HidesFromHurricanes
Warrior
289 Posts
    
 | | 02/19/2006 7:48 AM |
| When commander ratings are equal we have an equal chance to win initiative. But what is the chance to win initiative based on difference in commander rating?
Difference % with Advantage % with Disadvantage
0 ............. 52.50 ................. 47.50
1 ............. 57.25 ................. 42.75
2 ............. 61.75 ................. 38.25
3 ............. 66.00 ................. 34.00
4 ............. 70.00 ................. 30.00
5 ............. 73.75 ................. 26.25
6 ............. 77.25 ................. 22.75
7 ............. 80.50 ................. 19.50
8 ............. 83.50 ................. 16.50
9 ............. 86.25 ................. 13.75
10 ............ 88.75 ................. 11.25
11 ............ 91.00 ................. 9.00
So the first row is a rather odd beast, Commander 0 vs no commander. The rest are fairly explanatory. So how did I get the values for the table? Well there are 400 combinations of initiative rolls, but there is an easily countable number of times the lower beats the higher commander rating. Start where the lower Commander rating rolls 20, there are 20 - D -1 rolls for the higher commander that lower commander wins. This goes down on per each roll until there is only one number where the lower commander wins. This sum works out to be (20-D-1)*(20-D)/2 different rolls where the lower commander rating beats the higher. Divide this number by 4(divide by 400 multiply by 100) to figure the percentage. This gives the third column and the second column is just the third subtracted from 100%. | |
Champion of Savage Bard (Unearthed Arcana: Bard Variant)
Bloodwars Called shot (vindicated) Demonic Gnoll Adept/Priestess
Old Jagermonster Saying: Any Plan vere you luz your hat iz a BAD Plan. | |
|
Tactician
Sergeant
888 Posts
| |
HidesFromHurricanes
Warrior
289 Posts
| | 02/19/2006 8:07 AM |
| quote:
Originally posted by Tactician
you need to edit your post[:p]
Edits done (sorry for the wonky table). So is what is the trick to posting tables? | |
Champion of Savage Bard (Unearthed Arcana: Bard Variant)
Bloodwars Called shot (vindicated) Demonic Gnoll Adept/Priestess
Old Jagermonster Saying: Any Plan vere you luz your hat iz a BAD Plan. | |
|
Vrecknidj
Warlord
10425 Posts
United States
| | 02/19/2006 10:00 AM |
| You can practice using the code tag. Just start a thread and use the tag around your table for a while, playing around with different spacing and tabs until you see how it works. Then delete your thread.
It took me a little while before I figured it out.
By the way, the odds of winning initiative get rather complicated because when two people get the same roll, the one with the higher commander rating wins.
I have an Excel table around here somewhere, that compares all the inits up to +15 v. +15.
Dave | |
Knowledge Arcana editor issues 5-9, Phoenix Lore Magazine editor, assistant editor for Rite Publishing;
My Trade Thread and My Reference Thread; Winner of WBC IV, IX and XIII; Rule #0: bshugg is always right! | |
|
HidesFromHurricanes
Warrior
289 Posts
| | 02/19/2006 10:47 AM |
| quote:
Originally posted by Vrecknidj
By the way, the odds of winning initiative get rather complicated because when two people get the same roll, the one with the higher commander rating wins.
I have an Excel table around here somewhere, that compares all the inits up to +15 v. +15.
Dave
But if you look at the difference in commander rating, it simplies to the table above. | |
Champion of Savage Bard (Unearthed Arcana: Bard Variant)
Bloodwars Called shot (vindicated) Demonic Gnoll Adept/Priestess
Old Jagermonster Saying: Any Plan vere you luz your hat iz a BAD Plan. | |
|
Vrecknidj
Warlord
10425 Posts
United States
| | 02/19/2006 10:53 AM |
| Oh right, your system is much simpler (and the one that I eventually realized was more convenient for analysis). I ended up doing away with that enormous file and just looking at differences.
Here's what I've come up with. High means, the chances of the one with the higher initiative modifier winning. Low means, the chances of the one with the lower initiative modifier winning. The X - (X-1) column is the change in the odds as the difference changes.
I'm ignoring the difference between a commander 0 and no commander.
Oh, and I'm using the code tags.
Diff High Low X - (X-1)<br>0 50 50 NA<br>1 57.5 42.5 7.5<br>2 61.75 38.25 4.25<br>3 66 34 4.25<br>4 70 30 4<br>5 73.75 26.25 3.75<br>6 77.25 22.75 3.5<br>7 80.5 19.5 3.25<br>8 83.5 16.5 3<br>9 86.25 13.75 2.75<br>10 88.75 11.25 2.5<br>11 91 9 2.25<br>12 93 7 2<br>13 94.75 5.25 1.75<br>14 96.25 3.75 1.5<br>15 97.5 2.5 1.25<br>16 98.5 1.5 1<br>17 99.25 0.75 0.75<br>18 99.75 0.25 0.5<br>19 100 0 0.25<br>
Dave | |
Knowledge Arcana editor issues 5-9, Phoenix Lore Magazine editor, assistant editor for Rite Publishing;
My Trade Thread and My Reference Thread; Winner of WBC IV, IX and XIII; Rule #0: bshugg is always right! | |
|
HidesFromHurricanes
Warrior
289 Posts
| | 02/19/2006 1:48 PM |
| quote:
Originally posted by Vrecknidj
Oh right, your system is much simpler (and the one that I eventually realized was more convenient for analysis). I ended up doing away with that enormous file and just looking at differences.
Here's what I've come up with. High means, the chances of the one with the higher initiative modifier winning. Low means, the chances of the one with the lower initiative modifier winning. The X - (X-1) column is the change in the odds as the difference changes.
I'm ignoring the difference between a commander 0 and no commander.
Thanks for the double check, our tables match. I really appreciate someone checking my work. And thanks for posting the code example Dave.
HfH | |
Champion of Savage Bard (Unearthed Arcana: Bard Variant)
Bloodwars Called shot (vindicated) Demonic Gnoll Adept/Priestess
Old Jagermonster Saying: Any Plan vere you luz your hat iz a BAD Plan. | |
|
HidesFromHurricanes
Warrior
289 Posts
| | 02/19/2006 1:54 PM |
| So what I find interesting was for example in the Water Bracket finals, you have Ghaele vs Dark Traveler (Difference 6). In one initiative out of four, the DT wins. If I could chose my one out of the first initiatives to win, it would be round 2. So one game in four with this match up Ghaele has a bad second round.
Also it looks like a Satyr improves your chances of winning initiative between 20- 25% overall when he uses his pipes. | |
Champion of Savage Bard (Unearthed Arcana: Bard Variant)
Bloodwars Called shot (vindicated) Demonic Gnoll Adept/Priestess
Old Jagermonster Saying: Any Plan vere you luz your hat iz a BAD Plan. | |
|
Dagni
Sergeant
870 Posts
| | 02/20/2006 1:45 AM |
| quote:
Originally posted by Vrecknidj
Diff High Low X - (X-1)<br>0 50 50 NA<br>1 57.5 42.5 7.5<br>2 61.75 38.25 4.25<br>3 66 34 4.25<br>4 70 30 4<br>5 73.75 26.25 3.75<br>6 77.25 22.75 3.5<br>7 80.5 19.5 3.25<br>8 83.5 16.5 3<br>9 86.25 13.75 2.75<br>10 88.75 11.25 2.5<br>11 91 9 2.25<br>12 93 7 2<br>13 94.75 5.25 1.75<br>14 96.25 3.75 1.5<br>15 97.5 2.5 1.25<br>16 98.5 1.5 1<br>17 99.25 0.75 0.75<br>18 99.75 0.25 0.5<br>19 100 0 0.25<br>
Dave
Did you copy his table, then add that extra column? Because it seems odd if you guys both made the same mistake. [:)]
I don't even need to run the numbers to know there's a mistake. The final column appropriately goes down by 0.25% every single time... except between commander difference of '1' vs '2' (and between 0 and 1, but that's due to the tiebreak rule). Therefore, that's a mistake. Specifically, there must be a 57.25% chance for a difference of 1, which checks out.
- Dagni | |
Proud member of the GRUUMSH fan club! | |
|
Pauper
Sergeant
508 Posts
| | 02/20/2006 2:01 AM |
| quote:
Originally posted by HidesFromHurricanes
Also it looks like a Satyr improves your chances of winning initiative between 20- 25% overall when he uses his pipes.
That's at best - if you're Piping from a -2 initiative disadvantge to a +2 advantage for a single round, you're nearly improving your winning chances by 25%. If you already have an advantage, especially an advantage of +3 or better, the added bonus from Pipes doesn't really increase your percentage odds all that significantly - sometimes less than 10%.
This also suggests that some bands I've seen, where the Satyr is paired with a Ghaele or Ryld or some other figure that is already likely to have a good initiative advantage (and sometimes then added with the Large Copper Dragon, seeking to 'max' the init edge) isn't the most effective use of the figure - or at least not that ability.
--
Pauper | |
Champion of the War Wizard of Cormyr | |
|
Vrecknidj
Warlord
10425 Posts
United States
| | 02/20/2006 8:38 AM |
| quote:
Originally posted by Dagni
Did you copy his table, then add that extra column? Because it seems odd if you guys both made the same mistake. [:)]
Yep, I copied his table.
I noticed that the differences seemed kinda wacky, but then I remembered that the last time I ran the numbers I saw that there was some unusual discrepancy. I didn't remember what it was, so I just convinced myself that this must have been it.
Teach me to not double-check. Good thing I don't get graded on this stuff anymore. [:)]
Dave | |
Knowledge Arcana editor issues 5-9, Phoenix Lore Magazine editor, assistant editor for Rite Publishing;
My Trade Thread and My Reference Thread; Winner of WBC IV, IX and XIII; Rule #0: bshugg is always right! | |
|
Wrackspawn
ChristopherGroves
Warlord
6093 Posts
| |
Wrackspawn
ChristopherGroves
Warlord
6093 Posts
| |