Simulhammer - Casting power with Book of Hoeth.

[Daeron]

Right. To get an idea of what we're up against, I tried to check the value of the book of Hoeth. I found it a bit hard to calculate so I thought I'd try to simulate it first. The simulator rolls a choosen number of dice for a spell and rerolls the lowest result if the spell is failed. This simulation was run roughly 100,000 times for each combination of cast value and number of dice used.

The simulator is available here:
http://warhammer.orderoftheathanor.eu/b ... hoeth.html

The results below give the total chance to cast a spell with the book of Hoeth, and then gives a table which shows the benefit that the book of hoeth has given.


Chance to case a spell with book of hoeth:
Castv\1 PD. . . . .2 PD. . . . .3 PD. . . . .4 PD. . . . .5 PD. . . . .6 PD
03+. . .88,8%. . . .99,6%. . . .100.%. . . .100.%. . . .100.%. . . .100.%
04+. . .74,9%. . . .98,1%. . . .99,9%. . . .100.%. . . .100.%. . . .100.%
05+. . .55,3%. . . .94,9%. . . .99,6%. . . .100.%. . . .100.%. . . .100.%
06+. . .30,4%. . . .89,2%. . . .98,8%. . . .99,9%. . . .100.%. . . .100.%
07+. . .00,0%. . . .80,6%. . . .97,3%. . . .99,7%. . . .100.%. . . .100.%
08+. . .00,0%. . . .68,1%. . . .94,4%. . . .99,3%. . . .99,9%. . . .100.%
09+. . .00,0%. . . .52,2%. . . .89,5%. . . .98,4%. . . .99,8%. . . .100.%
10+. . .00,0%. . . .35,6%. . . .82,7%. . . .96,7%. . . .99,6%. . . .99,9%
11+. . .00,0%. . . .20,0%. . . .73,1%. . . .93,8%. . . .99,0%. . . .99,9%
12+. . .00,0%. . . .07,4%. . . .61,8%. . . .89,8%. . . .98,1%. . . .99,7%
13+. . .00,0%. . . .07,4%. . . .48,7%. . . .83,8%. . . .96,4%. . . .99,4%
14+. . .00,0%. . . .07,4%. . . .36,0%. . . .76,3%. . . .93,7%. . . .98,7%
15+. . .00,0%. . . .07,4%. . . .25,1%. . . .67,1%. . . .90,0%. . . .97,8%
16+. . .00,0%. . . .07,3%. . . .17,3%. . . .57,1%. . . .85,0%. . . .96,1%
17+. . .00,0%. . . .07,3%. . . .13,3%. . . .46,1%. . . .78,6%. . . .93,9%
18+. . .00,0%. . . .07,4%. . . .13,4%. . . .36,8%. . . .71,1%. . . .90,4%
19+. . .00,0%. . . .07,5%. . . .13,3%. . . .29,3%. . . .62,8%. . . .86,0%
20+. . .00,0%. . . .07,5%. . . .13,1%. . . .23,9%. . . .53,9%. . . .80,9%



Bonus given by the book of hoeth (bonus compared to regular casting)
Castv\1 PD. . . . .2 PD. . . . .3 PD. . . . .4 PD. . . . .5 PD. . . . .6 PD
03+. . .22,1%. . . .02,3%. . . .00,0%. . . .00,0%. . . .00,0%. . . .00,0%
04+. . .24,7%. . . .06,4%. . . .00,4%. . . .00,0%. . . .00,0%. . . .00,0%
05+. . .22,2%. . . .11,7%. . . .01,4%. . . .00,1%. . . .00,0%. . . .00,0%
06+. . .13,9%. . . .17,0%. . . .03,4%. . . .00,4%. . . .00,0%. . . .00,0%
07+. . .00,0%. . . .22,4%. . . .06,4%. . . .00,9%. . . .00,0%. . . .00,0%
08+. . .00,0%. . . .26,6%. . . .10,6%. . . .02,0%. . . .00,2%. . . .00,0%
09+. . .00,0%. . . .24,5%. . . .15,6%. . . .03,6%. . . .00,5%. . . .00,0%
10+. . .00,0%. . . .18,9%. . . .20,1%. . . .06,5%. . . .01,2%. . . .00,1%
11+. . .00,0%. . . .11,6%. . . .23,0%. . . .09,8%. . . .02,3%. . . .00,3%
12+. . .00,0%. . . .04,6%. . . .24,3%. . . .13,6%. . . .03,8%. . . .00,7%
13+. . .00,0%. . . .04,6%. . . .22,8%. . . .17,6%. . . .06,2%. . . .01,3%
14+. . .00,0%. . . .04,6%. . . .18,4%. . . .20,5%. . . .09,1%. . . .02,4%
15+. . .00,0%. . . .04,6%. . . .13,0%. . . .22,0%. . . .12,1%. . . .03,9%
16+. . .00,0%. . . .04,6%. . . .08,4%. . . .21,9%. . . .15,5%. . . .05,8%
17+. . .00,0%. . . .04,5%. . . .05,9%. . . .19,4%. . . .18,4%. . . .08,2%
18+. . .00,0%. . . .04,6%. . . .05,9%. . . .16,3%. . . .19,9%. . . .10,9%
19+. . .00,0%. . . .04,6%. . . .05,9%. . . .12,5%. . . .20,0%. . . .13,5%
20+. . .00,0%. . . .04,7%. . . .05,7%. . . .09,1%. . . .19,0%. . . .15,7%

[Daeron]

If we compare these numbers with a 'safe' strategy from using the sac dagger, where we do not add a dice if we already rolled a 6, then it seems the sac dagger on its own scores the same power as the book of hoeth with the +1 to cast from the mages.

In the future, I'll do other strategies for the book of hoeth, such as the chance to prevent a misscast by rerolling a 6 (in case of a double 6).

[Dalamar]

Book of Hoeth can't reroll a six

[Daeron]

Oh? Can you clarify the rules for me then? I thought it permitted to reroll a single power dice.

[Dalamar]

It allows the user to reroll a single power dice per casting attempt and single dispel dice per dispel attempt with the exception of sixes. So it can't stop miscasts.

[Setomidor]

Very interesting stats, thank you very much!

Since the HE basically got a dagger-equivalent I'm hopeful that we get to keep ours. Point for point the Book is probably better, since we have to pay 25 + what ever models we kill, which in most cases means another 72 points for 12 dead spearmen (assuming max two extra dice per round).

[Daeron]

I had to make some corrections to account for irresistible force. The table has been updated and the simulator is now uploaded and provided in the OP.

[Rabidnid]

Could you do a comparison of the book of ashur? I'm debating the two. Thank you.

[Daeron]

I suppose I could.. but I don't know the rules for the book of Ashur

[Forumite]

I suppose I could.. but I don't know the rules for the book of Ashur

Expensive Arcane item in the core rulebook. +1 to both casting and dispel. I don´t think it´s anywhere near as powerful as the Book of Hoeth, +1 is weaker on average compared to rerolling a low die and the Book of Ashur doesn´t help against getting 1 or 2 on the power dice and failing due to "Not Enough Power".

[Daeron]

The benefit from the book of ashur

Castv\1 PD. . . . .2 PD. . . . .3 PD. . . . .4 PD. . . . .5 PD. . . . .6 PD
03+. . .16,7%. . . .02,8%. . . .00,0%. . . .00,0%. . . .00,0%. . . .00,0%
04+. . .16,7%. . . .05,6%. . . .00,5%. . . .00,0%. . . .00,0%. . . .00,0%
05+. . .16,7%. . . .08,3%. . . .01,4%. . . .00,1%. . . .00,0%. . . .00,0%
06+. . .16,7%. . . .11,1%. . . .02,8%. . . .00,3%. . . .00,0%. . . .00,0%
07+. . .16,7%. . . .13,9%. . . .04,6%. . . .00,8%. . . .00,1%. . . .00,0%
08+. . .00,0%. . . .16,7%. . . .06,9%. . . .01,5%. . . .00,2%. . . .00,0%
09+. . .00,0%. . . .13,9%. . . .09,7%. . . .02,7%. . . .00,5%. . . .00,1%
10+. . .00,0%. . . .11,1%. . . .11,6%. . . .04,3%. . . .00,9%. . . .00,1%
11+. . .00,0%. . . .08,3%. . . .12,5%. . . .06,2%. . . .01,6%. . . .00,3%
12+. . .00,0%. . . .05,6%. . . .12,5%. . . .08,0%. . . .02,6%. . . .00,5%
13+. . .00,0%. . . .00,0%. . . .11,6%. . . .09,7%. . . .03,9%. . . .01,0%
14+. . .00,0%. . . .00,0%. . . .08,3%. . . .10,8%. . . .05,4%. . . .01,6%
15+. . .00,0%. . . .00,0%. . . .05,6%. . . .10,8%. . . .06,9%. . . .02,5%
16+. . .00,0%. . . .00,0%. . . .03,2%. . . .09,9%. . . .08,2%. . . .03,6%
17+. . .00,0%. . . .00,0%. . . .01,4%. . . .08,3%. . . .09,1%. . . .04,8%
18+. . .00,0%. . . .00,0%. . . .00,0%. . . .06,2%. . . .09,3%. . . .06,0%
19+. . .00,0%. . . .00,0%. . . .00,0%. . . .03,9%. . . .08,7%. . . .07,0%
20+. . .00,0%. . . .00,0%. . . .00,0%. . . .02,2%. . . .07,5%. . . .07,7%



The difference:
- Green is a big advantage for book of hoeth
- Yellow is a small (but important) advantage for book of hoeth
- Red means book of Ashur is better
- Gray is negligible.

Castv\1 PD. . . . .2 PD. . . . .3 PD. . . . .4 PD. . . . .5 PD. . . . .6 PD
03. . . .05.6%. . . -00.4%. . . .00.0%. . . .00.0%. . . .00.0%. . . .00.0%
04. . . .08.2%. . . .01.0%. . . -00.1%. . . .00.0%. . . .00.0%. . . .00.0%
05. . . .05.6%. . . .03.3%. . . .00.0%. . . .00.0%. . . .00.0%. . . .00.0%
06. . . -02.9%. . . .06.0%. . . .00.6%. . . .00.0%. . . .00.0%. . . .00.0%
07. . . -16.7%. . . .08.5%. . . .01.8%. . . .00.1%. . . .00.0%. . . .00.0%
08. . . .00.0%. . . .09.8%. . . .03.7%. . . .00.5%. . . .00.0%. . . .00.0%
09. . . .00.0%. . . .10.5%. . . .05.8%. . . .01.0%. . . .00.2%. . . -00.1%
10. . . .00.0%. . . .07.9%. . . .08.3%. . . .02.2%. . . .00.3%. . . .00.0%
11. . . .00.0%. . . .03.3%. . . .10.6%. . . .03.6%. . . .00.7%. . . .00.0%
12. . . .00.0%. . . -01.0%. . . .11.8%. . . .05.7%. . . .01.3%. . . .00.2%
13. . . .00.0%. . . .04.6%. . . .11.2%. . . .07.9%. . . .02.3%. . . .00.3%
14. . . .00.0%. . . .04.6%. . . .10.0%. . . .09.8%. . . .03.5%. . . .00.8%
15. . . .00.0%. . . .04.6%. . . .07.5%. . . .11.5%. . . .05.4%. . . .01.5%
16. . . .00.0%. . . .04.7%. . . .05.2%. . . .12.1%. . . .07.1%. . . .02.2%
17. . . .00.0%. . . .04.6%. . . .04.4%. . . .11.5%. . . .08.9%. . . .03.5%
18. . . .00.0%. . . .04.7%. . . .05.9%. . . .10.2%. . . .10.3%. . . .04.9%
19. . . .00.0%. . . .04.7%. . . .05.8%. . . .08.7%. . . .11.3%. . . .06.6%
20. . . .00.0%. . . .04.7%. . . .05.7%. . . .06.8%. . . .11.5%. . . .08.2%


So you can see that the book of hoeth scales well with the difficulty of the spell and the number of dice that can be used, where the book of ashur weighs in pretty well in low cast value spells. It could be noted that part of the benefit from the book of hoeth lies in the increased chance for IF.

[Rabidnid]

Perfect, thank you.

[Rabidnid]

Well, I had my first game with the book and was remarkably underwhelmed. You have the potential to be lucky with it, but the average result is hardly worth the trouble. Loremasters can make better use of the points, though it might be worth it on a lvl 4