Earlier this week Wizards implemented a massive change to their sanctioned play rating system. They'd established the old system, I believe, 15 years ago. They've been tinkering with it recently but I guess it became clear to them that it simply wasn't accomplishing what they now wanted it to accomplish.
The old system was a standard ELO system like they use in chess. Each player has a rating and when two players face each other you can work out the odds of each player winning. Then after the match you see what actually happened and adjust each player's rating accordingly. The winner would always trend upwards but if he as expected to win the gain would be smaller than if he pulled off an 'upset'. The loser would always loss the opposite amount which kept the system zero-sum.
The system works really well for chess which is entirely skill based and where working out the odds of success seems like something that could actually be done reasonably. With Magic it doesn't really work that way. Over the long run the randomness would even out but the problem was your rating could swing wildly one way or the other with a particularly lucky or unlucky event. There was just too much volatility involved to make ratings a true indicator of skill the way it can be in chess.
Another issue with the old system is the way event invitations and byes were handled. I kept getting invited to Nationals based on rating year after year because my rating ended up being pretty high when I pretty much stopped playing Magic 6 years ago. Maybe my rating is where it should be and I deserved to be considered one of the top players in Canada still. More likely my true rating should have been substantially lower but it never got a chance to fall since I didn't play anymore. I'd like to think if I still played a lot and put in a lot of practice that I could be a top player but realistically World of Warcraft took that away.
Even if I had been playing a lot of Magic (on Magic Online, say, or just testing constructed with a team) I wouldn't have wanted to play in events. I was close to the Nationals invite mark as it was (tied for last place invitation in 2011, 2009, and 2007 I think?) and couldn't afford to lose even a single rating point. Playing random sanctioned matches simply couldn't help and could really hurt a lot. It was a high risk, low reward scenario. Maybe playing in a PTQ would be worth the risk, but maybe not. Certainly something like FNM or a random GP trial would be right out.
The new system is designed to deal with both of those problems. It no longer even claims to measure player skill, instead tracking participation as a primary factor. You can no longer lose anything by playing a match against anyone at all. How did they do this?
Each event type gets assigned a multiplier (x1 for a prerelease, x3 for FNM, x8 for Nationals, x12 for the Pro Tour, etc...) and then you earn 3 times the multiplier for each win and 1 times the multiplier for each draw. You also get some extra points just for showing up based on the number of entrants. You can't lose points in any way, shape, or form other than when a season resets (at which point everyone loses everything).
It doesn't matter how much better I may be than Joe Schmoe. As long as he actually shows up and plays in tournaments he's going to have more points than I do if I just sit at home and play WoW. If I want to get points I need to actually go out and play too. (And then presumably I'll earn more than he does since I'll get more winning points to go with the participating points.) Not playing to sit on your rating is a thing of the past for sure!
How does qualifying for events go now? What do I need to do to make sure I can keep getting invited to Nationals? It turns out they're making a few different buckets for these points.
You have a lifetime total which gets accumulated over your entire career. It's retroactive and will include all forms of sanctioned play. It will even include casual pick-up games if you bother to get them reported in. Want some points? Have some! They're free! They also don't seem to do anything at all except make a number bigger. (I'm level 38 out of a maximum of 50!)
You have a competitive total which gets reset every 4 months. Everything you play in except casual matches and Worlds contributes to this number. After the 4 months are up they lock in the totals, use those to hand out invitations and byes to any Pro Tours, Grand Prix, or Nationals in the next 4 months, and then wipe the slate clean. For the PT they give the top 5 uninvited finishers in each region an invite and flight, and then they give the top 65 uninvited finishers in the world an invite and flight. You can also get an invite by winning a PTQ, having a high Pro Club level, or by being in the Hall of Fame. Grand Prix byes are simpler. Top 300 in the world get 3 byes. Top 2000 get 2 byes. Top 15000 get 1 bye. Nationals invitation rules are actually not yet determined, but will care about the season which takes place from Dec 26th, 2011 to Apr 1st, 2012. (Which is actually not 4 months... I guess the seasons run 4 months, 3 months, 5 months?)
You have a Friday Night Magic total which seems to reset once a year. Only points earned at FNM go in this bucket. Wizards is going to hold an FNM championship for 100 people based on this point total (top 48 from North America) which I believe comes with a flight to wherever they end up holding it which seems pretty neat.
You have a professional total which only counts points earned at PT, GP, and Worlds. It resets once a year and is used solely to invite players to Worlds. Exactly how that works has yet to be determined just like the Nationals info.
How does this impact me and qualifying for Nationals? Well, it seems like if I want to play in Nationals again I need to start playing Magic 8 months before the event instead of 2 weeks before the event. This certainly will cause me to be better prepared for the constructed portion! I also like how you get a free flight if you qualify for the Pro Tour on planeswalker points. It certainly makes me want to at least look into when different events are held in the Toronto area. It's entirely possible I could find some sort of tournament after work each day which seems like it would give quite an advantage to someone living in a big city. Though I suppose a smaller town could just have one store run an event every day if there was demand for it. The multiplier on a random sanctioned tournament is low (x1) but it could really add up.
I really like the look of the cards being spoiled for the new set. Maybe I'll play some Magic this season and see what kind of numbers get put up...
Thursday, September 08, 2011
Wednesday, September 07, 2011
Galaxy Legion: Damage Formula?
People on the message boards keep coming up with guesses as to what the damage formula is in Galaxy Legion. I care what the formula is because I want to be able to establish precisely what will happen when I add on specific amounts of extra attack. When, if ever, will it be better for leveling to spend my rank points on tactical officers instead of engineers, for example. Or exactly what impact switching to the Konqul or Drannik races will have.
The developer gave a hint early on that the formula wasn't just simple subtraction or anything and used a combination of a tanh function, a random factor, and the size of the ship being attacked. People have narrowed the likely formula down to the following:
dam = tanh(A*R/(5*D))*C
A = attacker's attack stat
R = some random factor
D = defender's defense stat
C = damage cap (2.5*rank for NPCs, MAX(decks/2, rank+19) for PCs)
It's not clear what the random factor is, or even where it should be in the formula. I've tracked 1180 shots against NPCs and it looks like R varies between .6 and 1.66 or so, with a single weird outlier at 2.1. Scan doesn't seem to impact the damage done to NPCs at all. It averages right around 1.01 and occurs more often around that point. Is is a sine wave? A normal distribution? I don't know!
What I care about most is how changing A changes the damage done. The random factor can be considered as a constant here since as far as I know it is fixed on any individual shot.
d/dA(dam) = d/dA(tanh(A*R/(5*D))*C) = C*R/(5*D)*sech^2(A*R/(5*D))
sech is a function that varies from 0 to 1. All of A, R, and D are positive so sech^2(A*R/5*D) is going to be strictly decreasing and is going to come awfully close to 0 when AR/5D gets into the 4-5 range.
As an example lets take a look at a typical NPC boss that seems to be cropping up a lot recently: lazuli fabrication plant. This guy has 2500 defense, a damage cap of 775, and 45000 health. 3 people can get rewards for him so I tend to do around 15000 damage to him. My buffed attack is 3678. Plugging this stuff into the formula above gets us:
d/dA(dam) = 775*R/(5*2500)*sech^2(3678*R/(5*2500))
Which for typical and extreme values of R gives us:
d/dA(dam){R=.6} = .036
d/dA(dam){R=1.01} = .057
d/dA(dam){R=1.66} = .082
dam{R=.6} = 135
dam{R=1.01} = 224
dam{R=1.66} = 351
To do my 15000 damage I need 67 'average' shots. Each shot costs 5 energy and I could, when I spend rank points, get 5 attack instead of that 5 energy. Adding 5 to my attack would increase my damage on every average shot by .285. So in order to break even on energy against this guy I would need to be taking average shots at him 786 times per level.
There are a few problems with that. For one, this boss is near optimal for adding attack, I think. He has a reasonably high defense and he has enough health that I'm less likely to get hurt by rounding issues. To explain what I mean about that, take a look at the flimsiest NPC that I can spawn, the sha'din charger. When I last attacked him (he levels as I do so things change a little) his stats were 1120 defense, 1400 health, damage cap of 815. My attack at the time was 4438. So for him...
d/dA(dam) = 815*R/(5*1120)*sech^2(4438*R/(5*1120))
Which for typical and extreme values of R gives us:
d/dA(dam){R=.6} = .070
d/dA(dam){R=1.01} = .082
d/dA(dam){R=1.66} = .061
dam{R=.6} = 361
dam{R=1.01} = 541
dam{R=1.66} = 706
I find it interesting that if I roll high on the random number roll here the impact of more attack is actually decreased. A high roll edges me closer and closer to the 4-5 range of X where sech^2x trends to 0, so even though I'm multiplying by a bigger external factor out front with the higher R it gets overshadowed by the much smaller sech^2 factor. Do note that I was Konqul at the time with a 20% bonus to my attack, and probably had used a limited attack buff as well.
I almost always killed these guys in 3 shots. On one occasion I did manage to kill one in 2 shots. But in general it feels like adding on an extra couple damage isn't going to be able to bring me down from 3 shots to 2 shots and therefore any actual 'gain' is completely wasted as overkill. I'd need to know the distribution of R to work out how many shots I could expect to save but I'm pretty confident it wouldn't ever overpower the impact of just having more energy to shoot with.
Of course I'm actually somewhere between these two extremes. I kill some chargers. I kill some boss refineries. If I was fighting exclusively bosses then going with more attack makes sense for now. But since I'm fighting a lot of lesser guys and spending an awful lot of energy on missions instead of fighting it makes sense to keep pounding away at engineers.
The developer gave a hint early on that the formula wasn't just simple subtraction or anything and used a combination of a tanh function, a random factor, and the size of the ship being attacked. People have narrowed the likely formula down to the following:
dam = tanh(A*R/(5*D))*C
A = attacker's attack stat
R = some random factor
D = defender's defense stat
C = damage cap (2.5*rank for NPCs, MAX(decks/2, rank+19) for PCs)
It's not clear what the random factor is, or even where it should be in the formula. I've tracked 1180 shots against NPCs and it looks like R varies between .6 and 1.66 or so, with a single weird outlier at 2.1. Scan doesn't seem to impact the damage done to NPCs at all. It averages right around 1.01 and occurs more often around that point. Is is a sine wave? A normal distribution? I don't know!
What I care about most is how changing A changes the damage done. The random factor can be considered as a constant here since as far as I know it is fixed on any individual shot.
d/dA(dam) = d/dA(tanh(A*R/(5*D))*C) = C*R/(5*D)*sech^2(A*R/(5*D))
sech is a function that varies from 0 to 1. All of A, R, and D are positive so sech^2(A*R/5*D) is going to be strictly decreasing and is going to come awfully close to 0 when AR/5D gets into the 4-5 range.
As an example lets take a look at a typical NPC boss that seems to be cropping up a lot recently: lazuli fabrication plant. This guy has 2500 defense, a damage cap of 775, and 45000 health. 3 people can get rewards for him so I tend to do around 15000 damage to him. My buffed attack is 3678. Plugging this stuff into the formula above gets us:
d/dA(dam) = 775*R/(5*2500)*sech^2(3678*R/(5*2500))
Which for typical and extreme values of R gives us:
d/dA(dam){R=.6} = .036
d/dA(dam){R=1.01} = .057
d/dA(dam){R=1.66} = .082
dam{R=.6} = 135
dam{R=1.01} = 224
dam{R=1.66} = 351
To do my 15000 damage I need 67 'average' shots. Each shot costs 5 energy and I could, when I spend rank points, get 5 attack instead of that 5 energy. Adding 5 to my attack would increase my damage on every average shot by .285. So in order to break even on energy against this guy I would need to be taking average shots at him 786 times per level.
There are a few problems with that. For one, this boss is near optimal for adding attack, I think. He has a reasonably high defense and he has enough health that I'm less likely to get hurt by rounding issues. To explain what I mean about that, take a look at the flimsiest NPC that I can spawn, the sha'din charger. When I last attacked him (he levels as I do so things change a little) his stats were 1120 defense, 1400 health, damage cap of 815. My attack at the time was 4438. So for him...
d/dA(dam) = 815*R/(5*1120)*sech^2(4438*R/(5*1120))
Which for typical and extreme values of R gives us:
d/dA(dam){R=.6} = .070
d/dA(dam){R=1.01} = .082
d/dA(dam){R=1.66} = .061
dam{R=.6} = 361
dam{R=1.01} = 541
dam{R=1.66} = 706
I find it interesting that if I roll high on the random number roll here the impact of more attack is actually decreased. A high roll edges me closer and closer to the 4-5 range of X where sech^2x trends to 0, so even though I'm multiplying by a bigger external factor out front with the higher R it gets overshadowed by the much smaller sech^2 factor. Do note that I was Konqul at the time with a 20% bonus to my attack, and probably had used a limited attack buff as well.
I almost always killed these guys in 3 shots. On one occasion I did manage to kill one in 2 shots. But in general it feels like adding on an extra couple damage isn't going to be able to bring me down from 3 shots to 2 shots and therefore any actual 'gain' is completely wasted as overkill. I'd need to know the distribution of R to work out how many shots I could expect to save but I'm pretty confident it wouldn't ever overpower the impact of just having more energy to shoot with.
Of course I'm actually somewhere between these two extremes. I kill some chargers. I kill some boss refineries. If I was fighting exclusively bosses then going with more attack makes sense for now. But since I'm fighting a lot of lesser guys and spending an awful lot of energy on missions instead of fighting it makes sense to keep pounding away at engineers.
Tuesday, September 06, 2011
Third Boss: Time To Scum
I spent a good chunk of yesterday turning what I learned about the monster leveling system into an Excel spreadsheet that would help me know what to eat. I built all the transitions and monster stats into the sheet and set it up so I could input my current four monster races and the meat I could possibly eat. It then spits out what race the monsters would turn into, what tier of monsters those would be, and the change in stats. I figured this would be good enough and started wandering around fighting things and trying to do the early plot.
I made it to the first boss, a p-frog, and managed to beat him with only two deaths. Fortunately for me one of the surviving members of my party was able to eat his meat and turn into a tier 2 monster. (An oni, I believe.) The oni is substantially stronger and tougher than the rest of my party. (My red bull hits about as hard but only has 10 uses of his only attack before I have to rest in an inn which is a bit of a problem when you're killing everything you run into to see if it'll drop meat.)
I made it to the second boss, a human something, and managed to beat him with two more deaths. (If a character dies 3 times they're permanently dead which is an interesting mechanic. Interesting in that I should probably immediately re-roll those characters. Only I can't because one was my main character and it's simply game over if he dies twice... I can farm up a lot of gold to buy extra hearts, I guess, though restarting from scratch is probably faster.) He was tough, but having an oni meant I could pull it off.
I did the third castle and it didn't really have a boss. I returned to the town to cash in my quest items from each castle for what I was hoping would be a big reward. My reward turned out to be a boss fight, and I hadn't thought to rest in the inn or even save before starting the fight... I did save in the fight so I could try it a few times. The results of my tries were that he one-shots most of my team (everyone but the oni who dies in 2 or 3 hits) and my whole team combined did about 10% of his health in a round. Yeah, there's no way that math ever adds up to a kill.
I was hoping to get a chance to wander around and fool around a bit before the game decided to get hard but clearly that isn't the case. I did learn some things from yesterday's adventures though. Monsters can make no use of loot and little use of money. I can buy and use healing potions which is nice if I'm not constantly transforming. If I fought a bunch my tier 1 dudes would end up running out of attacks, especially my red bull. This makes me think I should start checking if I want to eat the meat before fighting any fights and run away if I wouldn't. This goes against my typical RPG plan of killing everything in sight but when fighting only hurts me and can't have any benefit... Probably not right to fight.
I also need to build up my guys to the highest tier I can ASAP. My spreadsheet as currently configured is only looking ahead one step each time... What am I, what will I turn into after this fight. Instead I think I need to plot out chains of progressions based off of the enemies I can currently run into in random encounters. On one try I did manage to make a slime which is tier 2 but I got wiped out shortly thereafter by an unexpected boss fight. So clearly there is a way to get to tier 2 with the random encounters that exist, I just need to figure out what that is and then farm for it.
I'm thinking a spreadsheet may be the wrong way to go. Possibly I should just write a java program to do it...
I made it to the first boss, a p-frog, and managed to beat him with only two deaths. Fortunately for me one of the surviving members of my party was able to eat his meat and turn into a tier 2 monster. (An oni, I believe.) The oni is substantially stronger and tougher than the rest of my party. (My red bull hits about as hard but only has 10 uses of his only attack before I have to rest in an inn which is a bit of a problem when you're killing everything you run into to see if it'll drop meat.)
I made it to the second boss, a human something, and managed to beat him with two more deaths. (If a character dies 3 times they're permanently dead which is an interesting mechanic. Interesting in that I should probably immediately re-roll those characters. Only I can't because one was my main character and it's simply game over if he dies twice... I can farm up a lot of gold to buy extra hearts, I guess, though restarting from scratch is probably faster.) He was tough, but having an oni meant I could pull it off.
I did the third castle and it didn't really have a boss. I returned to the town to cash in my quest items from each castle for what I was hoping would be a big reward. My reward turned out to be a boss fight, and I hadn't thought to rest in the inn or even save before starting the fight... I did save in the fight so I could try it a few times. The results of my tries were that he one-shots most of my team (everyone but the oni who dies in 2 or 3 hits) and my whole team combined did about 10% of his health in a round. Yeah, there's no way that math ever adds up to a kill.
I was hoping to get a chance to wander around and fool around a bit before the game decided to get hard but clearly that isn't the case. I did learn some things from yesterday's adventures though. Monsters can make no use of loot and little use of money. I can buy and use healing potions which is nice if I'm not constantly transforming. If I fought a bunch my tier 1 dudes would end up running out of attacks, especially my red bull. This makes me think I should start checking if I want to eat the meat before fighting any fights and run away if I wouldn't. This goes against my typical RPG plan of killing everything in sight but when fighting only hurts me and can't have any benefit... Probably not right to fight.
I also need to build up my guys to the highest tier I can ASAP. My spreadsheet as currently configured is only looking ahead one step each time... What am I, what will I turn into after this fight. Instead I think I need to plot out chains of progressions based off of the enemies I can currently run into in random encounters. On one try I did manage to make a slime which is tier 2 but I got wiped out shortly thereafter by an unexpected boss fight. So clearly there is a way to get to tier 2 with the random encounters that exist, I just need to figure out what that is and then farm for it.
I'm thinking a spreadsheet may be the wrong way to go. Possibly I should just write a java program to do it...
Monday, September 05, 2011
Trying Out Blogger Pages
I've decided it's high time I figure out how Blogger pages work, and how to start using CSS on them. As a first start I built a little summary page for my Final Fantasy marathon with a table showing the names of all the games, their initial release dates, when I started playing them, when I finished playing them, and my relative ranking after I finish a game compared to the other finished ones in the marathon. The table is ugly right now but that's what relearning CSS is going to fix! Maybe! It's also got links to all of the posts about each game to make it easy to go back and find something in the future.
Sunday, September 04, 2011
The Final Fantasy Legend: Level Systems!
After reading Sthenno's comment to my previous post about this game I decided to actually do a little research into the level system of the game. Part of me feels like I've lost my gamer nerve to be doing so instead of just plowing in and mapping it all out as I go, but so be it... One interesting thing I discovered is this game was apparently the first game Square put out which sold over a million copies which is pretty cool.
As far as the leveling system goes it turns out there are actually three pretty distinct leveling systems! One for humans, one for mutants, and one for monsters.
Humans level up pretty much solely by spending money on potions for permanent stat boosts. They can also put on up to 8 pieces of gear. Actually doing combats does nothing for them, except maybe earn some cash to use on stat boosts in town. Humans are apparently the easiest to twink out and therefore make for the easiest playthrough.
Mutants level up randomly at the end of every fight. They can gain or lose stats or abilities. The guide I found even went so far as to suggest saving after every single fight since if you randomly lost a critical ability you were in a lot of trouble. This sort of works like FFII in that you're more likely to gain stats by taking actions which use that stat. Mutants can also wear 4 pieces of gear. Mutants are random but tend to trend upwards and have a reasonable time beating the game.
Monsters have one stat that matters: their current race. That determines their stats and their abilities. They can't use gear. They can't power up in any way. One goblin is the same as every other goblin. The way you level up is by killing enemy monsters and eating them. There's a huge transformation table based on a few simple rules and I think I may just make a spreadsheet to track the possible changes. Monsters have a finite cap on power and are therefore the hardest race.
Part of me wants to fire some of my dudes and hire one of each type to experience all the leveling systems. But part of me acknowledges that I'm unlikely to play again, and that I want to do the hard thing, and that I already randomly chose the four monster party anyway. So I'm going to stick it out and see if I can't play through the plot with four monsters and find out how hard it really is. I was a little disappointed at how easy FFII actually was once I'd twinked out, so maybe being unable to actually twink out will be a good thing!
As far as the leveling system goes it turns out there are actually three pretty distinct leveling systems! One for humans, one for mutants, and one for monsters.
Humans level up pretty much solely by spending money on potions for permanent stat boosts. They can also put on up to 8 pieces of gear. Actually doing combats does nothing for them, except maybe earn some cash to use on stat boosts in town. Humans are apparently the easiest to twink out and therefore make for the easiest playthrough.
Mutants level up randomly at the end of every fight. They can gain or lose stats or abilities. The guide I found even went so far as to suggest saving after every single fight since if you randomly lost a critical ability you were in a lot of trouble. This sort of works like FFII in that you're more likely to gain stats by taking actions which use that stat. Mutants can also wear 4 pieces of gear. Mutants are random but tend to trend upwards and have a reasonable time beating the game.
Monsters have one stat that matters: their current race. That determines their stats and their abilities. They can't use gear. They can't power up in any way. One goblin is the same as every other goblin. The way you level up is by killing enemy monsters and eating them. There's a huge transformation table based on a few simple rules and I think I may just make a spreadsheet to track the possible changes. Monsters have a finite cap on power and are therefore the hardest race.
Part of me wants to fire some of my dudes and hire one of each type to experience all the leveling systems. But part of me acknowledges that I'm unlikely to play again, and that I want to do the hard thing, and that I already randomly chose the four monster party anyway. So I'm going to stick it out and see if I can't play through the plot with four monsters and find out how hard it really is. I was a little disappointed at how easy FFII actually was once I'd twinked out, so maybe being unable to actually twink out will be a good thing!
Saturday, September 03, 2011
About Iron
I posted a couple days ago about a Through The Ages challenge I was issued by a guy who was upset that he didn't get an iron card. He said the game is bad because you simply can't win without getting an iron. I'd disagreed that it was impossible to win without iron and he said he'd play 5 one-on-one games with me and doubted I could win even one game. He was so confident he even volunteered to spot me 30 points (about 20% of a winning score)!
We played one game and he ended up conceding on turn 12. (Games typically last around 20 turns.) I don't think I was guaranteed to win the game by any stretch (though if you take the 30 point buffer into account I probably couldn't lose) but I was certainly in a strong position. Knowing I wasn't going to get an iron meant I had to play a little differently, and I ended up focusing heavily on getting more actions and stockpiling research for age II. I used the actions to pick up extra cards which generated minerals themselves so I was able to function pretty well without iron. Coal (the upgrade to iron) came up very soon in age II and I'm pretty sure my opponent had a chance to grab it for 3 of his 4 actions but didn't.
He then started up a second game. This one was a little weird in that both of the iron cards were near the bottom of the age I deck. He picked up an iron card on turn 7 and played it on turn 8. I picked up and played coal on turn 9. So really, we were both playing the game without iron, but I'd been planning on not having an iron and was better positioned since I had focused on other ways of making minerals with actions and leaders. I had Leonardo as my age I leader and he gives you a research per turn and a mineral every time you play a tech card.
He stuck out the second game a little longer but eventually conceded it as well. In this game I don't blame him though as I don't think he had a chance of mounting a comeback. I'd built a really ridiculous military lead (Napolean was my age II leader and I got an early air forces in age III to go with my hussars tactics card. My military was 40 to his 15.) He also got a very powerful age III leader himself but I had the assassinate card and immediately killed off Sid Meier. When he scooped I was up 60 points, was making 5 more points per turn, and was making more research and food than he was. The turn before he gave up I also played an attack to steal all 8 of his minerals for the turn!
He ended the game with this parting shot...
"thanks, I won't be playing with you ever again. please do not ever join or contact me for a game. all the best bye"
Ouch! I wasn't taunting him or even saying anything at all in chat in either game. All I did was argue with him in the initial game that you didn't need an iron and then beat him twice at his own challenge. Oh well!
We played one game and he ended up conceding on turn 12. (Games typically last around 20 turns.) I don't think I was guaranteed to win the game by any stretch (though if you take the 30 point buffer into account I probably couldn't lose) but I was certainly in a strong position. Knowing I wasn't going to get an iron meant I had to play a little differently, and I ended up focusing heavily on getting more actions and stockpiling research for age II. I used the actions to pick up extra cards which generated minerals themselves so I was able to function pretty well without iron. Coal (the upgrade to iron) came up very soon in age II and I'm pretty sure my opponent had a chance to grab it for 3 of his 4 actions but didn't.
He then started up a second game. This one was a little weird in that both of the iron cards were near the bottom of the age I deck. He picked up an iron card on turn 7 and played it on turn 8. I picked up and played coal on turn 9. So really, we were both playing the game without iron, but I'd been planning on not having an iron and was better positioned since I had focused on other ways of making minerals with actions and leaders. I had Leonardo as my age I leader and he gives you a research per turn and a mineral every time you play a tech card.
He stuck out the second game a little longer but eventually conceded it as well. In this game I don't blame him though as I don't think he had a chance of mounting a comeback. I'd built a really ridiculous military lead (Napolean was my age II leader and I got an early air forces in age III to go with my hussars tactics card. My military was 40 to his 15.) He also got a very powerful age III leader himself but I had the assassinate card and immediately killed off Sid Meier. When he scooped I was up 60 points, was making 5 more points per turn, and was making more research and food than he was. The turn before he gave up I also played an attack to steal all 8 of his minerals for the turn!
He ended the game with this parting shot...
"thanks, I won't be playing with you ever again. please do not ever join or contact me for a game. all the best bye"
Ouch! I wasn't taunting him or even saying anything at all in chat in either game. All I did was argue with him in the initial game that you didn't need an iron and then beat him twice at his own challenge. Oh well!
So, do you need iron? Clearly the answer is no, but I'm not sure it's as clearcut as these games showed. Both games were a little weird in terms of when coal showed up. We were also playing with an expansion and in both games I made good use of an expansion card. (The first game I played an age A leader which made all action cards better and I generated a fair number of 'free' resources that way. The second game I played an age A leader that got buffed so he was just straight up a civil action every turn. My tactics card at the end which let me get such a huge military lead was also expansion only.) Also, in both games I built the pyramids as my age A wonder and it really feels like it's just the best. (It gives an extra civil action every turn for the whole game.) Especially when you won't get an iron that extra action a turn helps with playing more cards.
Perhaps most importantly I'm just better at the game than this guy is. In the second game he took Genghis Khan as his age I leader. Genghis makes all your mounted units stronger and makes them generate points. (I'd used him in our first game to build up my lead.) But after he took Khan both of the knights cards were on the board. One was going to cost me 1 action and disappear if I didn't take it. The other was going to cost me 3 actions. So I took the one that cost me 3 actions and then Khan was useless for all of age I. It also made most of the tactics cards in the deck useless for him as well since they mostly need mounted units.
Through The Ages feels like it should be random enough that anyone can win any game but the more I play the less I believe that to be true. There is some randomness, sure, but it really feels like one of the more skill intensive games around. I still haven't beaten Robb yet!
Do you need iron to win? Not if you're better than your opponent, that's for sure. I'm less convinced if you're on equal footing...
I recalled they posted statistics about the game at WBC and went to check last year's write-up. Unfortunately it only broke down the winning percentage of leaders, wonders, and governments but not techs. On the other hand I read the recap of the final and the winner, Randy Buehler, was the one person in the finals who didn't get an iron. But that may just be more evidence that you have to be better than your opponents to win without iron? I do hear he's pretty good at games...
Friday, September 02, 2011
Final Fantasy II Conclusions
Well, I finished off Final Fantasy II last night. It turns out there are only 3 dungeons left in the game after getting flare and ultima so those spells really are terrible. There's simply not enough time to level them up unless you cheat or grind for hours and hours. I feel like they needed to either start those spells at a higher level, make them so powerful that even at level 1 or 2 they're good, or really ramp up the leveling formula so low level spells would improve quickly in the end game. Oh well.
The final dungeon was both a let down and rather scary. I never really felt like I could get wiped out, or even like I could lose a party member (other than the new 4th guy). But it really seemed like just a little bit less twinkage and I wouldn't have stood a chance. As it was I had to use all of my elixirs to get to the end. The final boss didn't even land an attack (I think he tried to blind someone) before he fell over dead to the might of my berserk spell.
Some final thoughts:
The final dungeon was both a let down and rather scary. I never really felt like I could get wiped out, or even like I could lose a party member (other than the new 4th guy). But it really seemed like just a little bit less twinkage and I wouldn't have stood a chance. As it was I had to use all of my elixirs to get to the end. The final boss didn't even land an attack (I think he tried to blind someone) before he fell over dead to the might of my berserk spell.
Some final thoughts:
- Leila didn't actually die when we got swallowed by Leviathan. I guess she fell overboard and drifted to the capital or something? My party seemed about as interested in her being alive again as they were when she went missing: not at all.
- You start the game by naming four characters, and then you immediately lose the fourth one. (The four people are main male character, his girlfriend, their dimwitted friend, and the girl's brother.) In the third last dungeon of the game you end up killing the evil emperor and it seems like all is well... Until your fourth guy suddenly reappears and picks up where the emperor left off. The second last dungeon has you invade his castle to kill him... But when you get to the end the evil emperor comes back from hell to conquer the world. Your random jobber commits suicide to stall the undead emperor (pretty sure I could have just killed him there, but whatever...) while the rest run away. Fourth guy decides he has nothing better to do so he tags along to kill the undead emperor. And then after you do? His sister wants to be friends again but the fourth guy is all "everything has changed, screw you guys" and walks off. And you don't try to stop him! He tried to conquer the world, of his own volition, and it's clear he hasn't repented... But you let him leave to scheme a new plot to conquer the world? Kain in FFIV turns evil for a while but at least he had the excuse of being 'mind controlled'.
- In order to get into the emperor's castle you need an airship. You go to visit Pavel who has been taking care of Cid. As soon as you walk up to talk to Cid he falls into bed, gives you his airship, and dies. I guess Pavel is a lazy jerk and was feeding him the slow fish.
- I was trying to hit for 9999 damage but it looks like berserk actually has a cap. I'm guessing attack is limited (maybe at 99 or 256?) since it didn't seem to matter how often I cast berserk on my guy, I was stuck doing around 3300 max. I bet if I cared I could come close to 9999 though, by maxing weapon skill and haste.
- Mental note: get osmose for all of your characters, not just the black mage. I was stuck chugging elixirs to restore my healer's mana.
- All told it took 15 hours and 44 minutes to complete. Before the final dungeon I was thinking I'd wasted a lot of time and would really be able to shave time off next time around. I'm not so sure anymore, since I think the final dungeon might actually be a problem. Though maybe with multiple copies of osmose it won't be...
Thursday, September 01, 2011
Ultimate Spells?
I finally returned to the world of Final Fantasy II and plowed through the Ultima Tower. Supposedly this dungeon is hard but it has awesome spells at the top to make it all worthwhile. I found the dungeon to be reasonable trivial and the awesome spells at the top seem terrible. I needed to get Ultima to progress the plot so it still made sense to go get it, but it doesn't seem worth casting. Flare was also up at the top of the tower and is supposed to be the best black magic spell in the game. Unfortunately it starts at level 1, so by default it is bad. But maybe if I level it up a bunch it will become good? How exactly do spells work?
Damage spells, like flare, hit a variable number of times. You make an attack roll for each level of the spell (using magic accuracy which for flare starts at 0% but which gets an extra 1% for every int you have) and the defender makes a magic defense roll for each level of magic defense they have (just like how melee attacks and dodges work). Subtract the defender's successes from the attacker's successes to determine a number of hits, rounding up to 0 I think. Then add the level of the spell on to this number. So, basically, you hit somewhere between L and 2L times with the spell.
Then you work out the power of the spell. Flare's power is 20. The other black magic spells have a power of 10. To that number you add on a quarter of your int.
Finally, for each hit you obtained in the first step roll a number between P and 2P where P is the spell power from the second step. Add up all these numbers to see the damage done.
Ignoring enemy magic defense for a moment your expected number of hits, based on your intelligence I, is:
(L+IL) {assuming I stays less than 100% anyway}
which means the expected damage for a normal spell is:
(15+75/2*I)*(L+IL) = 15L+105/2IL+75/2IIL
and for flare is:
(30+75/2*I)*(L+IL) = 30L + 135/2IL+75/2IIL
So flare should just do more damage. And against a generic monster it will, but the tricky part is monsters tend to be vulnerable to some element of magic and flare is non-elemental. What happens when you shoot a monster which is vulnerable to fire with the fire spell?
Two things, both of which are awesome. The first is that the spell simply can't miss. Instead of getting a number of hits somewhere between L and 2L (with some 'dodged') you just get a full 2L. The second is that every hit does double damage. So the damage for a vulnerable spell is:
2*(15+75/2*I)*(2L) = 60L+150IL
Comparing flare to a same level vulnerable spell isn't useful since it's guaranteed to be worse. (All flare has going for it is double the base power. The vulnerable spell has that same doubling, but it also doubles the int factor and removes misses. The question I have is how many levels do we need to give flare before it beats out a vulnerable spell? Call the level of flare F.
30F+135/2IF+75/2IIF = 60L+150IL
F=L*(60+150I)/(30+135/2I+75/2II)
My caster has 52 int right now, so lets use that as a starting point and then also look at a couple bigger points for I.
F(I=.52)=1.81*L
F(I=.75)=1.70*L
F(I=.99)=1.56*L
These numbers are even high since flare can miss! Even if I managed to cap my int and get flare to max level (16) all I would need is the elemental spells at 11 and a vulnerable enemy. But here's the thing... There may be something even better...
I have a black mage now and the spell she's got the most levels in isn't an attack spell at all. It's berserk. So far it's seemed really ridiculously good but I'm wondering if that's just because my fighter has a high axe skill and it would even out if I power leveled a damage spell or not. So, how does berserk work compared to a damage spell?
The first difference right off the hop is you don't get the free hits. You need to actually roll your hits on your friend in order to land berserk. Fortunately you don't roll magic resistance checks on buff spells! Berserk also has a base +50% to accuracy instead of the base 0% which means that my mage with 52 int can't actually miss a cast of berserk. The base power for berserk is only 5. What berserk does is it 'attacks' once per level of the spell, and for every hit it adds the base power of the spell to the target's attack stat.
So in order to really work out what it does we'd need to go into all the details about melee attacks, and hits, and crit strikes, and such. I'm just going to wave hands and abstract a bit. My fighter gets 10 swings a round with pretty much perfect accuracy. But the monsters do dodge, probably around 2 a round. Crits are rare so I don't care. There's also enemy armor, but I'm going to assert that my base attack beats the enemy armor and therefore the bonus damage from berserk is all used. (I don't know that this is true against some bosses necessarily, but it's probably close.) So I'm probably getting 8 swings a round and the damage added to each swing is going to be a random number between X and 2X where X is the added attack power.
Assume berserk goes off before the attack this round. How much damage is added?
8*3/2*(L*(5+I*25)) = 60L+300LI
With all spells at level 6 and 52 int, flare will do 451 damage. Vulnerable fire will do 828 damage. Berserk will do 1296 damage.
With all spells at level 16 and 99 int, flare will do 2137 damage. Vulnerable fire will do 3336 damage. Berserk will do 5712 damage.
At any fixed int a level 6 berserk actually does more damage than a level 16 flare!
And all this ignores the most salient point for berserk... It carries over between rounds. Flare is going to do 451 damage once. Berserk is going to do 1296 damage every round! It even stacks, so I can cast berserk again on the same person so they do 2592 extra damage the second round. Of course, the downside is this damage only hits one mob at a time... Darn!
There is also a haste spell, but it doesn't stack up round after round and I don't have a second black mage. Though next time I play the game I may well set up my 3 fixed characters as two guys who cast berserk and one that casts haste and just have jobber mcbag in the 4th slot be an absolute monster!
Damage spells, like flare, hit a variable number of times. You make an attack roll for each level of the spell (using magic accuracy which for flare starts at 0% but which gets an extra 1% for every int you have) and the defender makes a magic defense roll for each level of magic defense they have (just like how melee attacks and dodges work). Subtract the defender's successes from the attacker's successes to determine a number of hits, rounding up to 0 I think. Then add the level of the spell on to this number. So, basically, you hit somewhere between L and 2L times with the spell.
Then you work out the power of the spell. Flare's power is 20. The other black magic spells have a power of 10. To that number you add on a quarter of your int.
Finally, for each hit you obtained in the first step roll a number between P and 2P where P is the spell power from the second step. Add up all these numbers to see the damage done.
Ignoring enemy magic defense for a moment your expected number of hits, based on your intelligence I, is:
(L+IL) {assuming I stays less than 100% anyway}
which means the expected damage for a normal spell is:
(15+75/2*I)*(L+IL) = 15L+105/2IL+75/2IIL
and for flare is:
(30+75/2*I)*(L+IL) = 30L + 135/2IL+75/2IIL
So flare should just do more damage. And against a generic monster it will, but the tricky part is monsters tend to be vulnerable to some element of magic and flare is non-elemental. What happens when you shoot a monster which is vulnerable to fire with the fire spell?
Two things, both of which are awesome. The first is that the spell simply can't miss. Instead of getting a number of hits somewhere between L and 2L (with some 'dodged') you just get a full 2L. The second is that every hit does double damage. So the damage for a vulnerable spell is:
2*(15+75/2*I)*(2L) = 60L+150IL
Comparing flare to a same level vulnerable spell isn't useful since it's guaranteed to be worse. (All flare has going for it is double the base power. The vulnerable spell has that same doubling, but it also doubles the int factor and removes misses. The question I have is how many levels do we need to give flare before it beats out a vulnerable spell? Call the level of flare F.
30F+135/2IF+75/2IIF = 60L+150IL
F=L*(60+150I)/(30+135/2I+75/2II)
My caster has 52 int right now, so lets use that as a starting point and then also look at a couple bigger points for I.
F(I=.52)=1.81*L
F(I=.75)=1.70*L
F(I=.99)=1.56*L
These numbers are even high since flare can miss! Even if I managed to cap my int and get flare to max level (16) all I would need is the elemental spells at 11 and a vulnerable enemy. But here's the thing... There may be something even better...
I have a black mage now and the spell she's got the most levels in isn't an attack spell at all. It's berserk. So far it's seemed really ridiculously good but I'm wondering if that's just because my fighter has a high axe skill and it would even out if I power leveled a damage spell or not. So, how does berserk work compared to a damage spell?
The first difference right off the hop is you don't get the free hits. You need to actually roll your hits on your friend in order to land berserk. Fortunately you don't roll magic resistance checks on buff spells! Berserk also has a base +50% to accuracy instead of the base 0% which means that my mage with 52 int can't actually miss a cast of berserk. The base power for berserk is only 5. What berserk does is it 'attacks' once per level of the spell, and for every hit it adds the base power of the spell to the target's attack stat.
So in order to really work out what it does we'd need to go into all the details about melee attacks, and hits, and crit strikes, and such. I'm just going to wave hands and abstract a bit. My fighter gets 10 swings a round with pretty much perfect accuracy. But the monsters do dodge, probably around 2 a round. Crits are rare so I don't care. There's also enemy armor, but I'm going to assert that my base attack beats the enemy armor and therefore the bonus damage from berserk is all used. (I don't know that this is true against some bosses necessarily, but it's probably close.) So I'm probably getting 8 swings a round and the damage added to each swing is going to be a random number between X and 2X where X is the added attack power.
Assume berserk goes off before the attack this round. How much damage is added?
8*3/2*(L*(5+I*25)) = 60L+300LI
With all spells at level 6 and 52 int, flare will do 451 damage. Vulnerable fire will do 828 damage. Berserk will do 1296 damage.
With all spells at level 16 and 99 int, flare will do 2137 damage. Vulnerable fire will do 3336 damage. Berserk will do 5712 damage.
At any fixed int a level 6 berserk actually does more damage than a level 16 flare!
And all this ignores the most salient point for berserk... It carries over between rounds. Flare is going to do 451 damage once. Berserk is going to do 1296 damage every round! It even stacks, so I can cast berserk again on the same person so they do 2592 extra damage the second round. Of course, the downside is this damage only hits one mob at a time... Darn!
There is also a haste spell, but it doesn't stack up round after round and I don't have a second black mage. Though next time I play the game I may well set up my 3 fixed characters as two guys who cast berserk and one that casts haste and just have jobber mcbag in the 4th slot be an absolute monster!
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