Genetic optimization re-started

[stegemma]

After a lot of time, I finally re-started the genetical optimization in Sabrina (ex Satana). The success of AlphaZero with its NN has convinced me that I can do something good even with GA. I've worked on my GA algorithm to avoid the problems found in the old try and I think that I can get some result, now.

To avoid too random games, I use a 300ms per move time and I filter starting positions, accepting only those with no more than one pawn difference (from a large set of real games). The new GA follows this rules:

1) at start (generation 0), one half of the individual gets original parameters and one half random ones

2) the ORIGINAL engine always appears (one individual) in the population and its parameters are constant

3) any individual plays a game starting from a random position, with white and then with black, against any other engine that follows in the actual ranking; the starting position changes at any individual couple

4) after all games in a generation, sort individuals by score

5) the GA start "crossing" individuals, with this actions:

a) it chooses two random individuals (for 1/8 of the times); lets' say PlayerA and PlayerB
b) re-order the two individuals so that only the weakest would be changed
c) merge values from PlayerB to PlayerA (the weakest) with: random mutations (2%), average (6%), copy (60%), no changes (30%)

Code: Select all

	for &#40;int i = 0; i<ARRAY_COUNT&#40;iiValues&#41;; i++)
	&#123;
		int k = objRandom.Rand&#40;100&#41;;
		if&#40;k < 2&#41; // mutazione
		&#123;
			iiValues&#91;i&#93; = objRandom.Rand&#40;0, valPawn&#41;;
		&#125;else if&#40;k<10&#41; // media dei valori
		&#123;
			iiValues&#91;i&#93; = &#40;iiValues&#91;i&#93; + pEngine->iiValues&#91;i&#93;) / 2;
		&#125;else if&#40;k<70&#41; // copia
		&#123;
			iiValues&#91;i&#93; = pEngine->iiValues&#91;i&#93;;
		&#125; // else&#58; invariato
	&#125;

6) set score to zero for all individuals
7) next generation

This way, the best engine wouldn't be changed by GA, until it rest the best one. The good genes "migrates" from top to bottom. The original parameters always occurs in the population, so that I can know that individuals are not competing around a local maximum worst that actual engine 8they could do it but I'll notice immediately, because ORIGINAL becomes the first).

Do to "long" time control, it requires more time to complete but still I can get some interesting result, because one individual seems to becomes stronger at any generation. As said in our G6 group, maybe it is only lucky... and in effect it is called "Lucky Man" (name choosen at random, not by me!).

Here's actual results:

Code: Select all

0	1	The Three Fates'	16	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
0	2	Battlefield'	14	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
0	3	Jeremy Bender'	13	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
0	4	Take a Pebble'	12	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
0	5	Tank'	12	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
0	6	Lucky Man'	12	1	27	90	66	27	7	19	38	35	75	42	27	66	87	87	2	9	57	47	3	3
0	7	Mass'	11	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
0	8	Stones of Years'	10	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
0	9	Lachesis'	8	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
0	10	ORIGINAL'	6	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
0	11	Tarkus'	4	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
0	12	Iconoclast'	-2	61	17	92	103	33	13	26	59	40	95	69	101	98	34	32	19	16	82	18	49	73
0	13	Bitches Crystal'	-5	60	34	26	1	97	84	12	53	88	49	26	32	58	38	103	1	38	84	71	21	2
0	14	The Barbarian'	-10	58	5	63	62	71	55	78	94	103	22	33	51	72	61	20	53	49	34	53	37	56
0	15	Aquatarkus'	-13	21	50	103	21	78	73	93	79	104	35	65	65	47	66	92	65	15	93	39	88	92
0	16	Eruption'	-13	90	87	5	17	43	87	81	34	90	44	54	10	56	35	27	62	10	8	23	22	28
0	17	Clotho'	-16	20	0	7	13	8	50	35	75	4	21	36	13	82	19	65	7	67	98	20	70	89
0	18	Manticore'	-18	90	12	73	90	16	100	26	3	5	97	44	69	63	59	0	92	51	9	29	47	35
0	19	Knife Edge'	-20	54	99	55	16	90	33	65	3	98	34	10	87	5	81	64	9	94	15	37	13	104
0	20	Atropos'	-21	21	76	67	31	1	24	63	94	37	18	67	45	69	10	12	100	37	88	70	70	40
																								
1	1	Stones of Years'	20	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
1	2	The Three Fates'	17	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
1	3	Take a Pebble'	14	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
1	4	Jeremy Bender'	13	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
1	5	Battlefield'	11	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
1	6	Mass'	9	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
1	7	Lucky Man'	9	1	27	90	66	27	7	19	38	35	75	42	27	66	87	87	2	9	57	47	3	3
1	8	Lachesis'	8	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
1	9	Tank'	5	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
1	10	Bitches Crystal'	1	60	34	26	1	97	84	12	53	88	49	26	32	58	38	103	1	38	84	71	21	2
1	11	ORIGINAL'	0	7	88	2	66	27	26	19	38	35	75	42	8	66	10	87	2	1	57	10	3	10
1	12	Iconoclast'	-3	61	17	92	103	33	13	26	59	40	95	69	101	98	34	32	19	16	82	18	49	73
1	13	The Barbarian'	-7	58	5	63	62	71	55	78	94	103	22	33	51	72	61	20	53	49	34	53	37	56
1	14	Aquatarkus'	-7	21	50	103	21	78	73	93	79	104	35	65	65	47	66	92	65	15	93	39	88	92
1	15	Tarkus'	-9	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	91	1	5	10	5	10
1	16	Eruption'	-11	90	87	5	17	43	87	81	34	90	44	54	10	56	35	27	62	10	8	23	22	28
1	17	Knife Edge'	-16	54	99	55	16	90	33	65	3	98	34	10	87	5	81	64	9	94	15	37	13	104
1	18	Clotho'	-16	20	0	7	13	8	50	35	75	4	21	36	13	82	19	65	7	67	98	20	70	89
1	19	Manticore'	-18	90	12	73	90	16	100	26	3	5	97	44	69	63	59	0	92	51	9	29	47	35
1	20	Atropos'	-20	21	76	67	31	1	24	63	94	37	18	67	45	69	10	12	100	37	88	70	70	40
																								
2	1	Jeremy Bender'	16	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
2	2	The Three Fates'	15	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
2	3	Stones of Years'	14	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
2	4	Take a Pebble'	13	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
2	5	Mass'	11	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
2	6	Lucky Man'	11	7	70	90	20	27	7	5	2	35	8	42	8	10	87	53	5	1	5	47	4	10
2	7	Battlefield'	10	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
2	8	Tank'	9	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
2	9	Lachesis'	8	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
2	10	Iconoclast'	7	61	70	92	20	4	26	5	2	5	8	1	29	10	22	20	12	16	5	10	5	10
2	11	ORIGINAL'	7	7	88	2	66	27	26	19	38	35	75	42	8	66	10	87	2	1	57	10	3	10
2	12	Bitches Crystal'	-2	60	34	26	1	97	84	12	53	88	49	26	32	58	38	103	1	38	84	71	21	2
2	13	The Barbarian'	-6	58	5	63	20	4	26	5	2	5	15	1	8	72	10	20	5	1	34	10	37	56
2	14	Eruption'	-10	90	87	5	17	43	87	81	34	90	44	54	10	56	35	27	62	10	8	23	22	28
2	15	Aquatarkus'	-14	21	50	103	21	78	73	93	79	104	35	65	65	47	66	92	65	15	93	39	88	92
2	16	Atropos'	-15	21	76	67	31	1	24	63	94	37	18	67	45	69	10	12	100	37	88	70	70	40
2	17	Clotho'	-15	20	0	7	13	8	50	35	75	4	21	36	13	82	19	65	7	67	98	20	70	89
2	18	Manticore'	-17	90	12	73	90	16	100	26	3	5	97	44	69	63	59	0	92	51	9	29	47	35
2	19	Tarkus'	-20	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	91	1	5	10	5	10
2	20	Knife Edge'	-22	54	99	55	16	90	33	65	3	98	34	10	87	5	81	64	9	94	15	37	13	104
																								
3	1	Take a Pebble'	13	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
3	2	Stones of Years'	13	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
3	3	Lucky Man'	13	7	70	90	20	27	7	5	2	35	8	42	8	10	87	53	5	1	5	47	4	10
3	4	The Three Fates'	12	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
3	5	Battlefield'	10	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
3	6	Jeremy Bender'	10	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
3	7	Mass'	9	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
3	8	ORIGINAL'	9	7	88	2	66	27	26	19	38	35	75	42	8	66	10	87	2	1	57	10	3	10
3	9	Atropos'	8	7	70	2	20	4	25	63	94	37	18	1	45	10	10	12	5	37	5	40	5	52
3	10	Iconoclast'	3	7	70	92	20	27	7	5	2	35	8	1	8	10	87	53	5	1	5	47	5	10
3	11	Bitches Crystal'	0	60	34	26	1	97	84	12	53	88	49	26	32	58	38	103	1	38	84	71	21	2
3	12	The Barbarian'	0	60	34	26	1	4	84	8	53	88	15	1	8	58	38	103	5	38	84	10	37	37
3	13	Tank'	0	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
3	14	Lachesis'	0	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
3	15	Eruption'	-4	90	87	5	17	43	87	81	34	90	44	54	10	56	35	27	62	10	8	23	22	28
3	16	Aquatarkus'	-14	21	50	103	21	78	73	93	79	104	35	65	65	47	66	92	65	15	93	39	88	92
3	17	Tarkus'	-17	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	91	1	5	10	5	10
3	18	Clotho'	-17	20	0	7	13	8	50	35	75	4	21	36	13	82	19	65	7	67	98	20	70	89
3	19	Manticore'	-19	90	12	73	90	16	100	26	3	5	97	44	69	63	59	0	92	51	9	29	47	35
3	20	Knife Edge'	-29	54	99	55	16	90	33	65	3	98	34	10	87	5	81	64	9	94	15	37	13	104
																								
4	1	Lucky Man'	15	7	70	90	20	27	7	5	2	35	8	42	8	10	87	53	5	1	5	47	4	10
4	2	Jeremy Bender'	10	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
4	3	Stones of Years'	9	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
4	4	Bitches Crystal'	9	33	80	2	20	4	26	5	2	88	8	1	32	10	10	20	5	1	5	10	5	10
4	5	Iconoclast'	8	7	70	92	20	27	7	5	2	35	8	1	8	10	87	53	5	1	5	47	5	10
4	6	Battlefield'	8	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
4	7	ORIGINAL'	6	7	88	2	66	27	26	19	38	35	75	42	8	66	10	87	2	1	57	10	3	10
4	8	The Three Fates'	6	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
4	9	Take a Pebble'	5	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
4	10	Mass'	5	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
4	11	Tank'	3	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
4	12	Lachesis'	2	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
4	13	Manticore'	1	90	12	90	90	16	7	26	3	20	97	42	8	63	87	53	5	1	9	47	47	10
4	14	Atropos'	-2	7	70	2	20	4	25	63	94	37	18	1	45	10	10	12	5	37	5	40	5	52
4	15	Aquatarkus'	-5	21	50	103	21	78	73	93	79	104	35	65	65	47	66	92	65	15	93	39	88	92
4	16	The Barbarian'	-7	60	34	26	1	4	84	8	53	88	15	1	8	58	38	103	5	38	84	10	37	37
4	17	Eruption'	-13	90	87	5	17	43	87	81	34	90	44	54	10	56	35	27	62	10	8	23	22	28
4	18	Tarkus'	-17	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	91	1	5	10	5	10
4	19	Clotho'	-20	20	0	7	13	8	50	35	75	4	21	36	13	82	19	65	7	67	98	20	70	89
4	20	Knife Edge'	-23	54	99	55	16	90	33	65	3	98	34	10	87	5	81	64	9	94	15	37	13	104
																								
5	1	Lucky Man'	22	7	70	90	20	27	7	5	2	35	8	42	8	10	87	53	5	1	5	47	4	10
5	2	Mass'	19	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
5	3	Battlefield'	19	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
5	4	Take a Pebble'	18	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
5	5	Iconoclast'	18	7	70	92	20	27	7	5	2	35	8	1	8	10	87	53	5	1	5	47	5	10
5	6	Jeremy Bender'	18	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
5	7	ORIGINAL'	16	7	20	2	20	4	1	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
5	8	Bitches Crystal'	15	33	80	2	20	4	26	5	2	88	8	1	32	10	10	20	5	1	5	10	5	10
5	9	Stones of Years'	14	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
5	10	Lachesis'	14	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
5	11	The Three Fates'	12	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
5	12	Tank'	10	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
5	13	Manticore'	3	90	12	90	90	16	7	26	3	20	97	42	8	63	87	53	5	1	9	47	47	10
5	14	Atropos'	-5	7	70	2	20	4	25	63	94	37	18	1	45	10	10	12	5	37	5	40	5	52
5	15	The Barbarian'	-10	60	34	26	1	4	84	8	53	88	15	1	8	58	38	103	5	38	84	10	37	37
5	16	Eruption'	-27	90	87	5	17	43	87	81	34	90	44	54	10	56	35	27	62	10	8	23	22	28
5	17	Aquatarkus'	-27	21	50	103	21	78	73	93	79	104	35	65	65	47	66	92	65	15	93	39	88	92
5	18	Clotho'	-39	20	0	7	13	8	50	35	75	4	21	36	13	82	19	65	7	67	98	20	70	89
5	19	Tarkus'	-41	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	91	1	5	10	5	10
5	20	Knife Edge'	-49	54	99	55	16	90	33	65	3	98	34	10	87	5	81	64	9	94	15	37	13	104

(generation ranking name score p1 p2...)

Notice that many individuals still have original parameters (so ORIGINAL has other clones still alive) but "Lucky Man" looks to be stronger.

Of course, a tournament of "Lucky Man" with real engines could negate this partial result but I'll do it when more generations has been completed.

PS: in the first generations, there were a bug and ORIGINAL gets changed; this bug has been corrected and the session has been re-started with its original values

[hgm]

When you start to get really improved versions, keeping the original one will no longer protect you from regression.

This kind of evolutionary development has a danger: a trait A can be a refutation for trait B. Good to have, but only if B is common in the population. So A will get selected for, and individuals with trait A will start to dominate the population. B does not work anymore, and gets extinct. Then A is not needed anymore, and will get defunct by random genetic drift. The population becomes defenseless against B. Now after some time a mutation produces B...

I think that to guard against such a scenario, you would have to re-introduce winners of former generations periodically back into the population.

I am also planning to do a GA development, for producing an engine for Peace Chess. Basically nothing is known here, for what constitutes good strategy. No piece values, no positioning... An AlphaZero-like approach would be an alternative.

[stegemma]

When you start to get really improved versions, keeping the original one will no longer protect you from regression.

This kind of evolutionary development has a danger: a trait A can be a refutation for trait B. Good to have, but only if B is common in the population. So A will get selected for, and individuals with trait A will start to dominate the population. B does not work anymore, and gets extinct. Then A is not needed anymore, and will get defunct by random genetic drift. The population becomes defenseless against B. Now after some time a mutation produces B...

I think that to guard against such a scenario, you would have to re-introduce winners of former generations periodically back into the population.

I am also planning to do a GA development, for producing an engine for Peace Chess. Basically nothing is known here, for what constitutes good strategy. No piece values, no positioning... An AlphaZero-like approach would be an alternative.

Remember that ORIGINAL is everytime present in the population, so that nobody weaker than it can becomes the leader. For sure I plan to start a session using a set of best individuals, choosen with some rule from the best of any generation (the one who stand longer, or with the major score and so on).

the generation 7 has finished now and Lucky Man is not the best anymore, but still it is in the first ones:

Code: Select all

6	1	Take a Pebble'	29
6	2	Iconoclast'	29
6	3	Mass'	28
6	4	Battlefield'	27
6	5	Lucky Man'	26
6	6	Lachesis'	24
6	7	Jeremy Bender'	23
6	8	Bitches Crystal'	20
6	9	ORIGINAL'	20
6	10	Stones of Years'	18
6	11	Tank'	17
6	12	The Three Fates'	16
6	13	Manticore'	6
6	14	Atropos'	-3
6	15	The Barbarian'	-13
6	16	Aquatarkus'	-34
6	17	Eruption'	-42
6	18	Tarkus'	-59
6	19	Clotho'	-60
6	20	Knife Edge'	-72

Do to the bug in the first generations, some parameter has been kept only in ORIGINAL but this is good, because help having more variations.

[hgm]

Remember that ORIGINAL is everytime present in the population, so that nobody weaker than it can becomes the leader.

Sure, but yiu could revert to the original every time. And when the purposE was to create something far stronger, that is sort of a bummer.

In my case, where the original is basically a random mover, it would be quite undesirable.

[stegemma]

Remember that ORIGINAL is everytime present in the population, so that nobody weaker than it can becomes the leader.

Sure, but yiu could revert to the original every time. And when the purposE was to create something far stronger, that is sort of a bummer.

In my case, where the original is basically a random mover, it would be quite undesirable.

Of course my ORIGINAL has the hand made parameters and it works somehow (it is not random) but I have never done a true tuning, by hand. What happens now (generation 9) is that the best individual is very similar to ORIGINAL, and it differs for one parameter only. Other 3 individual are better than ORIGINAL and they have up to 8 parameters modified over 21 (I have even an unused parameter, that I must throw away from tuning). In this situation, the most of the population after the first individual would slowly takes parameters from ORIGINAL and its stronger friends. When the population would be more similar to the first individuals, then some mutation could creates a new leader, because that mutation would be over a strong individual (even if it is at the end of the ranking).

Of course GA is a bet and nothing is guaranteed but looking at the dynamic of the system is very interesting for me.

PS: here's the whole dynamic right now:

Code: Select all

0	1	The Three Fates'	16	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
0	2	Battlefield'	14	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
0	3	Jeremy Bender'	13	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
0	4	Take a Pebble'	12	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
0	5	Tank'	12	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
0	6	Lucky Man'	12	1	27	90	66	27	7	19	38	35	75	42	27	66	87	87	2	9	57	47	3	3
0	7	Mass'	11	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
0	8	Stones of Years'	10	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
0	9	Lachesis'	8	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
0	10	ORIGINAL'	6	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
0	11	Tarkus'	4	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
0	12	Iconoclast'	-2	61	17	92	103	33	13	26	59	40	95	69	101	98	34	32	19	16	82	18	49	73
0	13	Bitches Crystal'	-5	60	34	26	1	97	84	12	53	88	49	26	32	58	38	103	1	38	84	71	21	2
0	14	The Barbarian'	-10	58	5	63	62	71	55	78	94	103	22	33	51	72	61	20	53	49	34	53	37	56
0	15	Aquatarkus'	-13	21	50	103	21	78	73	93	79	104	35	65	65	47	66	92	65	15	93	39	88	92
0	16	Eruption'	-13	90	87	5	17	43	87	81	34	90	44	54	10	56	35	27	62	10	8	23	22	28
0	17	Clotho'	-16	20	0	7	13	8	50	35	75	4	21	36	13	82	19	65	7	67	98	20	70	89
0	18	Manticore'	-18	90	12	73	90	16	100	26	3	5	97	44	69	63	59	0	92	51	9	29	47	35
0	19	Knife Edge'	-20	54	99	55	16	90	33	65	3	98	34	10	87	5	81	64	9	94	15	37	13	104
0	20	Atropos'	-21	21	76	67	31	1	24	63	94	37	18	67	45	69	10	12	100	37	88	70	70	40
																								
1	1	Stones of Years'	20	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
1	2	The Three Fates'	17	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
1	3	Take a Pebble'	14	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
1	4	Jeremy Bender'	13	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
1	5	Battlefield'	11	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
1	6	Mass'	9	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
1	7	Lucky Man'	9	1	27	90	66	27	7	19	38	35	75	42	27	66	87	87	2	9	57	47	3	3
1	8	Lachesis'	8	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
1	9	Tank'	5	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
1	10	Bitches Crystal'	1	60	34	26	1	97	84	12	53	88	49	26	32	58	38	103	1	38	84	71	21	2
1	11	ORIGINAL'	0	7	88	2	66	27	26	19	38	35	75	42	8	66	10	87	2	1	57	10	3	10
1	12	Iconoclast'	-3	61	17	92	103	33	13	26	59	40	95	69	101	98	34	32	19	16	82	18	49	73
1	13	The Barbarian'	-7	58	5	63	62	71	55	78	94	103	22	33	51	72	61	20	53	49	34	53	37	56
1	14	Aquatarkus'	-7	21	50	103	21	78	73	93	79	104	35	65	65	47	66	92	65	15	93	39	88	92
1	15	Tarkus'	-9	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	91	1	5	10	5	10
1	16	Eruption'	-11	90	87	5	17	43	87	81	34	90	44	54	10	56	35	27	62	10	8	23	22	28
1	17	Knife Edge'	-16	54	99	55	16	90	33	65	3	98	34	10	87	5	81	64	9	94	15	37	13	104
1	18	Clotho'	-16	20	0	7	13	8	50	35	75	4	21	36	13	82	19	65	7	67	98	20	70	89
1	19	Manticore'	-18	90	12	73	90	16	100	26	3	5	97	44	69	63	59	0	92	51	9	29	47	35
1	20	Atropos'	-20	21	76	67	31	1	24	63	94	37	18	67	45	69	10	12	100	37	88	70	70	40
																								
2	1	Jeremy Bender'	16	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
2	2	The Three Fates'	15	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
2	3	Stones of Years'	14	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
2	4	Take a Pebble'	13	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
2	5	Mass'	11	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
2	6	Lucky Man'	11	7	70	90	20	27	7	5	2	35	8	42	8	10	87	53	5	1	5	47	4	10
2	7	Battlefield'	10	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
2	8	Tank'	9	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
2	9	Lachesis'	8	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
2	10	Iconoclast'	7	61	70	92	20	4	26	5	2	5	8	1	29	10	22	20	12	16	5	10	5	10
2	11	ORIGINAL'	7	7	88	2	66	27	26	19	38	35	75	42	8	66	10	87	2	1	57	10	3	10
2	12	Bitches Crystal'	-2	60	34	26	1	97	84	12	53	88	49	26	32	58	38	103	1	38	84	71	21	2
2	13	The Barbarian'	-6	58	5	63	20	4	26	5	2	5	15	1	8	72	10	20	5	1	34	10	37	56
2	14	Eruption'	-10	90	87	5	17	43	87	81	34	90	44	54	10	56	35	27	62	10	8	23	22	28
2	15	Aquatarkus'	-14	21	50	103	21	78	73	93	79	104	35	65	65	47	66	92	65	15	93	39	88	92
2	16	Atropos'	-15	21	76	67	31	1	24	63	94	37	18	67	45	69	10	12	100	37	88	70	70	40
2	17	Clotho'	-15	20	0	7	13	8	50	35	75	4	21	36	13	82	19	65	7	67	98	20	70	89
2	18	Manticore'	-17	90	12	73	90	16	100	26	3	5	97	44	69	63	59	0	92	51	9	29	47	35
2	19	Tarkus'	-20	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	91	1	5	10	5	10
2	20	Knife Edge'	-22	54	99	55	16	90	33	65	3	98	34	10	87	5	81	64	9	94	15	37	13	104
																								
3	1	Take a Pebble'	13	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
3	2	Stones of Years'	13	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
3	3	Lucky Man'	13	7	70	90	20	27	7	5	2	35	8	42	8	10	87	53	5	1	5	47	4	10
3	4	The Three Fates'	12	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
3	5	Battlefield'	10	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
3	6	Jeremy Bender'	10	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
3	7	Mass'	9	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
3	8	ORIGINAL'	9	7	88	2	66	27	26	19	38	35	75	42	8	66	10	87	2	1	57	10	3	10
3	9	Atropos'	8	7	70	2	20	4	25	63	94	37	18	1	45	10	10	12	5	37	5	40	5	52
3	10	Iconoclast'	3	7	70	92	20	27	7	5	2	35	8	1	8	10	87	53	5	1	5	47	5	10
3	11	Bitches Crystal'	0	60	34	26	1	97	84	12	53	88	49	26	32	58	38	103	1	38	84	71	21	2
3	12	The Barbarian'	0	60	34	26	1	4	84	8	53	88	15	1	8	58	38	103	5	38	84	10	37	37
3	13	Tank'	0	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
3	14	Lachesis'	0	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
3	15	Eruption'	-4	90	87	5	17	43	87	81	34	90	44	54	10	56	35	27	62	10	8	23	22	28
3	16	Aquatarkus'	-14	21	50	103	21	78	73	93	79	104	35	65	65	47	66	92	65	15	93	39	88	92
3	17	Tarkus'	-17	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	91	1	5	10	5	10
3	18	Clotho'	-17	20	0	7	13	8	50	35	75	4	21	36	13	82	19	65	7	67	98	20	70	89
3	19	Manticore'	-19	90	12	73	90	16	100	26	3	5	97	44	69	63	59	0	92	51	9	29	47	35
3	20	Knife Edge'	-29	54	99	55	16	90	33	65	3	98	34	10	87	5	81	64	9	94	15	37	13	104
																								
4	1	Lucky Man'	15	7	70	90	20	27	7	5	2	35	8	42	8	10	87	53	5	1	5	47	4	10
4	2	Jeremy Bender'	10	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
4	3	Stones of Years'	9	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
4	4	Bitches Crystal'	9	33	80	2	20	4	26	5	2	88	8	1	32	10	10	20	5	1	5	10	5	10
4	5	Iconoclast'	8	7	70	92	20	27	7	5	2	35	8	1	8	10	87	53	5	1	5	47	5	10
4	6	Battlefield'	8	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
4	7	ORIGINAL'	6	7	88	2	66	27	26	19	38	35	75	42	8	66	10	87	2	1	57	10	3	10
4	8	The Three Fates'	6	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
4	9	Take a Pebble'	5	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
4	10	Mass'	5	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
4	11	Tank'	3	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
4	12	Lachesis'	2	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
4	13	Manticore'	1	90	12	90	90	16	7	26	3	20	97	42	8	63	87	53	5	1	9	47	47	10
4	14	Atropos'	-2	7	70	2	20	4	25	63	94	37	18	1	45	10	10	12	5	37	5	40	5	52
4	15	Aquatarkus'	-5	21	50	103	21	78	73	93	79	104	35	65	65	47	66	92	65	15	93	39	88	92
4	16	The Barbarian'	-7	60	34	26	1	4	84	8	53	88	15	1	8	58	38	103	5	38	84	10	37	37
4	17	Eruption'	-13	90	87	5	17	43	87	81	34	90	44	54	10	56	35	27	62	10	8	23	22	28
4	18	Tarkus'	-17	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	91	1	5	10	5	10
4	19	Clotho'	-20	20	0	7	13	8	50	35	75	4	21	36	13	82	19	65	7	67	98	20	70	89
4	20	Knife Edge'	-23	54	99	55	16	90	33	65	3	98	34	10	87	5	81	64	9	94	15	37	13	104
																								
5	1	Lucky Man'	22	7	70	90	20	27	7	5	2	35	8	42	8	10	87	53	5	1	5	47	4	10
5	2	Mass'	19	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
5	3	Battlefield'	19	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
5	4	Take a Pebble'	18	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
5	5	Iconoclast'	18	7	70	92	20	27	7	5	2	35	8	1	8	10	87	53	5	1	5	47	5	10
5	6	Jeremy Bender'	18	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
5	7	ORIGINAL'	16	7	20	2	20	4	1	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
5	8	Bitches Crystal'	15	33	80	2	20	4	26	5	2	88	8	1	32	10	10	20	5	1	5	10	5	10
5	9	Stones of Years'	14	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
5	10	Lachesis'	14	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
5	11	The Three Fates'	12	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
5	12	Tank'	10	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
5	13	Manticore'	3	90	12	90	90	16	7	26	3	20	97	42	8	63	87	53	5	1	9	47	47	10
5	14	Atropos'	-5	7	70	2	20	4	25	63	94	37	18	1	45	10	10	12	5	37	5	40	5	52
5	15	The Barbarian'	-10	60	34	26	1	4	84	8	53	88	15	1	8	58	38	103	5	38	84	10	37	37
5	16	Eruption'	-27	90	87	5	17	43	87	81	34	90	44	54	10	56	35	27	62	10	8	23	22	28
5	17	Aquatarkus'	-27	21	50	103	21	78	73	93	79	104	35	65	65	47	66	92	65	15	93	39	88	92
5	18	Clotho'	-39	20	0	7	13	8	50	35	75	4	21	36	13	82	19	65	7	67	98	20	70	89
5	19	Tarkus'	-41	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	91	1	5	10	5	10
5	20	Knife Edge'	-49	54	99	55	16	90	33	65	3	98	34	10	87	5	81	64	9	94	15	37	13	104
																								
6	1	Take a Pebble'	29	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
6	2	Iconoclast'	29	7	70	92	20	27	7	5	2	35	8	1	8	10	87	53	5	1	5	47	5	10
6	3	Mass'	28	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
6	4	Battlefield'	27	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
6	5	Lucky Man'	26	7	70	90	20	27	7	5	2	35	8	42	8	10	87	53	5	1	5	47	4	10
6	6	Lachesis'	24	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
6	7	Jeremy Bender'	23	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
6	8	Bitches Crystal'	20	33	80	2	20	4	26	5	2	88	8	1	32	10	10	20	5	1	5	10	5	10
6	9	ORIGINAL'	20	7	20	2	20	4	1	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
6	10	Stones of Years'	18	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
6	11	Tank'	17	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
6	12	The Three Fates'	16	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
6	13	Manticore'	6	90	12	90	90	16	7	26	3	20	97	42	8	63	87	53	5	1	9	47	47	10
6	14	Atropos'	-3	7	70	2	20	4	25	63	94	37	18	1	45	10	10	12	5	37	5	40	5	52
6	15	The Barbarian'	-13	60	34	26	1	4	84	8	53	88	15	1	8	58	38	103	5	38	84	10	37	37
6	16	Aquatarkus'	-34	21	50	103	21	78	73	93	79	104	35	65	65	47	66	92	65	15	93	39	88	92
6	17	Eruption'	-42	90	87	5	17	43	87	81	34	90	44	54	10	56	35	27	62	10	8	23	22	28
6	18	Tarkus'	-59	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	91	1	5	10	5	10
6	19	Clotho'	-60	20	0	7	13	8	50	35	75	4	21	36	13	82	19	65	7	67	98	20	70	89
6	20	Knife Edge'	-72	54	99	55	16	90	33	65	3	98	34	10	87	5	81	64	9	94	15	37	13	104
																								
7	1	Iconoclast'	12	7	70	92	20	27	7	5	2	35	8	1	8	10	87	53	5	1	5	47	5	10
7	2	Lachesis'	12	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
7	3	Jeremy Bender'	10	7	70	92	20	27	7	5	2	35	8	1	8	10	10	20	5	1	5	47	5	10
7	4	ORIGINAL'	10	7	20	2	20	4	1	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
7	5	Mass'	10	7	70	47	20	27	26	5	2	35	8	1	8	10	87	53	5	1	5	47	5	10
7	6	Take a Pebble'	7	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
7	7	Tank'	6	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
7	8	Bitches Crystal'	6	33	80	2	20	4	26	5	2	88	8	1	32	10	10	20	5	1	5	10	5	10
7	9	Stones of Years'	4	7	70	2	20	4	26	46	88	46	8	1	8	10	10	20	5	1	5	10	5	10
7	10	Lucky Man'	4	7	70	90	20	27	7	5	2	35	8	42	8	10	87	53	5	1	5	47	4	10
7	11	The Three Fates'	3	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
7	12	Atropos'	1	7	70	2	20	4	25	63	94	37	18	1	45	10	10	12	5	37	5	40	5	52
7	13	Battlefield'	1	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
7	14	Manticore'	-1	90	12	90	90	16	7	26	3	20	97	42	8	63	87	53	5	1	9	47	47	10
7	15	The Barbarian'	-8	60	34	26	1	4	84	8	53	88	15	1	8	58	38	103	5	38	84	10	37	37
7	16	Knife Edge'	-12	54	99	55	16	90	33	65	3	98	34	10	87	5	81	64	9	94	15	37	13	104
7	17	Eruption'	-14	90	87	5	17	43	87	81	34	90	44	54	10	56	35	27	62	10	8	23	22	28
7	18	Aquatarkus'	-15	21	50	103	21	78	73	93	79	104	35	65	65	47	66	92	65	15	93	39	88	92
7	19	Clotho'	-17	20	0	7	13	8	50	35	75	4	21	36	13	82	19	65	7	67	98	20	70	89
7	20	Tarkus'	-19	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	91	1	5	10	5	10
																								
8	1	The Three Fates'	17	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
8	2	Battlefield'	13	7	70	2	20	27	26	5	2	35	8	1	8	10	10	20	5	1	5	47	5	10
8	3	Lucky Man'	10	7	70	90	20	27	7	5	2	35	8	42	8	10	87	53	5	1	5	47	4	10
8	4	Mass'	8	7	70	47	20	27	26	5	2	35	8	1	8	10	87	53	5	1	5	47	5	10
8	5	ORIGINAL'	8	7	20	2	20	4	1	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
8	6	Bitches Crystal'	6	33	80	2	20	4	26	5	2	88	8	1	32	10	10	20	5	1	5	10	5	10
8	7	Take a Pebble'	5	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
8	8	Jeremy Bender'	5	7	70	92	20	27	7	5	2	35	8	1	8	10	10	20	5	1	5	47	5	10
8	9	Lachesis'	4	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
8	10	Knife Edge'	4	2	70	55	20	47	29	46	88	98	8	10	8	10	81	64	5	1	5	10	9	10
8	11	Stones of Years'	4	7	70	2	20	4	26	46	88	46	8	1	8	10	10	20	5	1	5	10	5	10
8	12	Iconoclast'	2	7	70	92	20	27	7	5	2	35	8	1	8	10	87	53	5	1	5	47	5	10
8	13	Tank'	1	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	5	1	5	10	5	10
8	14	The Barbarian'	-4	60	34	26	1	4	84	8	53	88	15	1	8	58	38	103	5	38	84	10	37	37
8	15	Manticore'	-8	90	12	90	90	16	7	26	3	20	97	42	8	63	87	53	5	1	9	47	47	10
8	16	Atropos'	-9	7	70	2	20	4	25	63	94	37	18	1	45	10	10	12	5	37	5	40	5	52
8	17	Aquatarkus'	-12	21	50	103	21	78	73	93	79	104	35	65	65	47	66	92	65	15	93	39	88	92
8	18	Clotho'	-14	20	0	7	13	8	50	35	75	4	21	36	13	82	19	65	7	67	98	20	70	89
8	19	Tarkus'	-20	7	70	2	20	4	26	5	2	5	8	1	8	10	10	20	91	1	5	10	5	10
8	20	Eruption'	-20	90	87	5	17	43	87	81	34	90	44	54	10	56	35	27	62	10	8	23	22	28

The 6th parametrs has not been used by Evaluate, so it has no real meanings.

[Henk]

You can also use genetic optimization to learn the weights of a neural network.

[stegemma]

12th generation; the difference between strongest and weaker has diminished and the number of draw has augmented:

Code: Select all

11	1	Jeremy Bender'	11
11	2	Stones of Years'	7
11	3	The Three Fates'	7
11	4	Manticore'	7
11	5	Lachesis'	6
11	6	Tank'	6
11	7	ORIGINAL'	4
11	8	Mass'	4
11	9	Take a Pebble'	4
11	10	Aquatarkus'	3
11	11	Iconoclast'	3
11	12	Bitches Crystal'	3
11	13	Lucky Man'	2
11	14	Knife Edge'	2
11	15	Clotho'	1
11	16	Battlefield'	-2
11	17	Atropos'	-8
11	18	The Barbarian'	-13
11	19	Eruption'	-19
11	20	Tarkus'	-28

[stegemma]

You can also use genetic optimization to learn the weights of a neural network.

The mathematics around neural networks is too hard for me (and I like to fully understand what I'm doing), so I keep working on GA, for now.

[hgm]

I did not really see the benefit of all that math. It seems you don't need it at all. Just change the weight in proportion to their effect on the error. To efficiently do that, work your way back layer by layer, to firsr calculate the effect of changing the input of the layer, and then the effect of the weights of the previous layer on that input. That way you avoid having to propagate the effect of each weight through all layers that follow.

[stegemma]

I've stopped the learning session at the 13th generation. The best individual has only one parameter changed against ORIGINAL but I've seen that there are multiple parameters that my Evaluate function doesn't use anymore (I've removed one by one, time by time). This unused parameters slow down mutations, so I plan to re-start the session without them.

There are some other individual still stronger than ORIGINAL and with more different parameters than the strongest one.

This is the actual result of the learning session, without unused parameters:

Code: Select all

0	1	The Three Fates'	16	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
0	2	Battlefield'	14	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
0	3	Jeremy Bender'	13	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
0	4	Take a Pebble'	12	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
0	5	Tank'	12	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
0	6	Lucky Man'	12	1	27	66	19	35	75	27	66	87	87	2	9	57	47	3	3
0	7	Mass'	11	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
0	8	Stones of Years'	10	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
0	9	Lachesis'	8	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
0	10	ORIGINAL'	6	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
0	11	Tarkus'	4	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
0	12	Iconoclast'	-2	61	17	103	26	40	95	101	98	34	32	19	16	82	18	49	73
0	13	Bitches Crystal'	-5	60	34	1	12	88	49	32	58	38	103	1	38	84	71	21	2
0	14	The Barbarian'	-10	58	5	62	78	103	22	51	72	61	20	53	49	34	53	37	56
0	15	Aquatarkus'	-13	21	50	21	93	104	35	65	47	66	92	65	15	93	39	88	92
0	16	Eruption'	-13	90	87	17	81	90	44	10	56	35	27	62	10	8	23	22	28
0	17	Clotho'	-16	20	0	13	35	4	21	13	82	19	65	7	67	98	20	70	89
0	18	Manticore'	-18	90	12	90	26	5	97	69	63	59	0	92	51	9	29	47	35
0	19	Knife Edge'	-20	54	99	16	65	98	34	87	5	81	64	9	94	15	37	13	104
0	20	Atropos'	-21	21	76	31	63	37	18	45	69	10	12	100	37	88	70	70	40
																			
1	1	Stones of Years'	20	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
1	2	The Three Fates'	17	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
1	3	Take a Pebble'	14	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
1	4	Jeremy Bender'	13	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
1	5	Battlefield'	11	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
1	6	Mass'	9	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
1	7	Lucky Man'	9	1	27	66	19	35	75	27	66	87	87	2	9	57	47	3	3
1	8	Lachesis'	8	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
1	9	Tank'	5	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
1	10	Bitches Crystal'	1	60	34	1	12	88	49	32	58	38	103	1	38	84	71	21	2
1	11	ORIGINAL'	0	7	88	66	19	35	75	8	66	10	87	2	1	57	10	3	10
1	12	Iconoclast'	-3	61	17	103	26	40	95	101	98	34	32	19	16	82	18	49	73
1	13	The Barbarian'	-7	58	5	62	78	103	22	51	72	61	20	53	49	34	53	37	56
1	14	Aquatarkus'	-7	21	50	21	93	104	35	65	47	66	92	65	15	93	39	88	92
1	15	Tarkus'	-9	7	70	20	5	5	8	8	10	10	20	91	1	5	10	5	10
1	16	Eruption'	-11	90	87	17	81	90	44	10	56	35	27	62	10	8	23	22	28
1	17	Knife Edge'	-16	54	99	16	65	98	34	87	5	81	64	9	94	15	37	13	104
1	18	Clotho'	-16	20	0	13	35	4	21	13	82	19	65	7	67	98	20	70	89
1	19	Manticore'	-18	90	12	90	26	5	97	69	63	59	0	92	51	9	29	47	35
1	20	Atropos'	-20	21	76	31	63	37	18	45	69	10	12	100	37	88	70	70	40
																			
2	1	Jeremy Bender'	16	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
2	2	The Three Fates'	15	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
2	3	Stones of Years'	14	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
2	4	Take a Pebble'	13	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
2	5	Mass'	11	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
2	6	Lucky Man'	11	7	70	20	5	35	8	8	10	87	53	5	1	5	47	4	10
2	7	Battlefield'	10	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
2	8	Tank'	9	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
2	9	Lachesis'	8	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
2	10	Iconoclast'	7	61	70	20	5	5	8	29	10	22	20	12	16	5	10	5	10
2	11	ORIGINAL'	7	7	88	66	19	35	75	8	66	10	87	2	1	57	10	3	10
2	12	Bitches Crystal'	-2	60	34	1	12	88	49	32	58	38	103	1	38	84	71	21	2
2	13	The Barbarian'	-6	58	5	20	5	5	15	8	72	10	20	5	1	34	10	37	56
2	14	Eruption'	-10	90	87	17	81	90	44	10	56	35	27	62	10	8	23	22	28
2	15	Aquatarkus'	-14	21	50	21	93	104	35	65	47	66	92	65	15	93	39	88	92
2	16	Atropos'	-15	21	76	31	63	37	18	45	69	10	12	100	37	88	70	70	40
2	17	Clotho'	-15	20	0	13	35	4	21	13	82	19	65	7	67	98	20	70	89
2	18	Manticore'	-17	90	12	90	26	5	97	69	63	59	0	92	51	9	29	47	35
2	19	Tarkus'	-20	7	70	20	5	5	8	8	10	10	20	91	1	5	10	5	10
2	20	Knife Edge'	-22	54	99	16	65	98	34	87	5	81	64	9	94	15	37	13	104
																			
3	1	Take a Pebble'	13	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
3	2	Stones of Years'	13	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
3	3	Lucky Man'	13	7	70	20	5	35	8	8	10	87	53	5	1	5	47	4	10
3	4	The Three Fates'	12	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
3	5	Battlefield'	10	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
3	6	Jeremy Bender'	10	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
3	7	Mass'	9	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
3	8	ORIGINAL'	9	7	88	66	19	35	75	8	66	10	87	2	1	57	10	3	10
3	9	Atropos'	8	7	70	20	63	37	18	45	10	10	12	5	37	5	40	5	52
3	10	Iconoclast'	3	7	70	20	5	35	8	8	10	87	53	5	1	5	47	5	10
3	11	Bitches Crystal'	0	60	34	1	12	88	49	32	58	38	103	1	38	84	71	21	2
3	12	The Barbarian'	0	60	34	1	8	88	15	8	58	38	103	5	38	84	10	37	37
3	13	Tank'	0	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
3	14	Lachesis'	0	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
3	15	Eruption'	-4	90	87	17	81	90	44	10	56	35	27	62	10	8	23	22	28
3	16	Aquatarkus'	-14	21	50	21	93	104	35	65	47	66	92	65	15	93	39	88	92
3	17	Tarkus'	-17	7	70	20	5	5	8	8	10	10	20	91	1	5	10	5	10
3	18	Clotho'	-17	20	0	13	35	4	21	13	82	19	65	7	67	98	20	70	89
3	19	Manticore'	-19	90	12	90	26	5	97	69	63	59	0	92	51	9	29	47	35
3	20	Knife Edge'	-29	54	99	16	65	98	34	87	5	81	64	9	94	15	37	13	104
																			
4	1	Lucky Man'	15	7	70	20	5	35	8	8	10	87	53	5	1	5	47	4	10
4	2	Jeremy Bender'	10	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
4	3	Stones of Years'	9	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
4	4	Bitches Crystal'	9	33	80	20	5	88	8	32	10	10	20	5	1	5	10	5	10
4	5	Iconoclast'	8	7	70	20	5	35	8	8	10	87	53	5	1	5	47	5	10
4	6	Battlefield'	8	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
4	7	ORIGINAL'	6	7	88	66	19	35	75	8	66	10	87	2	1	57	10	3	10
4	8	The Three Fates'	6	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
4	9	Take a Pebble'	5	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
4	10	Mass'	5	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
4	11	Tank'	3	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
4	12	Lachesis'	2	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
4	13	Manticore'	1	90	12	90	26	20	97	8	63	87	53	5	1	9	47	47	10
4	14	Atropos'	-2	7	70	20	63	37	18	45	10	10	12	5	37	5	40	5	52
4	15	Aquatarkus'	-5	21	50	21	93	104	35	65	47	66	92	65	15	93	39	88	92
4	16	The Barbarian'	-7	60	34	1	8	88	15	8	58	38	103	5	38	84	10	37	37
4	17	Eruption'	-13	90	87	17	81	90	44	10	56	35	27	62	10	8	23	22	28
4	18	Tarkus'	-17	7	70	20	5	5	8	8	10	10	20	91	1	5	10	5	10
4	19	Clotho'	-20	20	0	13	35	4	21	13	82	19	65	7	67	98	20	70	89
4	20	Knife Edge'	-23	54	99	16	65	98	34	87	5	81	64	9	94	15	37	13	104
																			
5	1	Lucky Man'	22	7	70	20	5	35	8	8	10	87	53	5	1	5	47	4	10
5	2	Mass'	19	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
5	3	Battlefield'	19	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
5	4	Take a Pebble'	18	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
5	5	Iconoclast'	18	7	70	20	5	35	8	8	10	87	53	5	1	5	47	5	10
5	6	Jeremy Bender'	18	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
5	7	ORIGINAL'	16	7	20	20	5	5	8	8	10	10	20	5	1	5	10	5	10
5	8	Bitches Crystal'	15	33	80	20	5	88	8	32	10	10	20	5	1	5	10	5	10
5	9	Stones of Years'	14	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
5	10	Lachesis'	14	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
5	11	The Three Fates'	12	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
5	12	Tank'	10	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
5	13	Manticore'	3	90	12	90	26	20	97	8	63	87	53	5	1	9	47	47	10
5	14	Atropos'	-5	7	70	20	63	37	18	45	10	10	12	5	37	5	40	5	52
5	15	The Barbarian'	-10	60	34	1	8	88	15	8	58	38	103	5	38	84	10	37	37
5	16	Eruption'	-27	90	87	17	81	90	44	10	56	35	27	62	10	8	23	22	28
5	17	Aquatarkus'	-27	21	50	21	93	104	35	65	47	66	92	65	15	93	39	88	92
5	18	Clotho'	-39	20	0	13	35	4	21	13	82	19	65	7	67	98	20	70	89
5	19	Tarkus'	-41	7	70	20	5	5	8	8	10	10	20	91	1	5	10	5	10
5	20	Knife Edge'	-49	54	99	16	65	98	34	87	5	81	64	9	94	15	37	13	104
																			
6	1	Take a Pebble'	29	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
6	2	Iconoclast'	29	7	70	20	5	35	8	8	10	87	53	5	1	5	47	5	10
6	3	Mass'	28	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
6	4	Battlefield'	27	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
6	5	Lucky Man'	26	7	70	20	5	35	8	8	10	87	53	5	1	5	47	4	10
6	6	Lachesis'	24	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
6	7	Jeremy Bender'	23	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
6	8	Bitches Crystal'	20	33	80	20	5	88	8	32	10	10	20	5	1	5	10	5	10
6	9	ORIGINAL'	20	7	20	20	5	5	8	8	10	10	20	5	1	5	10	5	10
6	10	Stones of Years'	18	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
6	11	Tank'	17	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
6	12	The Three Fates'	16	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
6	13	Manticore'	6	90	12	90	26	20	97	8	63	87	53	5	1	9	47	47	10
6	14	Atropos'	-3	7	70	20	63	37	18	45	10	10	12	5	37	5	40	5	52
6	15	The Barbarian'	-13	60	34	1	8	88	15	8	58	38	103	5	38	84	10	37	37
6	16	Aquatarkus'	-34	21	50	21	93	104	35	65	47	66	92	65	15	93	39	88	92
6	17	Eruption'	-42	90	87	17	81	90	44	10	56	35	27	62	10	8	23	22	28
6	18	Tarkus'	-59	7	70	20	5	5	8	8	10	10	20	91	1	5	10	5	10
6	19	Clotho'	-60	20	0	13	35	4	21	13	82	19	65	7	67	98	20	70	89
6	20	Knife Edge'	-72	54	99	16	65	98	34	87	5	81	64	9	94	15	37	13	104
																			
7	1	Iconoclast'	12	7	70	20	5	35	8	8	10	87	53	5	1	5	47	5	10
7	2	Lachesis'	12	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
7	3	Jeremy Bender'	10	7	70	20	5	35	8	8	10	10	20	5	1	5	47	5	10
7	4	ORIGINAL'	10	7	20	20	5	5	8	8	10	10	20	5	1	5	10	5	10
7	5	Mass'	10	7	70	20	5	35	8	8	10	87	53	5	1	5	47	5	10
7	6	Take a Pebble'	7	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
7	7	Tank'	6	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
7	8	Bitches Crystal'	6	33	80	20	5	88	8	32	10	10	20	5	1	5	10	5	10
7	9	Stones of Years'	4	7	70	20	46	46	8	8	10	10	20	5	1	5	10	5	10
7	10	Lucky Man'	4	7	70	20	5	35	8	8	10	87	53	5	1	5	47	4	10
7	11	The Three Fates'	3	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
7	12	Atropos'	1	7	70	20	63	37	18	45	10	10	12	5	37	5	40	5	52
7	13	Battlefield'	1	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
7	14	Manticore'	-1	90	12	90	26	20	97	8	63	87	53	5	1	9	47	47	10
7	15	The Barbarian'	-8	60	34	1	8	88	15	8	58	38	103	5	38	84	10	37	37
7	16	Knife Edge'	-12	54	99	16	65	98	34	87	5	81	64	9	94	15	37	13	104
7	17	Eruption'	-14	90	87	17	81	90	44	10	56	35	27	62	10	8	23	22	28
7	18	Aquatarkus'	-15	21	50	21	93	104	35	65	47	66	92	65	15	93	39	88	92
7	19	Clotho'	-17	20	0	13	35	4	21	13	82	19	65	7	67	98	20	70	89
7	20	Tarkus'	-19	7	70	20	5	5	8	8	10	10	20	91	1	5	10	5	10
																			
8	1	The Three Fates'	17	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
8	2	Battlefield'	13	7	70	20	5	35	8	8	10	10	20	5	1	5	47	5	10
8	3	Lucky Man'	10	7	70	20	5	35	8	8	10	87	53	5	1	5	47	4	10
8	4	Mass'	8	7	70	20	5	35	8	8	10	87	53	5	1	5	47	5	10
8	5	ORIGINAL'	8	7	20	20	5	5	8	8	10	10	20	5	1	5	10	5	10
8	6	Bitches Crystal'	6	33	80	20	5	88	8	32	10	10	20	5	1	5	10	5	10
8	7	Take a Pebble'	5	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
8	8	Jeremy Bender'	5	7	70	20	5	35	8	8	10	10	20	5	1	5	47	5	10
8	9	Lachesis'	4	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
8	10	Knife Edge'	4	2	70	20	46	98	8	8	10	81	64	5	1	5	10	9	10
8	11	Stones of Years'	4	7	70	20	46	46	8	8	10	10	20	5	1	5	10	5	10
8	12	Iconoclast'	2	7	70	20	5	35	8	8	10	87	53	5	1	5	47	5	10
8	13	Tank'	1	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
8	14	The Barbarian'	-4	60	34	1	8	88	15	8	58	38	103	5	38	84	10	37	37
8	15	Manticore'	-8	90	12	90	26	20	97	8	63	87	53	5	1	9	47	47	10
8	16	Atropos'	-9	7	70	20	63	37	18	45	10	10	12	5	37	5	40	5	52
8	17	Aquatarkus'	-12	21	50	21	93	104	35	65	47	66	92	65	15	93	39	88	92
8	18	Clotho'	-14	20	0	13	35	4	21	13	82	19	65	7	67	98	20	70	89
8	19	Tarkus'	-20	7	70	20	5	5	8	8	10	10	20	91	1	5	10	5	10
8	20	Eruption'	-20	90	87	17	81	90	44	10	56	35	27	62	10	8	23	22	28
																			
9	1	Battlefield'	20	7	70	20	5	35	8	8	10	10	20	5	1	5	47	5	10
9	2	The Three Fates'	19	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
9	3	Lachesis'	19	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
9	4	Lucky Man'	17	7	70	20	5	35	8	8	10	87	53	5	1	5	47	4	10
9	5	ORIGINAL'	17	7	20	20	5	5	8	8	10	10	20	5	1	5	10	5	10
9	6	Mass'	17	7	70	20	5	35	8	8	10	87	53	5	1	5	47	5	10
9	7	Bitches Crystal'	15	33	80	20	5	88	8	32	10	10	20	5	1	5	10	5	10
9	8	Take a Pebble'	13	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
9	9	Tank'	13	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
9	10	Stones of Years'	11	7	70	20	46	46	8	8	10	10	20	5	1	5	10	5	10
9	11	Knife Edge'	10	2	70	20	46	98	8	8	10	81	64	5	1	5	10	9	10
9	12	Iconoclast'	5	7	70	20	5	35	8	8	10	87	53	5	1	5	47	5	10
9	13	Jeremy Bender'	4	7	70	20	5	35	8	8	10	10	20	5	1	5	47	5	10
9	14	Manticore'	-11	90	12	90	26	20	97	8	63	87	53	5	1	9	47	47	10
9	15	Atropos'	-14	7	70	20	63	37	18	45	10	10	12	5	37	5	40	5	52
9	16	The Barbarian'	-15	60	34	1	8	88	15	8	58	38	103	5	38	84	10	37	37
9	17	Aquatarkus'	-27	21	50	21	93	104	35	65	47	66	92	65	15	93	39	88	92
9	18	Clotho'	-30	20	0	13	35	4	21	13	82	19	65	7	67	98	20	70	89
9	19	Eruption'	-41	90	87	17	81	90	44	10	56	35	27	62	10	8	23	22	28
9	20	Tarkus'	-42	7	70	20	5	5	8	8	10	10	20	91	1	5	10	5	10
																			
10	1	Mass'	10	7	70	20	5	35	8	8	10	87	53	5	1	5	47	5	10
10	2	Tank'	9	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
10	3	The Three Fates'	8	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
10	4	Lucky Man'	8	7	70	20	5	35	8	8	10	87	53	5	1	5	47	4	10
10	5	Stones of Years'	8	7	70	20	46	46	8	8	10	10	20	5	1	5	10	5	10
10	6	Lachesis'	7	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
10	7	Take a Pebble'	7	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
10	8	ORIGINAL'	7	7	20	20	5	5	8	8	10	10	20	5	1	5	10	5	10
10	9	Jeremy Bender'	6	7	70	20	5	35	8	8	10	10	20	5	1	5	47	5	10
10	10	Atropos'	3	7	70	20	63	37	18	45	10	10	12	5	37	5	40	5	52
10	11	Iconoclast'	2	7	70	20	5	35	8	8	10	87	53	5	1	5	47	5	10
10	12	Bitches Crystal'	1	33	80	20	5	88	8	32	10	10	20	5	1	5	10	5	10
10	13	Knife Edge'	0	2	70	20	46	98	8	8	10	81	64	5	1	5	10	9	10
10	14	Aquatarkus'	-1	7	70	20	5	35	8	65	10	10	92	5	8	5	39	5	51
10	15	Battlefield'	-2	7	70	20	5	35	8	8	10	10	20	5	1	5	47	5	10
10	16	Clotho'	-6	20	20	20	5	5	8	8	10	19	20	16	28	51	20	5	10
10	17	Manticore'	-8	90	12	90	26	20	97	8	63	87	53	5	1	9	47	47	10
10	18	The Barbarian'	-8	60	34	1	8	88	15	8	58	38	103	5	38	84	10	37	37
10	19	Eruption'	-25	90	87	17	81	90	44	10	56	35	27	62	10	8	23	22	28
10	20	Tarkus'	-26	7	70	20	5	5	8	8	10	10	20	91	1	5	10	5	10
																			
11	1	Jeremy Bender'	11	7	70	20	5	40	8	8	10	10	20	5	1	5	10	5	10
11	2	Stones of Years'	7	7	70	20	46	46	8	8	10	10	20	5	1	5	10	5	10
11	3	The Three Fates'	7	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
11	4	Manticore'	7	90	12	90	26	20	97	8	63	87	53	5	1	9	47	47	10
11	5	Lachesis'	6	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
11	6	Tank'	6	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
11	7	ORIGINAL'	4	7	20	20	5	5	8	8	10	10	20	5	1	5	10	5	10
11	8	Mass'	4	7	70	20	5	35	8	8	10	87	53	5	1	5	47	5	10
11	9	Take a Pebble'	4	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
11	10	Aquatarkus'	3	7	70	20	5	35	8	65	10	10	92	5	8	5	39	5	51
11	11	Iconoclast'	3	85	70	20	46	46	8	8	10	10	20	5	1	5	47	24	10
11	12	Bitches Crystal'	3	33	80	20	5	88	8	32	10	10	20	5	1	5	10	5	10
11	13	Lucky Man'	2	7	70	20	5	35	8	8	10	87	53	5	1	5	47	4	10
11	14	Knife Edge'	2	2	70	20	46	98	8	8	10	81	64	5	1	5	10	9	10
11	15	Clotho'	1	20	70	20	5	35	8	8	15	19	20	16	28	5	47	5	10
11	16	Battlefield'	-2	7	70	20	5	35	8	8	10	10	20	5	1	5	47	5	10
11	17	Atropos'	-8	7	70	20	63	37	18	45	10	10	12	5	37	5	40	5	52
11	18	The Barbarian'	-13	60	34	1	8	88	15	8	58	38	103	5	38	84	10	37	37
11	19	Eruption'	-19	90	87	17	81	90	44	10	56	35	27	62	10	8	23	22	28
11	20	Tarkus'	-28	7	70	20	5	5	8	8	10	10	20	91	1	5	10	5	10
																			
12	1	Lachesis'	11	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
12	2	Take a Pebble'	10	7	70	20	46	46	8	8	10	10	20	5	1	5	64	5	10
12	3	Lucky Man'	9	7	70	20	5	5	8	8	10	10	20	5	1	5	10	4	10
12	4	Bitches Crystal'	7	33	80	20	5	88	8	32	10	10	20	5	1	5	10	5	10
12	5	Mass'	7	7	70	20	5	35	8	8	10	87	53	5	1	5	47	5	10
12	6	The Three Fates'	6	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
12	7	ORIGINAL'	5	7	20	20	5	5	8	8	10	10	20	5	1	5	10	5	10
12	8	Tank'	5	7	70	20	5	5	8	8	10	10	20	5	1	5	10	5	10
12	9	Jeremy Bender'	4	7	70	20	5	40	8	8	10	10	20	5	1	5	10	5	10
12	10	Stones of Years'	2	7	70	20	46	46	8	8	10	10	20	5	1	5	10	5	10
12	11	Aquatarkus'	2	7	70	20	5	35	8	65	10	10	92	5	8	5	39	5	51
12	12	Battlefield'	-1	7	70	20	5	35	8	8	10	10	20	5	1	5	47	5	10
12	13	Manticore'	-2	90	12	90	26	20	97	8	63	87	53	5	1	9	47	47	10
12	14	Clotho'	-3	20	70	20	5	35	8	8	15	19	20	16	28	5	47	5	10
12	15	Knife Edge'	-3	2	70	20	46	98	8	8	10	81	64	5	1	5	10	9	10
12	16	Iconoclast'	-4	85	70	20	46	46	8	8	10	10	20	5	1	5	47	24	10
12	17	Atropos'	-4	7	70	20	63	37	18	45	10	10	12	5	37	5	40	5	52
12	18	The Barbarian'	-6	60	34	1	8	88	15	8	58	38	103	5	38	84	10	37	37
12	19	Eruption'	-21	90	70	20	5	90	8	8	10	22	20	62	10	5	10	5	81
12	20	Tarkus'	-24	7	70	20	5	5	8	8	10	10	20	91	1	5	10	5	10