HOF Challenge Series II Discussion

Denniz said:
Trying to decide if the number of turns to finish\win matters between V&W games and BTS games given the difference in total turns available. (i.e. Epic speed: V&W=660 vs. BTS=750). Dates might but number of turns shouldn't. Thoughts?
Click to expand...

It's no matter.
First, the turn scale difference between V&W vs BTS is mostly at the end of table (21th century).
Second, the Formula should describe DELTA turns for each Levels for equalize its, but we shouldn't try to equalize turn/date of V&W and BTS. HOF tables contain the same cells for V, W and BTS except Space Victory and all players live with that.
 
We have 2 main problems:
1) Different victory types may require different level correction formulas;
2) Difference between Levels isn't linear and additionally depends on Civ and, may be, map type.
For example, Inca and Persia have a big bonus on Monarch-Deity levels comparing with Prince and lower levels so it requires more "flat" curve for formula. For other civs vice versa - Prince has a big bonus vs Monarch and requires "hole" between these levels. Of course, I talk about military and SS victories, Religious Victory is less sensitive to it.
 
But, it looks like we should do a hard decision and make simple enough formula that isn't always shows correct difference between levels, but allow us to play with different levels. And, may be it's even add new good feature - right level choice for every game. I think it's good.
 
Analysing my 2 games for GAME 6, I think the formula could be something like Delta Turn = -12*Level*Speed (Speed = 2/3, 1, 1.5, 3).

P.S. Of course, 12 is a little bit less than needed, but other numbers near it aren't multiplyed to 2/3 and 1.5 without fractional part. In other case 13 is better. :)
 
Dynamic said:
Analysing my 2 games for GAME 6, I think the formula could be something like Delta Turn = -12*Level*Speed (Speed = 2/3, 1, 1.5, 3).

P.S. Of course, 12 is a little bit less than needed, but other numbers near it aren't multiplyed to 2/3 and 1.5 without fractional part. In other case 13 is better. :)
Click to expand...
I think you are confusing Difficulty with Speed. All the challenge games allow different difficulties but only one speed.
 
Denniz said:
I think you are confusing Difficulty with Speed. All the challenge games allow different difficulties but only one speed.
Click to expand...

No, this Formula contains both Diffculty Level and Speed. So it's universal. Speed is constant just inside the game, but we have 6 games with different speeds.
 
I have spent most of the day analyzing the differences between difficutlies from the HOF results for each of the Challenge games. i.e. Games with same Condition, Map Size and Speed. I also looked at the general map type where possible. (i.e. Astronomy required or not.)

Not all conditions had the same kind of curve. One thing I noticed was that Settler and Deity games seem to have the most samples and probably the best results. For my first attempt at adjustments, I went with an exponential curve (using powers of 2) with the aim of making the best Settler and Deity finishing turns be the same after adjustment. (Not the best in the challenge but the best within the HOF as specified above.)


Values used by Game:
Code: 
	Game1	Game2	Game3	Game4	Game5	Game6
Settler	59	147	130	351	139	241
MaxDiff	180	268	218	492	85	370
MaxLvl	[COLOR="darkred"]7[/COLOR]	9	9	[COLOR="darkred"]7[/COLOR]	9	9
D-S	121	121	88	141	-54	129

Settler = lowest Settler finish turn
MaxDiff = lowest finish turn for the highest difficult sample available
MaxLvl = 7 is Emperor; 9 is Deity
D-S = MaxDiff turn minus Settler turn​

Turns adjustment by Game and Difficulty:
Code: 
	Game1	Game2	Game3	Game4	Game5	Game6
Settler	0	0	0	0	0	0
Chieftn	-4	-1	-1	-4	0	-1
Warlord	-8	-2	-1	-9	1	-2
Noble	-15	-4	-3	-18	2	-4
Prince	-30	-8	-6	-35	3	-8
Monarch	-61	-15	-11	-71	7	-16
Emperor	-121	-30	-22	-141	14	-32
Immortl	[COLOR="DarkRed"]-121[/COLOR]	-61	-44	[COLOR="darkred"]-141[/COLOR]	27	-65
Deity	[COLOR="darkred"]-121[/COLOR]	-121	-88	[COLOR="darkred"]-141[/COLOR]	54	-129
Notes:
  • A couple games didn't have Immortal or Deity games for comparison so their adjustment for Emperor is carried forward for now.
  • Religous Victories to be do better with Deity so the curve is going the other way.

Forumla: Diff * (DF / NP2)

Diff = MaxDiff turn minus Settler turn (D-S)
DF = Difficutly Factor - Powers of 2 by level (i.e. Chieftan=2; Warlord=4, Prince=8, Monarch=16, Emperior=32, Immortal=64, Deity=128)
NP2 = Next highest Powe of 2 after MaxLvl (i.e. MaxLvl of 7 = 64, MaxLvl of 9 = 256)

I am sure that there will be a lot of questions, concerns, math lessons, anglings for advantage, violent disagreements, etc. :mischief: Try not to freak out on me too much. :eek: :mischief:
 
Sorry, Denniz, but using power of 2 gives us results far away from reality. Linear Formula isn' ideal but MUCH closer to the real games then power of 2. 8 turns of Difference between Prince and Settler or 64 between Deity and Immortal is ridiculous. :(
 
Denniz said:
I did the games individually to take things like speed out of the equation. ;)
Click to expand...

Good, I agree with individual qualifying of games. We just should complete the Formula much earlier then tournament end for players could choose level right.
 
Dynamic said:
Sorry, Denniz, but using power of 2 gives us results far away from reality. Linear Formula isn' ideal but MUCH closer to the real games then power of 2. 8 turns of Difference between Prince and Settler or 64 between Deity and Immortal is ridiculous. :(
Click to expand...
Actually it is 8/256th's between settler and prince vs. 64/256th's between immortal and deity. That may be high. But linear isn't going to be quite right either. It gives more weight to the low-to-middle difficulties.

The problem is that most of the actual curves came out looking like a shallow bell curve. I didn't trust what I was seeing as that would say that the middle difficulties are harder than the high/low difficulties. I think that is just a reflection of fewer really good games in the middle.

I think the front half of the curve works pretty good. I probably need to smooth out the back half of the curve more towards linear.
 
Denniz said:
Turns adjustment by Game and Difficulty:
Code: 
	Game1	Game2	Game3	Game4	Game5	Game6
Settler	0	0	0	0	[COLOR="Blue"]0[/COLOR]	0
Chieftn	-4	-1	-1	-4	[COLOR="Blue"]0[/COLOR]	-1
Warlord	-8	-2	-1	-9	[COLOR="Blue"]1[/COLOR]	-2
Noble	-15	-4	-3	-18	[COLOR="Blue"]2[/COLOR]	-4
Prince	-30	-8	-6	-35	[COLOR="Blue"]3[/COLOR]	-8
Monarch	-61	-15	-11	-71	[COLOR="Blue"]7[/COLOR]	-16
Emperor	-121	-30	-22	-141	[COLOR="Blue"]14[/COLOR]	-32
Immortl	[COLOR="darkred"]-121[/COLOR]	-61	-44	[COLOR="darkred"]-141[/COLOR]	[COLOR="Blue"]27[/COLOR]	-65
Deity	[COLOR="darkred"]-121[/COLOR]	-121	-88	[COLOR="darkred"]-141[/COLOR]	[COLOR="Blue"]54[/COLOR]	-129
Notes:
  • A couple games didn't have Immortal or Deity games for comparison so their adjustment for Emperor is carried forward for now.
  • Religous Victories to be do better with Deity so the curve is going the other way.
Click to expand...

I understand that the above data is very preliminary, but I feel compelled to state the obvious as follows with regard to the Religious Victory column and the last sentence above ...

The Religious Victory column in the above table seems to be saying that Settler level Wins are later than Deity level Wins, so that Deity Games should suffer a turn penalty (rather than a bonus) with respect to Settler Games.

I don't agreed. It is more likely that the best Settler level Religious Victories are lame (not any where near as early as a motivated, experienced Player could make them). Your early Settler level Religious Victory Win Dates are extremely suspect. What possible advantage can a Deity level Religious Game have over a Settler level Religious Game? The Technology race is to Complete Writing and Monotheism followed by Mathematics or Alphabet and all Technology trading is done solely to improve Diplomacy as opposed to increasing Tech rate via trading. The best Deity level Religious Game is over before the AI's Economy recovers from its initial REX and the AI Technology level is often far behind. In many Religious Games, the Player need only give the AI's Theology and a few Technologies they are missing and possibly Alphabet too to gain the needed Diplomatic trading bonus (+4).

Conclusion: Settler level best Religious Victory Dates are much later than they should be. This results in a bogus Difficulty level turn adjustment curve for Religious Victories that gives a turn bonus to all difficulty levels that are above the Deity difficulty level. Thus, not only must the Deity level Religious Victory Player beat every lower level's Win Turn, he must do so by a margin that exceeds the turn difference in the above table. Although this certainly is a mathematical possibility, at any practical level this is pure nonsense (extremely low signal to noise; extremely high noise to signal; actually signal = 0 with respect to the Settler Win Dates).

I hope we can soon get some solid data to fix this anomaly.

Sun Tzu Wu
 
Sun Tzu Wu said:
I understand that the above data is very preliminary, but I feel compelled to state the obvious as follows with regard to the Religious Victory column and the last sentence above ...

The Religious Victory column in the above table seems to be saying that Settler level Wins are later than Deity level Wins, so that Deity Games should suffer a turn penalty (rather than a bonus) with respect to Settler Games.

I don't agreed. It is more likely that the best Settler level Religious Victories are lame (not any where near as early as a motivated, experienced Player could make them). Your early Settler level Religious Victory Win Dates are extremely suspect. What possible advantage can a Deity level Religious Game have over a Settler level Religious Game? The Technology race is to Complete Writing and Monotheism followed by Mathematics or Alphabet and all Technology trading is done solely to improve Diplomacy as opposed to increasing Tech rate via trading. The best Deity level Religious Game is over before the AI's Economy recovers from its initial REX and the AI Technology level is often far behind. In many Religious Games, the Player need only give the AI's Theology and a few Technologies they are missing and possibly Alphabet too to gain the needed Diplomatic trading bonus (+4).

Conclusion: Settler level best Religious Victory Dates are much later than they should be. This results in a bogus Difficulty level turn adjustment curve for Religious Victories that gives a turn bonus to all difficulty levels that are above the Deity difficulty level. Thus, not only must the Deity level Religious Victory Player beat every lower level's Win Turn, he must do so by a margin that exceeds the turn difference in the above table. Although this certainly is a mathematical possibility, at any practical level this is pure nonsense (extremely low signal to noise; extremely high noise to signal; actually signal = 0 with respect to the Settler Win Dates).

I hope we can soon get some solid data to fix this anomaly.

Sun Tzu Wu
Click to expand...

STW, you have no one but yourself to blame for this!:lol:

Sorry, I couldn't help myself. You religious superiority and supremacy have skewed the data. If I can get a Deity space victory, I will play some settler religious games to try to improve the best settler scores.
 
shulec said:
STW, you have no one but yourself to blame for this!:lol:

Sorry, I couldn't help myself. You religious superiority and supremacy have skewed the data. If I can get a Deity space victory, I will play some settler religious games to try to improve the best settler scores.
Click to expand...

You gave me a good laugh. Thanks shulec!

You are right. I work too hard at improving (at least some) Religious Victory Dates; actually I tend to quit as soon as I get a #1 slot.

Any help improving (correcting?) the Settler level Religious Victory Dates is greatly appreciated!

Sun Tzu Wu
 
It looks like Denniz has applied his Formula to the Challenge table... Game 5 looks especially nice. :)
With such Formula the best levels are Settler and Deity. Others are totally uncompetitive. :(
 
Dynamic said:
It looks like Denniz has applied his Formula to the Challenge table... Game 5 looks especially nice. :)
With such Formula the best levels are Settler and Deity. Others are totally uncompetitive. :(
Click to expand...

Yup... if scoring in the series is important to you, and you can't win the game at Deity, then Settler is the level to go for. And here I've been crashing to desktop trying to get an emperor-immortal penalty in game 5. :lol: What an idiot I must be. Either that or I must not care too much about having my immortal level games score lower than a string of settler games I'd have no trouble crushing. :mischief:


Perhaps I should go do it at settler just to see what makes that level so challenging. :crazyeye: Just for giggles, anyhow.
 
For example, using Linear formula for Game 6:
 

Attachments

  • Challenge2_6.JPG
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And Game 5 with the same Base Delta (may be we should decrease it for Religious):

P.S. Sorry, babaBrian's date is 580AD, not BC.
P.P.S. After some analysis it's obvious that Base Delta should be decreased.

For example, Second shot with Base Delta = 6:
 

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  • Challenge2_5.JPG
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  • Challenge2_5a.JPG
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