Book of Hoeth: Statistics & Tactics

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zuriel45
Posts: 67
Joined: Mon May 03, 2010 6:15 am

Re: Book of Hoeth: Statistics & Tactics

#31 Post by zuriel45 »

Question, and maybe its been asked and answered. Why does IF increase as the casting cost goes higher? Shouldn't IF only increase as the number of dice increase, or if a die is rerolled for BoH? I noticed this on the big chart of all casting values and dice.

Very nicely done overall though.
daid13
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Location: oxfordshire, albion

Re: Book of Hoeth: Statistics & Tactics

#32 Post by daid13 »

Because it increases the chance that you will roll a 6 and still be under the casting cost. An example would be if you need to roll a 8 on 2D6 the chance is 1 in 18 that you will roll a 1 and 6 but if you need 10 on 2D6 you have 1 in 6 chance of getting under 10 with a 6 and then for both senarios you then have a 1 in 6 chance of rolling a 6 which means a 1 in 108 Ithink and a 1 in 36 chance to miscast because of the reroll respectively.
zuriel45
Posts: 67
Joined: Mon May 03, 2010 6:15 am

Re: Book of Hoeth: Statistics & Tactics

#33 Post by zuriel45 »

Daid13: I'm not entirely sure if you're interpreting my question correctly or not. What i was trying to point out is that for some of the chart, the IF seems to increase as the casting cost increases, which doesn't make sense (at least to me).

For example lets say your rolling two dice (no book), your chance of IF if always going to be 1/36, regardless of casting cost. In turn 3D6 has a 216 possible combinations, 18 of which are considered IF, giving you a 1/12 chance of IF. The odds of rolling those 18 combinations would be independent of casting cost.

Of course throwing in the book would change the odds of IF to be dependent on casting cost as the player is (unlikely) to reroll a die if the casting cost has been reached (though it is conceivable that a spell going off could be so valuable that someone would intentionally aim for IF).
Worloch
Posts: 183
Joined: Fri Nov 30, 2007 9:44 pm

Re: Book of Hoeth: Statistics & Tactics

#34 Post by Worloch »

zuriel45 wrote:Daid13: I'm not entirely sure if you're interpreting my question correctly or not. What i was trying to point out is that for some of the chart, the IF seems to increase as the casting cost increases, which doesn't make sense (at least to me).

For example lets say your rolling two dice (no book), your chance of IF if always going to be 1/36, regardless of casting cost. In turn 3D6 has a 216 possible combinations, 18 of which are considered IF, giving you a 1/12 chance of IF. The odds of rolling those 18 combinations would be independent of casting cost.

Of course throwing in the book would change the odds of IF to be dependent on casting cost as the player is (unlikely) to reroll a die if the casting cost has been reached (though it is conceivable that a spell going off could be so valuable that someone would intentionally aim for IF).

You basically answered your own question - from the first post:
Jadex wrote:(Mind the "note" here though: calculations are made assuming you only use the reroll when your initial casting result is below the required casting value and you reroll the lowest die. You can increase your IF chances - as well as your casting total in general (without necessarily getting IF) - when you start rerolling dice even if you met the required casting value.)
The interaction with IF there is pretty interesting. As your CV increases, the amount of possibilities that equal or exceed your target number diminish for a given set of PD, increasing the likelihood that you will re-roll a die with the BoH. As you add PD, the chance you will roll 6's goes up, increasing the chance that you will IF natively, but also increasing the chance that you will have a single 6 in the set to match a BoH re-roll against, again increasing the chance for IF.
PadForce
Posts: 180
Joined: Wed Aug 18, 2010 1:21 pm

Re: Book of Hoeth: Statistics & Tactics

#35 Post by PadForce »

Very helpful charts chaps, cheers for the hard work.
Eirik
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Re: Book of Hoeth: Statistics & Tactics

#36 Post by Eirik »

Hi. I did some math with respect to Book of Hoeth probabilities and the average die roll increase when using it.

I find that using the Book of Hoeth does affect your probability of casting successfully similar to having +2 to cast for 2 or more dice, but it does not affect your average casting result by +2. In general the increase to your average casting result is much less. The reason for this is that your casting result is generally only being increased about half the time, when you actually use the reroll.

For example, I simulated 10,000 rolls requiring 2 dice to roll 7 or higher for a successful casting. Similar to your results, I get 81% success rate with the book, however, the average roll works out to about 7.86, an average increase of 0.86. When rolling 3 dice and requiring a 9 or higher, I get a 90% success rate with Book of Hoeth just like you, but an average dice result of 11.1 with the book, which is an increase of about 0.6. When rolling 3 dice to get 11 or higher, I confirm your 73% success rate, but get an average roll of 11.6, an average increase of about 1.1 to your total die roll using the book.

For purposes of reaching a casting value the book is similar to a +2, but for purposes of total casting value it is actually much lower. It would almost be more accurate to say "The Book of Hoeth is similar to having a casting value 2 points lower."

I imagine that the averages I have given here would increase slightly if I were rolling less conservatively and trying to get my value up when I could do so without the risk of miscast or failed cast, for example, when I rolled [1,5,5] on 3 dice, but not by much. I might try to calculate the theoretical maximum for each number of dice, it seems like a question for a 1st or 2nd year university stats course.
Ah, Floorhammer. A time honored tradition. Sadly, I no longer play since my brother tripped and right-angled the spears of a 15-man regiment.
-Original Dragon Prince, July 2011
Andros123
Posts: 263
Joined: Wed Jan 29, 2014 7:30 am

Re: Book of Hoeth: Statistics & Tactics

#37 Post by Andros123 »

I agree great work!

I just had some thoughts, that I wanna share and hear your opinions.
When looking at the tables it becomes clear, that we get most out of the book (incr. change) when taking very risky rolls (around 50 %). Then the book gives an extra 20-25 %. However, the caster will be in danger of suffering from loss of concentration and all is lost. At the other end, it can be seen that their is nothing to be gained from the book if you are very afraid of risk.
As pointed out in the beginning of this thread, the combination of a lvl. 4 AM with the BoH and rolling with 1 die for the smaller High magic spells is awesome. Your opponent will at least need 2-3 of his dispel dice if he wants to dispel it. That is a way of getting of a lot of spells (and wards!). However, in my mind, taking a support mage when using the BoH is simply a must. You need to throw your spells with some risk involved, so you need to have a backup mage.
So the question is, what is the "optimal risk" of running when having the book. On one hand you don't want to suffer from loss of concentration, but on the other you also wanna see some value of the book and difficult choices to make for your opp. What do you think?

Another thought is that you can actually also use to book to re-roll dice, even if you got the spell of in the first place. Maybe you want to re-roll a die if it is a 1 or a 2, just to get the overall casting value higher, so it is more difficult to dispel. Have anyone tried this?

I thought about going with a lvl. 4 with BoH and 2 lvl. 1 with channelling staff and forbidden rod, to really set the magic phase on fire. I think I should be able to get of 4-5 spells per turn at least. Is this stupid stupid?
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