think he can be overvalued. Freyja, on the other hand, is the perfect goddess to have around in case of a do-or-die situation with her ability of double actions.
I also agree with you, Brian, about Heimdall....in a game with more than one god, that is. But in a one god solitaire game, I find Heimdall to be surprisingly useful.
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Brian Modreski
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For the record, I've never played solo, so I can't even begin to comment on how useful gods are in a solo game. Usually I'm playing 2 player. Haven't yet played more than 4.
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Bryan Graham
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I've found Odin to be very useful in 2 player. We mostly put Fenrir on bottom, so we were able to avoid wasting actions on him until the very end. By then we had a bunch of vikings saved up and since no other gods were moving, losing the actions didn't hurt nearly so much. I do agree though that as the number of players increases, his power becomes less and less useful. We found this to be true with the Wizard's similar ability in Defenders of the Realm.
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Jeff Kayati
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Ten plays in and I'm not finding this to be true at all. Odin is incredibly useful to avoid enemies you can't afford to fight at the time and to know what you'll be facing at the endgame.

I'd rank him above Heimdall and Tyr, but below Frey and Thor. Freya can be very useful, so I'd rate about the same level. Not enough experience with Frigg yet, but I love the ability early in the game to really clear out fire giants.
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Brian Modreski
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Interesting that other people are finding Odin a lot more useful. This is a time when I'd be really curious to see what people are doing. We may need to experiment some more.

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We mostly put Fenrir on bottom...

We tried this at some point to, then got absolutely mauled at the end of the game

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By then we had a bunch of vikings saved up...

I don't think we've ever had a bunch of vikings saved up. Except immediately following getting the green rune.
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Juan Medina
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I think if you have all of the characters attempting to do the same roles, then yes, Odin might be the poorest choice. I have found out we do best if we keep the roles specialized, tailored to the capabilities of the character. In some cases this may mean your character will see very few fights.

Thor: Giant killer - Needs the least support tokens per Giant with its permanent +1 in combat. Giving him +3 weapons is the way to go.

Freya: Best support character. She can do great bag content management as well as moving the green support track twice. Critical for other characters to do their thing. A good Freya makes for a great Heimdall.

Heimdall: Combined with good bag management, he should build a good viking reserve and consistently draw 3-4 vikings per draw. He is the only character that builds up enough token support to share tokens, which will save your game.

Odin: Yes, a dull support role, but a very important one. Odin balances out any issues that may come from the card mix that cause you to lose early. Being able to place the next card at the top or bottom allows for you to know what you are pushing for the end, or to be prepared specifically for your next fight.

Frey: Four actions mean that he can "waste" one for the team on every turn. I would use that one to move forward the support track or do bag management, and the rest to stock on support tokens and fight. The most versatile character.

Tyr: This is your "risk it" character. I think this is the only one that can actually go to battle without a full compliment of tokens to support him.

I find it hard to "rank" them individually, particularly because the player count will affect how they rank.

I would say, if considered in a bubble or if forced to use a single character with no support, these would be my rankings:

Frey: One extra action means he can self support.
Thor: +1 in fight will keep enemies of all kinds in check.
Freya: Being able to do actions twice allows for setting up victories.
Odin: Knowledge is power. Picking your fights smartly will produce more overall victories.
Heimdall: On its own, pretty useless, as he would have to spend substantial amounts of actions to maximize his draws.
Tyr: Tipping your luck can work, but it still depends on luck.
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Bryan Graham
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PrivateMeggido wrote:

Freya: Best support character. She can do great bag content management as well as moving the green support track twice. Critical for other characters to do their thing. A good Freya makes for a great Heimdall.


Hehe, I find it a worthwhile testament to the versatility of the game that you tend to use Freya as a support role. In our games, we always made her a fighter. With double actions to obtain weapons in the early game, and double actions to fight in the late game, we found her pivotal in that role. We have used Heimdall to send her tokens as you suggest though, and Thor as the giant killer is pretty standard.

Good game. Glad there's so many ways to play it

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Brian Modreski
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We've always had everyone fighting, and Freya is certainly one of our main fighters for the same reasons Bryan mentioned.

Tyr doesn't need to rely on the luck; the thing to do is get him more elves! Elves allow you to get a benefit out of a good roll without taking an actual risk.

As a side note, we jut had our first 2 player win that included Odin this morning
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Andrew MacLeod
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StormKnight wrote:
Interesting that other people are finding Odin a lot more useful. This is a time when I'd be really curious to see what people are doing. We may need to experiment some more.

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We mostly put Fenrir on bottom...

We tried this at some point to, then got absolutely mauled at the end of the game

Quote:
By then we had a bunch of vikings saved up...

I don't think we've ever had a bunch of vikings saved up. Except immediately following getting the green rune.


You, sir, have just described my experience flawlessly!
 
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Andrew MacLeod
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PrivateMeggido wrote:
I think if you have all of the characters attempting to do the same roles, then yes, Odin might be the poorest choice. I have found out we do best if we keep the roles specialized, tailored to the capabilities of the character. In some cases this may mean your character will see very few fights.

Thor: Giant killer - Needs the least support tokens per Giant with its permanent +1 in combat. Giving him +3 weapons is the way to go.

Freya: Best support character. She can do great bag content management as well as moving the green support track twice. Critical for other characters to do their thing. A good Freya makes for a great Heimdall.

Heimdall: Combined with good bag management, he should build a good viking reserve and consistently draw 3-4 vikings per draw. He is the only character that builds up enough token support to share tokens, which will save your game.

Odin: Yes, a dull support role, but a very important one. Odin balances out any issues that may come from the card mix that cause you to lose early. Being able to place the next card at the top or bottom allows for you to know what you are pushing for the end, or to be prepared specifically for your next fight.

Frey: Four actions mean that he can "waste" one for the team on every turn. I would use that one to move forward the support track or do bag management, and the rest to stock on support tokens and fight. The most versatile character.

Tyr: This is your "risk it" character. I think this is the only one that can actually go to battle without a full compliment of tokens to support him.

I find it hard to "rank" them individually, particularly because the player count will affect how they rank.

I would say, if considered in a bubble or if forced to use a single character with no support, these would be my rankings:

Frey: One extra action means he can self support.
Thor: +1 in fight will keep enemies of all kinds in check.
Freya: Being able to do actions twice allows for setting up victories.
Odin: Knowledge is power. Picking your fights smartly will produce more overall victories.
Heimdall: On its own, pretty useless, as he would have to spend substantial amounts of actions to maximize his draws.
Tyr: Tipping your luck can work, but it still depends on luck.


Apart from Odin, I'm in general agreement with your assessment of the gods. As for specific rankings? Well....

#1: FREY: In addition to the extra power from his extra action, he's also the one who should be setting things up (particularly in Midgard) for the other players.

#2: TYR: Although there are never any guarantees with Tyr, his double die roll has the potential to shape Yggdrasil to the benefit of the gods. I find him especially wonderful in bag management. I've used Tyr to deliberately de-Vikingize an island (with Hel), and then Muspelheim all the fire giants out of there. Then, you're free to fill that island with nothing but Vikings.

#3: FREYJA: Freyja the Game Saver. Her ability to do the same action twice can get the rest of the players out of some game losing situations. The most clear cut example would be if the Nidhogg creates a situation where you have one more enemy in Asgard beyond the required number to lose, and therefore have to drive back two enemies in one turn. Of course, her abilities are limited by what resources she has at any given point.

#4: THOR: Yes, the permanent +1 strength is fabulous; but it's only +1! Not enough to defeat either enemy or frost giant on his own. Thor makes life easier, but he is not a game saver in most situations.

#5: HEIMDALL: Yes, Heimdall: stop laughing. As PrivateMeggido pointed out, Heimdall has the potential to be a game saver, IF the players going before him have set the bags up well. Generally speaking (apart from emergencies), I would not have Heimdall fighting a lot, but making frequent visits to Niflheim to supply other players for their combats.

#6: ODIN: "Shoot me now! Shoot me now!" As I said in my earlier post, Odin only delays the inevitable. And piling the baddies at the bottom of the deck makes one awful nightmare at game end: I have many scars to prove that! Again, as I said initially, I'm only a fan of Odin if Tyr is played right after him.
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Patrik Eden
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PrivateMeggido wrote:

Frey: One extra action means he can self support.
Thor: +1 in fight will keep enemies of all kinds in check.
Freya: Being able to do actions twice allows for setting up victories.
Odin: Knowledge is power. Picking your fights smartly will produce more overall victories.
Heimdall: On its own, pretty useless, as he would have to spend substantial amounts of actions to maximize his draws.
Tyr: Tipping your luck can work, but it still depends on luck.


This is very close to my rank. And I should point out that my solo games were not necessarily solo-god games. I've played 1-6 gods, different mixes. The god's powers are a bit dependent on number of players. In particular, I would swap ranks for Freya and Odin if there are few gods.

Freya's ability is strong with many gods - being able to fight twice in a late turn can be crucial - but pretty useless when she is on her own - when she has to deal with everything herself I tend to select three different actions anyway.

Odin's ability is strongest with fewer gods, because then he can really control the deck.

And yes, I too consider Frey strongest under all circumstances.
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Steve Rogers
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Wow, I can't believe anyone would rank Tyr at the bottom of their list. next time you play solo, kill a frost giant every turn and use all 4 runes. Then see if you don't move him up a few slots in your ranking.

I like Odin solo, but as the previous poster pointed out, he gets worse the more people you play with. I am thinking of houseruling that he gets to look at X cards (where X equals the number of players.

I'd personally put Tyr in my top spot, but clearly Frey is second at worst. I can't imagine someone putting him lower.

And poor Heimdall is a joke. I figure it as (1/3 of a standard action)*(1/9 of standard action choices), making his power literally 1/27 as valuable as Frey's!
 
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Jeremy Lennert
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CapAp wrote:
Wow, I can't believe anyone would rank Tyr at the bottom of their list. next time you play solo, kill a frost giant every turn and use all 4 runes. Then see if you don't move him up a few slots in your ranking.
...
I'd personally put Tyr in my top spot

That's a poor reason to put Tyr on top, since he's not the best fighter. Thor saves 2/9 of an elf per combat compared to Tyr's ideal combat arrangement--more if Tyr doesn't have 2 elves in reserve on every single attack. That adds up pretty fast. Tyr's ability also affects enemy abilities, but if your favorite part is killing the frost giants efficiently, Thor can do it significantly better.

In a solo game on max difficulty, you're probably making over 40 attacks against enemies plus 16 against frost giants, which means Thor will save around 13 actions compared to Tyr. He loses Tyr's benefit against Fenrir (about 1.2 actions), Surt (maybe 1.5), Hel (less than 1), and Jormungand (harder to estimate), but I'm pretty sure Thor still comes out ahead by quite a lot.

Of course, on lower difficulty, you don't need to attack as much, which makes Thor comparatively less useful, while enemies use their abilities roughly the same amount, keeping Tyr's fringe benefits about the same. Maybe Tyr's better on standard difficulty. But if your standard of comparison is solo on standard difficulty, you really shouldn't have trouble winning no matter what god you're playing.

CapAp wrote:
And poor Heimdall is a joke. I figure it as (1/3 of a standard action)*(1/9 of standard action choices), making his power literally 1/27 as valuable as Frey's!

I think the assumption that all 9 actions are used with equal frequency is a rather bigger joke. Do you seriously use the valkyries only 4-5 times in an entire solo game?

Plus, by that reasoning, Freyja's ability is worth zero--you're ignoring the fringe benefits of getting more at once in a game that limits how frequently you can do a given action. (On the other hand, you're neglecting that only the draw, and not the valkyries' movement, is increased by 1/3.)

Heimdall is certainly not as good as Thor, since you will attack more often than you draw vikings if you are playing at all competently. But his ability is worth FAR more than a mere 1/27 of Frey's, and Frey cannot duplicate his power.
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Antistone wrote:
That's a poor reason to put Tyr on top, since he's not the best fighter.

Good thing that's not my reason then!

I think your gross misunderestimation of Tyr ignores that he gets a re-roll *any time he rolls the die*, not just for combat. When you are playing solo, this means you get to re-roll everything. It's nuts.

But even in multiplayer games, it's incredibly powerful. I'd probably rather have Thor in a 3-player or higher game, but for solo and 2p, there's no doubt that Tyr is going to offer me a bigger advantage.

Quote:
Tyr's ability also affects enemy abilities, but if your favorite part is killing the frost giants efficiently, Thor can do it significantly better.

Again, only if you calculate straight combat odds. That ignores quite a large portion of the game; most specifically your ability to gather vikings, which feeds your ability to do battle.

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In a solo game on max difficulty, you're probably making over 40 attacks against enemies plus 16 against frost giants, which means Thor will save around 13 actions compared to Tyr. He loses Tyr's benefit against Fenrir (about 1.2 actions), Surt (maybe 1.5), Hel (less than 1), and Jormungand (harder to estimate), but I'm pretty sure Thor still comes out ahead by quite a lot.

I assume you have some reasoning behind those numbers? Tyr will save you far more than 3 actions over the course of 7+ Fenrir cards, 7+ Surt cards, and 7+ Hel cards. And let's not even get started on Jormungand, who can completely ruin Thor's battle plans if he hits the wrong island. Tyr has *much* lower odds of facing these difficulties.

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I think the assumption that all 9 actions are used with equal frequency is a rather bigger joke.

Indeed it was, glad you got it.

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Heimdall is certainly not as good as Thor, since you will attack more often than you draw vikings if you are playing at all competently. But his ability is worth FAR more than a mere 1/27 of Frey's, and Frey cannot duplicate his power.


Of course the latter comment is true, and I assumed so obvious that everyone reading would get my joke. Sorry for not using emoticons.
The fact remains that Heimdall is far worse than ALL the other gods, and I feel sorry for him.
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CapAp wrote:
I assume you have some reasoning behind those numbers? Tyr will save you far more than 3 actions over the course of 7+ Fenrir cards, 7+ Surt cards, and 7+ Hel cards. And let's not even get started on Jormungand, who can completely ruin Thor's battle plans if he hits the wrong island. Tyr has *much* lower odds of facing these difficulties.

Indeed I do. But it's exactly 7 cards per enemy, not 7+, because the angry card replaces a normal card, and the Ragnaroks do not trigger enemy abilities. (In fact, it can be less than 7, since abilities also do not activate in Odin's Residence.)


If Fenrir is in area 1, most gods have a 5/6 chance of calming him per attempt, which means it takes an average of 6/5 = 1.2 actions to succeed. Tyr has a 35/36 chance, which means it takes an average of 36/35 actions to succeed.

Multiply that by 7 Fenrir rages, and Tyr expects to lose 7 + 7/35 = 7.2 actions, while other gods expect to lose 7 * 1.2 = 8.4 actions, a difference of 1.2 actions over the course of the game. (It's actually very slightly less than that, because those averages include chains where you fail many times in a row, and I've neglected that those chains effectively get cut off if Fenrir rages again before you finish.)

Of course, that goes up if Fenrir gets past the wall of Asgard. In the middle area, it costs most gods 1.5 actions to calm him and costs Tyr 1.125 actions, so Tyr saves an additional ~0.2 actions for each Fenrir activation in that area. But that shouldn't happen very often, because keeping Fenrir back is obviously a high priority.


For Hel, if you're defending the white bag, with Tyr she hits it 1 time in 9, while for other gods it's 1 time in 3. That's a probability difference of 2/9, times 7 activations is 1.56. Even if those hits occur at Hel's max power, that's only 3 * 1.56 = 4.67 vikings removed from the white bag; you can add 5 back with a single action.

Similarly, if your primary concern is defending the white bag, Tyr blocks Surt 1.56 times over the course of a game. Surt putting fire giants in the white bag will often cost you about 1 action to clean (regardless of the number he adds). But in the early game, it will often cost you less than that, because you would have had to remove fire giants anyway, and it won't always increase the number of actions required to do so; again, in the very late game, the bag may not be worth cleaning, so he will cost you less than 1 action per hit there too. Tyr's reroll saving you about 1.5 actions over the course of the game due to redirecting Surt seems like a fairly reasonable estimate.

Of course, those both assume that you only care about the white bag. In the early game, that's probably not true; it's also not true when Jormungand sinks the white island, which is possible even as Tyr. Tyr's reroll doesn't change the number of tokens added or removed, only where; so a deflection away from the white bag isn't truly as useful as completely negating their powers, as the above analysis assumes. So those estimates are generous to Tyr.


Jormungand, as I said, is harder to estimate, because the ramifications of dealing with him are much more complex. In a very bad case, you might need to clean out both the white and blue bags, which might cost you about 4-5 extra actions of cleaning plus some wasted Valkyrie moves across the sunken white island, but in many games you can probably do better than that, especially if you save up vikings and/or complete the Sigel rune.

And remember the odds of being shut out of the white island are much less than 100% without Tyr, and still noticeably more than 0% with Tyr. And sinking the white island early in the game isn't a problem, since you'll want to make one trip to the black anyway. It's also quite likely Jormungand will use his power less than 7 times during a high-difficulty game, since it doesn't work in Odin's Residence, and his non-scaling power makes it relatively safe to let him get there. Tyr will probably redirect Jormungand away from the white island only once during an entire solo game, if that.

Based on the other numbers I've calculated, just rerolling Jormungand's ability would need to save you an average of about 9 actions over the course of the game in order for Tyr to keep up with Thor on max difficulty. That strikes me as far too high to be a realistic average; it's probably closer to a best-case.


Admittedly, I'm just counting average actions lost, which is not the whole story; winning really hard in 10% of games does not make up for a hair's-breadth loss in the other 90%, even if your "average performance" is in some sense equal to someone who wins 100% of games but only by the skin of his teeth. But it's not clear to me how to reliably calculate actual win rates or which god would look better if we did, so this is the best I can do.


Incidentally, I have actually played as both Tyr and Thor on max difficulty, and posted detailed session reports: Tyr, Thor. My luck was definitely better with Thor, but he appears to be better off even after compensating my analysis for the luck as best I can.
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Steve Rogers
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Heh, I hate to get so mathy into this game, but I find I am enjoying it.

I agree with you about Jormundgand, far too complex to be worth figuring out here, but I doubt that advantage reaches 9 actions either. However, combined with the overlooked actions from Fenrir chains (see below), I'd have no problem believing that in an 'average' game, Tyr reaches that 9-action threshold, and probably surpasses it most times.

Re: Fenrir
You're not figuring for the fact that a "lost action" to Fenrir leads to an immediate re-roll of the die (the 'chains' you mention), for which Tyr's action surplus is added again (the chain only 'ends' on a success, but compounds on a failure).

Each time the Fenrir die roll comes up bad, Tyr's actual advantage goes up by another 0.17, and is compounded again. There is no ceiling to how many times this can occur in an actual chain, though its expected distribution would only be 1/6 of rolls. However, you appear to be simply multiplying this expected return by the number of expected failures (1/6), and that's not an accurate reflection of the real odds. A perfect bell curve distribution over 7 Fenrirs (with a Tyr action surplus of 1.2) is no more likely than seven black results (with a Tyr action surplus of over 8). And in that case, Tyr's advantage would compound 7 times, with 7 additional compound opportunities.

Since the number of potential 'failures' has no limit (other than the number of lost actions required to lose the game), neither does Tyr's potential action advantage - only an expected degradation that is 5 times more likely to occur than to not.

I will grant that Tyr's strength is mitigation as opposed to Thor's brute advantage. In a very 'unlucky' game Tyr is mathematically superior to Thor based on Fenrir alone; but in a 'lucky' game his advantage disappears completely. I'm content to say that they both play mathematical second fiddle to Frey; but remain in a 'tier' of gods good enough that player preference can reasonably be used as the deciding factor on which to play.
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Brian Modreski
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I'd say another thing that's almost impossible to account for in a mathematical manner is that losing an action due to Fenrir or having an island blocked at the wrong time can be drastically worse than the straight action count would indicate.
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CapAp wrote:
Re: Fenrir
You're not figuring for the fact that a "lost action" to Fenrir leads to an immediate re-roll of the die (the 'chains' you mention), for which Tyr's action surplus is added again (the chain only 'ends' on a success, but compounds on a failure).

Yes I am. In area 1, it takes most gods an average of 1.2 actions to calm Tyr. That's not one plus the chance of failure on a single roll (that would be 1.167), it's the result of an infinite sum that includes (among other possibilities) the 0.00000827% chance that they will succeed exactly on the tenth die roll--that possibility just doesn't affect the average very much, because the probability goes down faster than the cost goes up.

CapAp wrote:
A perfect bell curve distribution over 7 Fenrirs (with a Tyr action surplus of 1.2) is no more likely than seven black results (with a Tyr action surplus of over 8).

I don't think you're following the math. 1.2 is an average. But the probability that you will lose exactly 1.2 actions in any particular game is, of course, zero, because you can't actually lose a fraction of an action.

But getting a number close to this average (say, 1) is in fact far, FAR more likely than getting an extreme outlier value like 8, both because any single die roll is much more likely to come up "not black" than to come up "black", and because there are many more permutations that give a mixed result over many rolls than there are permutations that give the same result over and over.

The average is 1.2. And since the minimum value (0) is only slightly smaller than that, but the maximum is very much higher, the odds of getting "some value less than average" are actually enormously higher than the odds of getting "some value higher than average". For example, you'd need 5 + 2/3 games getting zero (that is, no advantage to Tyr at all) to "balanace out" a single game with an advantage of 8 in order to keep the average at 1.2.

The "median" result (the point where getting strictly higher or strictly lower are both less than 50%) is definitely no higher than 1, and may in fact be 0. The probability of Tyr saving 0 or 1 actions on Fenrir is higher than the combined probability of saving any other numbers. If you played a million games as Tyr, over half of those games would result in you saving either 0 or 1 actions on Fenrir, and all other possibilities combined would need to fit into the other (less than) half.


Incidentally, a Bell Curve is, itself, a probability distribution; it describes how likely various outcomes are, but the likelihood of a bell curve itself is not something it normally makes sense to talk about. What a bell curve means is that possibilities near the center are much more likely than possibilities near the edges. However, the distribution we're talking about here is not symmetrical, and therefore will not make a symmetrical bell shape; it instead has a very sharp peak in the 0-1 area, and then exponential decay as you go to higher and higher numbers.

CapAp wrote:
Since the number of potential 'failures' has no limit (other than the number of lost actions required to lose the game), neither does Tyr's potential action advantage - only an expected degradation that is 5 times more likely to occur than to not.

Yes, it is possible that Fenrir will rage on the first turn and you'll roll nothing but blacks until you lose the game. If you're playing on a difficulty setting so low that you're absolutely 100% guaranteed to win as long as something stupid like that doesn't happen, then minimizing the odds of that might be an important consideration. But if you're playing on a difficulty setting that is not entirely a cakewalk for you, that possibility won't measurably affect your overall win rate.



StormKnight wrote:
I'd say another thing that's almost impossible to account for in a mathematical manner is that losing an action due to Fenrir or having an island blocked at the wrong time can be drastically worse than the straight action count would indicate.

True, not all actions are necessarily equal. But if Thor got to take an extra action several turns ago due to his general efficiency, odds are good that he can afford to lose an extra action now and still do whatever Tyr would do (e.g. Tyr will have just enough actions left to push an enemy back and avoid immediate loss, but Thor pushed an extra enemy back 5 turns ago and therefore isn't at risk of immediate loss in the first place).

In fact, getting extra actions earlier in the game is, in general, more helpful, because enemies that are earlier on the track are easier to defeat and don't cause as much damage with their powers.

Or another way of looking at it--Tyr could get a bad roll and lose an extra elf (compared to Thor) "at the wrong time" (in fact, I've neglected that Tyr effectively loses another action to Thor every game because he wants to save up 2 elves before attacking instead of 1). I suspect these sorts of considerations mostly cancel out.
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Steve Rogers
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OK, point taken on the Fenrir math, I was doing that wrong.

So, you've proven that if a player NEVER lets Fenrir get past the first section, rolls an expected distrubution on the dice throughout his game, and loses at most 8 actions to Jormundgand... then Thor is worth as much as Tyr.

I'll take Tyr.
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What we've proved is that when we make the best calculations we can about the approximate value of each god's ability, we get a significantly bigger number for Thor (on max difficulty). That doesn't conclusively prove either god better overall, but it strongly suggests Thor is better (on max difficulty).


You seem to think that we've created a list of conditions where Thor is "equal" when they're all true and Tyr is better if any of them are false. That's completely wrong.

We've been talking mostly about average local outcomes, because that's the easiest thing to analyze, but it's most likely that Thor is better than Tyr when they both have average luck, and Thor is still better than Tyr when they both have pretty good luck, and again that Thor is still better than Tyr when they both have pretty bad luck.

You've implied that Tyr is more resistant to bad luck, but actually the opposite is probably true: Thor gets a constant bonus, while Tyr gets a randomized one, so Tyr's performance is probably more variable depending on how lucky you get. Having more variable performance increases your overall win rate if your win rate is less than 50%, but it makes your overall win rate smaller if it was already above 50%. That makes Tyr the desperate gamble, not the safe choice.


You also seem to think that Fenrir getting into area 2 once or twice would somehow be a major determining factor. As I said earlier, Tyr has an additional advantage of about 0.2 actions for each Fenrir activation in the middle area. If that happens five times (the maximum on standard difficulty, and higher than I've ever personally seen), he's up one whole extra action (that is, he saves about 2.2 instead of about 1.2), which cancels out the one I forgot to ding him for needing to take an extra elf at the start of the game. The difference between Fenrir in areas 1 and 2 is actually quite small--much less than the uncertainty in our estimate of how big an effect Jormungand has.

If Fenrir gets into the third area, Tyr's reroll is worth a lot more (he spends 1.6 actions instead of 3). But if you let Fenrir into the third area, you deserve to lose, whether you're playing Tyr or not.
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Heh, count the number of "probably"s in that post.

Your stats don't prove any of those things at all (they actually prove the opposite, as I mentioned). Those are your conjectures.

And I've said all I'm interested in saying. Have fun with Yggdrasil!
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CapAp wrote:

Your stats don't prove any of those things at all (they actually prove the opposite, as I mentioned).


Huh? I'm totally with Antistone on this one. Tyr's ability helps less than Thor's in combat, but (obviously) more against Jörmungand, Hel, Surt and Fenrir. Now, if the average calculations can prove anything at all, it is that Thor is overall stronger. And the averages are relevant, because there is not a dramatic difference in fluctuations. (Whenever you come with a specific argument about a particular situation and a particual roll, not an average, you essentially point out that there are fluctuations. We know.)

CapAp wrote:

And I've said all I'm interested in saying. Have fun with Yggdrasil!


I'm having a lot of fun with Yggdrasil. In fact, your discussion has triggered a lot of solo-god play with Thor and Tyr. My empirical result is that Thor is stronger. My two games with Thor were won, and with reasonable margin (pushing enemies some 5-8 steps more than needed). My four games with Tyr are 2 wins and 2 losses, and the wins have been with small margins (0 and 4 extra pushes, respectively).

Not enough statistics for a conclusion, and even if it was one could just argue that I haven't understood Tyr, but for me, the math on averages and the games I've played settle the issue. Thor is a bit stronger in a solo-god play.



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