Hi,

So in the interest of better understanding character purchasing, I thought I'd throw together what happens if you purchased the same pattern every single turn. L5R has the neat context of 7 income per turn with time limits on (most) characters. We'll ignore the first pass fate and fate from other sources for the purposes of this exercise.

First, an apology for the notation. Things get a little hard to read at times. I didn't immediately find an intuitive notation to quickly express what was going on.

My assumptions:

1. You get the perfect dynasty flip every turn for what you are trying to buy
2. A characters "Power" is equal to its cost. So 5 1 cost characters equal 1 5 cost character.
3. As number of characters DO matter, I also charted how many total characters on any turn you have. As the importance of this number is relative to your opponent, I leave out any further number manipulation.
4. No character elimination
5. No special abilities taken into account
6. No further fate manipulation

How to read the pdf. On the first page you see the summary. The first column is how you buy characters each and every turn for 5 turns.

"3 1c1, 1 1c0" means 3 characters that cost 1 with 1 added fate and 1 character that costs 1 with 0 added fate.

"1 3c4" means 1 character that costs 3 with 4 added fate on it.

"1 3c2, 1 1c1" means 1 character that costs 3 with 2 fate on it plus another character that costs 1 with one added fate.

Next, you will see "P1" through "P5". This is the power level on that turn calculated by simply adding the costs of all characters present on that turn. So whatever was just bought plus any from previous turns. Then comes C1 through C5. These are the totals of characters ignoring cost. This is important particularly for values below 4 (because at 4, you theoretically have 1 character per potential conflict. Less than 4 you have potential problems).

The rest of the pdf is where I did my scratch work, ignore it unless you really care to double check my work.

So if you bought 3 2c0, 1 1c0 every turn you'd have 7 power every turn and 4 people. In english, if you bought three characters that cost 2 each every turn with no fate, plus a 1 cost character every turn, you'd always have 4 characters worth 7 costs.

The Summary:

Points of interest:

• if you could create a deck of nothing but 1 cost characters, you'd have 4 points of 4 cost characters turn 1, then 7 points and 7 characters every turn after that.
• 7 characters was the highest ever achieved (remember, no conflict, additional fate, or changes in buying here)
• Of 13 buying patterns examined, 1 produced 7 characters max, 5 produced 5, 5 produced 4, and 2 produced 3 characters max. Meaning, 4-5 characters is the average amount (ignoring endgame purchasing)
• Max points (16) came on turn 4 of 4c3 buying. This was better than 5c2 buying which hits a max 15 power with 3 characters.
• The best "Tempo" pattern is either "2 2c1, 1 1c0" producing 9 power and 5 characters on turn 2, "1 4c1, 2 1c0" producing 10 power and 4 character turn 2, or "1 5c1, 1c0" producing 11 power and 3 characters on turn 2.
• 3c4 is not advised as it is the slowest ramp in power and characters and doesn't start getting good until turn 4...
  • However, if your conflict deck was designed around stalling those first few turns, you'd out value most every other deck with 15 power and 5 characters every turn.
• 4c3 is probably better as it ramps to 12 on turn 3 (and its 4 power turn 2 isn't too bad) and then peaks at 4 characters worth 16 power on turn 4.
• "1 3c3, 1 1c0" has the highest value of any 5 character setup with 13 power on turn 4. It's main problem is that it is under curve for the similar (and more commonly seen) "1 3c2, 2 1c0" or "1 3c2, 1 2c0" for the first 3 turns of the game.
• If you can survive the first 2 turns, 5c2 is pretty boss with 15 power on three characters. Not technically possible with the small card pool, but something to watch as more 5 cost cards become available.

Your thoughts?

L5Rcosts.pdf

Tough because of power allocation granularity. If you have 3 characters with 5 strength each, and your opponent strikes you with 6, to win that engagement you'd need to overallocate 3-4 strength to win the engagement depending on if you're attacking or defending.

4 hours ago, Waywardpaladin said:

Tough because of power allocation granularity. If you have 3 characters with 5 strength each, and your opponent strikes you with 6, to win that engagement you'd need to overallocate 3-4 strength to win the engagement depending on if you're attacking or defending.

I'm guessing you're referring to my comment on 5c2 purchasing? If so, its why I included the data on number of characters as well. The 3c4 generation of 15 points across 5 characters would be superior to the 5c3 of 15 points across 3 characters for the very reason you point out. When looking at your own decks purchasing schema, this becomes more relevant once you know particular card examples.

Lets see an example deck using this theory. The following Phoenix deck based on a principle of eventually winning on value.

Deck Clan: Phoenix

Total Cards: (85)

Total Conflict: (40) Total Dynasty: (40)

Total Influence: (12/13)

Stronghold:
1x Isawa Mori Seidō (Core Set #5)

Role:
1x Keeper of Water (Core Set #217A)

Province: (5)
Air (1/1) Earth (1/1) Fire (1/1) Void (1/1) Water (1/1)
1x Kuroi Mori (Core Set #12)
1x Night Raid (Core Set #21)
1x Elemental Fury (Core Set #16)
1x Manicured Garden (Core Set #19)
1x Entrenched Position (Core Set #17)

Character [Dynasty]: (36)
3x Fearsome Mystic (Core Set #91)
3x Isawa Kaede (Tears of Amaterasu #9)
3x Isawa Atsuko (Core Set #92)
3x Prodigy of the Waves (Into the Forbidden City #46)
3x Shiba Yōjimbō (Core Set #89)
3x Shiba Peacemaker (Core Set #82)
3x Solemn Scholar (Core Set #83)
3x Asako Diplomat (Core Set #85)
2x Miya Mystic (Core Set #125)
3x Serene Warrior (Core Set #88)
2x Adept of the Waves (Core Set #84)
1x Haughty Magistrate (The Chrysanthemum Throne #69)

Character [Conflict]: (2/10)
2x Togashi Kazue (Core Set #150)

Attachment: (8)
3x Embrace the Void (Tears of Amaterasu #16)
2x Cloud the Mind (Core Set #202)
3x Pacifism (Core Set #174)

Event: (30)
3x Against the Waves (Core Set #177)
3x Benten’s Touch (Into the Forbidden City #55)
3x Display of Power (Core Set #179)
3x Court Games (Core Set #206)
3x Spies at Court (Core Set #209)
3x Assassination (Core Set #203)
3x Mirumoto’s Fury (Core Set #159)
1x Let Go (Core Set #155)
3x Harmonize (For Honor and Glory #37)
2x Censure (Into the Forbidden City #60)
3x Banzai! (Core Set #204)

Holding: (6)
3x Forgotten Library (Core Set #94)
3x Magnificent Lighthouse (For Honor and Glory #27)

A certain amount of the deck is, hey I needed cards to fill it out. We're still too small of a card pool. But let's examine what we do have.

We have 12 character cards costing 4, and 3 more at 5: Fearsome Mystic, Isawa Atsuko, Prodigy of the Waves, and Isawa Kaeda. 15 cards available to do a legitimate first turn single character buy for 4c3 or 5c2. This gives us a good chance to grab the extra fate for passing turning on many of our 1 cost conflict cards. Fearsome just gobbles up enemy fate. Kaeda makes her attack a void sucking more fate. The Prodigy is just good value if able to unbow multiple times a game. Atsuko is good vs swarms.

We have 7 characters at the 3 cost. Serene Warrior (if you have the ability to honor) can be a legitimate 3 extra fate purchase. I probably wouldn't go 4. Same as the haughty magistrate which when honored and strongholded can solo most provinces (check out how few characters are honor 3 or better). Filling out the 3 slot we have Shiba Yojimbo protecting our expensive Shugenja. A second or third turn 3c3 on one may not be horrible idea.

At the 2 slot we have 7 cards with Asako Diplomat, Miya Mystic, and Adept of the Waves. These cards are mostly filler. Asako is there for honoring, but Miya and Adept are essentially 2 cost Shugenja's meant to be bowed for Benten's touch.

Finally, at the 1 slot we have 6 card in Shiba Peacemaker and Solemn Scholar. Shiba Peacemaker is a boss against military decks justifying an extra fate or even 2 (if you think they don't have the assassinate). While the scholar is the type of cheap Shugenja we had more of. It bows for Benten while contributing a very useful ability.

Magnificent Lighthouse bears mention as a way to help seal the deal. We have some cards with heavy investment that certain enemy conflict cards can be a big problem for us. The lighthouse helps to make those go away proactively.

Notable Conflict Deck inclusions are basically Togashi Kazue. The slow leach of fate over to us can be back breaking. Each usage is a net 2 change in game state, meaning 2 uses makes profit. Even if only used once, if used well it can be very impactful. The big problem is a Let Go immediately after playing it, before it can be activated. Set up censure to help against this. Embrace the void is good in a deck like this where we want to play lots of fate out on characters. It shouldn't be hard to get 3 fate from it. The rest of the cards lean towards attrition.

So the deck looks to open 4c3 or 5c2, get the extra fate, then push Earth, Void, and Water depending upon circumstance. We're looking to suck out enemy value while keeping a dominant board presence. Mirimoto's Furys, Assassinations, Against the waves and a few other tricks help us keep pace in the early first few turns. We're just fine running 3c2plus2c0 or 1c1's and further variants. The deck seeks out the larger curves in the OP's gaining us the best long term power. Currently, I'm not sure if there is enough honoring, and there are plenty of cards that are just holding space. I'd prefer more honor to Banzai for instance.

Anywho, a fun project. Not quite there yet, but with the right card drops and tinkering could get quite fierce.

My problem with running a deck like this and even Phoenix in general is their biggest weakness seems to be sealing the deal in 50 minutes.

The assumptions really take the bite out of these numbers because the ring of void really makes 1 fate characters extraordinarily vulnerable to being one and done. You can't assume people won't **** with your stuff.

5 hours ago, Joe From Cincinnati said:

The assumptions really take the bite out of these numbers because the ring of void really makes 1 fate characters extraordinarily vulnerable to being one and done. You can't assume people won't **** with your stuff.

For folks who haven't read your article the link is here so they know there is more behind your comment: https://www.wardensofthemidwest.com/how-to-manage-your-fate/

Second, you r article uses an example of "1 3c1, 2 2c0" which I changed to "1 3c1, 1 2c0, 1 1c0" as I didn't know how they got extra fate. (Perhaps a conflict character after getting an extra fate). Regardless, this creates the following pattern

"1 3c1, 1 2c0, 1 1c0" 6 9 9 9 9 (power) and 3 4 4 4 4 (Characters)

So the void ring sets them back 1 character worth 3 for a single turn. It's a weaker sustained pattern regardless as sustained 9 isn't very strong. This pattern is more of "tempo" pattern presumably for a deck to strike early for advantage then win before the opponent catches up. Without knowing the rest of the deck, particularly their conflict hand, they could have been a fast deck on bad conflict, or a slow deck with a bad flop. Although a slow deck should have done the 3c2, 2c0 for better sustained presence. But my numbers bear that out.

I like your article Joe and essentially agree with it. However, I do disagree with the rule of thumb around 1 fate. "Susceptible to Void ring" sounds o me a lot like "Dies to removal" in MtG. "Dies to removal" was a commonly heard phrase during spoilers used to imply most any spoiled card was "bad" somehow because the enemy could remove it. It didn't matter how aggressively costed it was. "Dies to Removal" was applicable for anyone who didn't have a better complaint of a reasonable card.

Here, susceptible to void ring is something theory (might) want to ignore because it is otherwise an effect useful every turn to both players and can be contested. Your counter of 4c2,1c0 was put forward as making void ring less valuable to your opponent to take. To which I'd reply that your opponents best move is to either play their game of tempo, not caring about long term value, or attack into the void in which case they are able to do more long term damage to you than you are able to do to them. Them attacking you (and winning void) loses you 4 power two turns from now. You attacking them loses them 3 power 1 turn from now. Also, them spending 1 fate on a character makes the void ring valid for you. This ups your choices and perhaps they were more worried about the earth ring hitting a key conflict card from hand. (or something else)

The point being that unless you have a very firm set of rational why a balanced game affect should change valuing, its best to leave it out of calculations. So if you can give me a firmer example of why losing a character 1 turns from now is more important than a different character two turns from now, and how that can be applied in a reasonable way, I'm happy to run new numbers. You'll notice I don't go overboard on lots of fate on cheap characters due to the reality of Assassination. (It's also quickly less valuable and VERY delayed than bigger characters 2c5 vs 3c4)

I'd add an assumption of a game only lasting four or five turns to that. I'd also take into account conflict cards costing 1 or more since they directly affect the assumption of 7 fate a turn.

1 hour ago, Kubernes said:

I'd add an assumption of a game only lasting four or five turns to that. I'd also take into account conflict cards costing 1 or more since they directly affect the assumption of 7 fate a turn.

Most patterns result in stasis after 3 turns, with only fate additions of 3 or more creating longer term patterns. A slow starting pattern requires a strategy for surviving while the long term effects of more power build up.

As for conflict cards, it would be interesting to see how budgeting in 1 fate per turn for (non-character) conflict cards affects power levels. I'll try to run that later.

7 hours ago, Daigotsu Steve said:

My problem with running a deck like this and even Phoenix in general is their biggest weakness seems to be sealing the deal in 50 minutes.

Yeah. It's like playing certain control decks in Magic. Once to a certain point, the win becomes inevitable but a slow opponent can be rough. Lots of practice with our deck plus ruthless calling of judges on slow players is required. Slow play is bad for EVERYONE. Thankfully, having a better sense of purchase tables helps plan out future turns. Also, cards like an unopposed 4c3 Fearsome will quickly remove meaningful choices from the opposition. If they can't effectively remove it, the end up purchasing 2-3 characters per turn with no fate on them. Decks that do that are either super aggressive and you will win or lose quickly, or their deck isn't prepared for that and they will be quickly out valued by turn 3.

The big mistake is to think you're trying to win turn 10 because of slow build. Instead, you're still trying to win no later than turn 8. If all your build-up doesn't result in quick province smash once you're there, you need a better kill method.

3 hours ago, Asako Shinpi said:

For folks who haven't read your article the link is here so they know there is more behind your comment: https://www.wardensofthemidwest.com/how-to-manage-your-fate/

Second, you r article uses an example of "1 3c1, 2 2c0" which I changed to "1 3c1, 1 2c0, 1 1c0" as I didn't know how they got extra fate. (Perhaps a conflict character after getting an extra fate). Regardless, this creates the following pattern

"1 3c1, 1 2c0, 1 1c0" 6 9 9 9 9 (power) and 3 4 4 4 4 (Characters)

So the void ring sets them back 1 character worth 3 for a single turn. It's a weaker sustained pattern regardless as sustained 9 isn't very strong. This pattern is more of "tempo" pattern presumably for a deck to strike early for advantage then win before the opponent catches up. Without knowing the rest of the deck, particularly their conflict hand, they could have been a fast deck on bad conflict, or a slow deck with a bad flop. Although a slow deck should have done the 3c2, 2c0 for better sustained presence. But my numbers bear that out.

I like your article Joe and essentially agree with it. However, I do disagree with the rule of thumb around 1 fate. "Susceptible to Void ring" sounds o me a lot like "Dies to removal" in MtG. "Dies to removal" was a commonly heard phrase during spoilers used to imply most any spoiled card was "bad" somehow because the enemy could remove it. It didn't matter how aggressively costed it was. "Dies to Removal" was applicable for anyone who didn't have a better complaint of a reasonable card.

Here, susceptible to void ring is something theory (might) want to ignore because it is otherwise an effect useful every turn to both players and can be contested. Your counter of 4c2,1c0 was put forward as making void ring less valuable to your opponent to take. To which I'd reply that your opponents best move is to either play their game of tempo, not caring about long term value, or attack into the void in which case they are able to do more long term damage to you than you are able to do to them. Them attacking you (and winning void) loses you 4 power two turns from now. You attacking them loses them 3 power 1 turn from now. Also, them spending 1 fate on a character makes the void ring valid for you. This ups your choices and perhaps they were more worried about the earth ring hitting a key conflict card from hand. (or something else)

The point being that unless you have a very firm set of rational why a balanced game affect should change valuing, its best to leave it out of calculations. So if you can give me a firmer example of why losing a character 1 turns from now is more important than a different character two turns from now, and how that can be applied in a reasonable way, I'm happy to run new numbers. You'll notice I don't go overboard on lots of fate on cheap characters due to the reality of Assassination. (It's also quickly less valuable and VERY delayed than bigger characters 2c5 vs 3c4)

My example in the article is of a 4c2 and 1c0 vs a 3c1 and 2 1c0

"In the first round, I purchased my Steadfast Witch Hunter with 2 fate and a 1 cost character. My opponent purchased a 3 cost character with 1 fate and 2 1 cost characters."

As for how that argument sounds like "dies to removal," I think comparing a game where cards are permanent until they are specifically removed via battle or card effect and a game where cards are naturally ephemeral leads to a lot of false determinations. Especially considering we're not evaluating the strength of a card when we are talking about the strengths and weaknesses of a 1 fate drop on a big character. The conversation starts and ends at fate efficiency. Your entire post is regarding fate efficiency, so I figured you'd be interested in this hole in your theory.

When purchasing a 4 cost character with 1 fate, it is theoretically worth 8 fate. When purchasing it with 2 fate it is worth 12 fate, by your own definition. So saving one fate on your big guy to purchase an additional 1 cost character is "creating" 1 fate of value that round, but costing you 3 fate of value over the course of 2 turns. Or 1 turn if they do have a Meditations or Ring of the Void or any other fate removal ability affecting that character (which I know you aren't explicitly considering in this discussion for simplicity's sake). You could extend this comparison to putting 3 fate on a character as well, but then you encounter different problems, like the game ending before the fate on the character expires or the character being killed by some sort of alternative method due to the additional fate you expended on it (such as an ICS, NS or WotC). I know you are also not taking into account removal because it's impossible to accurately consider in an exercise like this. That's why I generally leave the 3 fate drop out of any conversation like this.

My only point is that, while the theory holds up under the assumption that your opponent is not doing anything to your cards, it quickly falls apart when you are placing 5 fate on a card that your opponent, with a simple always available action (especially if they're first player), can remove from the board in one round.

If you are evaluating a 4 coster with 1 fate as being worth 8 fate over 2 rounds, that is likely more accurate, for the most part, when considering a 4 fate with 2 fate on it, as those fate are very fragile. And only having 1 fate is just...so appealing to your opponent.

I'm not criticizing the theory, as I find it to be sound. I'm speaking purely in terms of the assessed value in practice. And I don't think it's an understatement to say that a character with 1 fate on it is hit by the void ring significantly more often than a character with 2 fate on it. So if you're trying to get 2 rounds of value out of a character, 2 fate will typically average that value for you, whereas 1 fate will typically only guarantee 1 round of value. That's very difficult to account for in the theory, but I do believe it's worth mentioning when evaluating the theory's results.

So the answer isn't Pi?

Remind me not to cheat of your test next time Joe.

On 12/7/2017 at 4:23 PM, Ishi Tonu said:

So the answer isn't Pi?

Not quite, but close. the answer is actually pie. (I think I ate too many cheese balls tonight.)

So, jokes aside, what's the conclusion for all this number crunching, in regular English?