Post by knoffles on Jan 1, 2023 12:34:53 GMT
Post 13 - Soul of Stone Math-hammer
Credit to Celt @ Lustria: www.lustria-online.com/threads/soul-of-stone-mathhammer.15800/
At first glance soul of stone looked very unimpressive to me so I decided to do the math.
Since there are two dice and six ways of rolling each dice, the total number of dice roll combinations is 6*6 = 36. The highest sum possible is 6+6 = 12, and the lowest sum possible is 1+1 = 2. The full list of combinations for each sum is:
• 2: 1+1
• 3: 1+2, 2+1
• 4: 1+3, 2+2, 3+1
• 5: 1+4, 2+03, 3+2, 4+1
• 6: 1+5, 2+4, 3+3, 4+2, 5+1
• 7: 1+6, 2+5, 3+4, 4+3, 5+2, 6+1
• 8: 2+6, 3+5, 4+4, 5+3, 6+2
• 9: 3+6, 4+5, 5+4, 6+3
• 10: 4+6, 5+5, 6+4
• 11: 5+6, 6+5
• 12: 6+6
The probabilities of each sum are simply the number of ways divided by 36. Here they are:
• 2: 1/36 = 0.0278
• 3: 2/36 = 0.0556
• 4: 3/36 = 0.0833
• 5: 4/36 = 0.1111
• 6: 5/36 = 0.1389
• 7: 6/36 = 0.1667
• 8: 5/36 = 0.1389
• 9: 4/36 = 0.1111
• 10: 3/36 = 0.0833
• 11: 2/36 = 0.0556
• 12: 1/36 = 0.0278
Miscast:
2-4 Very bad
5-6 Bad
7 best for the wizard but not so much for your bunker (except maybe if your slann is in a skirmisher unit)
8-9 Bad for all your wizards (although your slann can take a wound and sometimes even heal it if necessary) but good if you are in an expensive temple guard bunker (no template)
10-12 Very bad for your slann!
These are your chances with a normal miscast
2-4. (2.78 + 5.56 + 8.33) 16.67%
5-6. (11.11 + 13.89) 25%
7. 16.67%
8-9. (13.89 + 11.11) 25%
10-12. (8.33 + 5.56 + 8.33) 16.67%
With soul of stone there are two different scenarios: 1. Your slann is in a temple guard bunker that you like to avoid being hit by a template with strength 10 hits. 2. Your slann is in a skirmisher unit and you like to preserve you slann and do not really care about a few skinks dying.
In option one you can change your table to the following:
2-3. Very bad
4-5. Bad (lots of strength 10 hits in your temple guard bunker)
6. Still bad (lots of strength 10 hits but at least your wizard does not get hit)
7-10. (Remember you can go up one or down one on your miscast roll) All your wizards get hit but no template!
11-12. Very bad for your slann
These are your chances:
2-3. (2.78 + 5.56) 8.84 % (half of the original!)
4-5 (8.33 + 11.11) 19.44% (your slann will live)
6. 13.89 % (your slann will live)
7-10. (16.67 + 13.89 + 11.11 + 8.33) 50% (1/2 chance that your bunker does not get hit and your Slann will be able to handle the strength 6 hit, this is double the chances from the original!)
11-12. (5.56 + 2.78) 8.34% (Half the chance of something really bad happening!)
If you have your slann in a skimisher unit and rather have some dead skinks and protect your slann you can change the table in this way:
2-3. Very bad
4-5. ok (You will lose a few skinks but your slann will live but might take a wound)
6-8. Good (You will lose a few skinks but your slann won’t get hit)
9-10. ok (Your slann will live but might take a wound as well as your other spell casters)
11-12. Bad!
These are your chances:
2-3 (2.78 + 5.56) 8.34%
4-5 (8.33 + 11.11) 19.44%
6-8 (13.89 + 16.67 + 13.89) 44.45%
9-10 (11.11 + 8.33) 19.44%
11-12 (5.56 + 2.78) 8.34%
Under these circumstances you actually have a (19.44 + 44.45 + 19.44) 83.33% chance of surviving without anything major happening (you might lose a few skinks or suffer a wound). That means only 16.77% of something bad happening compared to 33.34% without soul of stone!
Considering that soul of stone is only 30pts (which is likely to be 7-10% of your total slann cost and 1.25% of your total list costs in 2400pts) the changes in the odds both with and without a bunker look pretty solid to me, especially considering that it is not unlikely to miscast at least once during a game (unless maybe when using WD, but then you have to consider that you cast a lot of spells which in turn also increases the chance to miscast on 2 or 3 dice).
Credit to Celt @ Lustria: www.lustria-online.com/threads/soul-of-stone-mathhammer.15800/
At first glance soul of stone looked very unimpressive to me so I decided to do the math.
Since there are two dice and six ways of rolling each dice, the total number of dice roll combinations is 6*6 = 36. The highest sum possible is 6+6 = 12, and the lowest sum possible is 1+1 = 2. The full list of combinations for each sum is:
• 2: 1+1
• 3: 1+2, 2+1
• 4: 1+3, 2+2, 3+1
• 5: 1+4, 2+03, 3+2, 4+1
• 6: 1+5, 2+4, 3+3, 4+2, 5+1
• 7: 1+6, 2+5, 3+4, 4+3, 5+2, 6+1
• 8: 2+6, 3+5, 4+4, 5+3, 6+2
• 9: 3+6, 4+5, 5+4, 6+3
• 10: 4+6, 5+5, 6+4
• 11: 5+6, 6+5
• 12: 6+6
The probabilities of each sum are simply the number of ways divided by 36. Here they are:
• 2: 1/36 = 0.0278
• 3: 2/36 = 0.0556
• 4: 3/36 = 0.0833
• 5: 4/36 = 0.1111
• 6: 5/36 = 0.1389
• 7: 6/36 = 0.1667
• 8: 5/36 = 0.1389
• 9: 4/36 = 0.1111
• 10: 3/36 = 0.0833
• 11: 2/36 = 0.0556
• 12: 1/36 = 0.0278
Miscast:
2-4 Very bad
5-6 Bad
7 best for the wizard but not so much for your bunker (except maybe if your slann is in a skirmisher unit)
8-9 Bad for all your wizards (although your slann can take a wound and sometimes even heal it if necessary) but good if you are in an expensive temple guard bunker (no template)
10-12 Very bad for your slann!
These are your chances with a normal miscast
2-4. (2.78 + 5.56 + 8.33) 16.67%
5-6. (11.11 + 13.89) 25%
7. 16.67%
8-9. (13.89 + 11.11) 25%
10-12. (8.33 + 5.56 + 8.33) 16.67%
With soul of stone there are two different scenarios: 1. Your slann is in a temple guard bunker that you like to avoid being hit by a template with strength 10 hits. 2. Your slann is in a skirmisher unit and you like to preserve you slann and do not really care about a few skinks dying.
In option one you can change your table to the following:
2-3. Very bad
4-5. Bad (lots of strength 10 hits in your temple guard bunker)
6. Still bad (lots of strength 10 hits but at least your wizard does not get hit)
7-10. (Remember you can go up one or down one on your miscast roll) All your wizards get hit but no template!
11-12. Very bad for your slann
These are your chances:
2-3. (2.78 + 5.56) 8.84 % (half of the original!)
4-5 (8.33 + 11.11) 19.44% (your slann will live)
6. 13.89 % (your slann will live)
7-10. (16.67 + 13.89 + 11.11 + 8.33) 50% (1/2 chance that your bunker does not get hit and your Slann will be able to handle the strength 6 hit, this is double the chances from the original!)
11-12. (5.56 + 2.78) 8.34% (Half the chance of something really bad happening!)
If you have your slann in a skimisher unit and rather have some dead skinks and protect your slann you can change the table in this way:
2-3. Very bad
4-5. ok (You will lose a few skinks but your slann will live but might take a wound)
6-8. Good (You will lose a few skinks but your slann won’t get hit)
9-10. ok (Your slann will live but might take a wound as well as your other spell casters)
11-12. Bad!
These are your chances:
2-3 (2.78 + 5.56) 8.34%
4-5 (8.33 + 11.11) 19.44%
6-8 (13.89 + 16.67 + 13.89) 44.45%
9-10 (11.11 + 8.33) 19.44%
11-12 (5.56 + 2.78) 8.34%
Under these circumstances you actually have a (19.44 + 44.45 + 19.44) 83.33% chance of surviving without anything major happening (you might lose a few skinks or suffer a wound). That means only 16.77% of something bad happening compared to 33.34% without soul of stone!
Considering that soul of stone is only 30pts (which is likely to be 7-10% of your total slann cost and 1.25% of your total list costs in 2400pts) the changes in the odds both with and without a bunker look pretty solid to me, especially considering that it is not unlikely to miscast at least once during a game (unless maybe when using WD, but then you have to consider that you cast a lot of spells which in turn also increases the chance to miscast on 2 or 3 dice).