=============== OGRE/GEV list, April 9th (Last: April 5th) =============== ===== Fuzzy logic, quantum uncertainty and the locations of the nuked From: sdorr@ix.netcom.com (Scott David Orr) ===== Playing the Odds in Ogre/G.E.V., revisited From: Chris Camfield ===== New GEV game via E mail opening. ============================== To: "Henry J. Cobb" From: sdorr@ix.netcom.com (Scott David Orr) Subject: Fuzzy logic, quantum uncertainty and the locations of the nuked Henry J. Cobb wrote: >From: sdorr@ix.netcom.com (Scott David Orr) >But in any case, a tank hull-down behind a wall is NOT where the >miniature says the tank is -- otherwise, there'd be a big gap (hundreds >of meters) between the tank and the wall, making the wall effectively >useless as cover -- and therefore you can't really measure to the center >of the _mini_ to determine LOS. Indeed, because Ogre counters are >bigger than those of regular units, and infantry counters smaller, these >two types of units are, in effect, using different LOS rules than those >used by armored units. > > [But a few hundred meters is a reasonable distance to dash up and >make an attack, followed by a quick step back, no? Hmm...not quick, no; esp. for a tracked vehcile, that might take a couple of minutes. But as I see it, the real problem is, again, that for cover to be effective you have to be close to the cover; I suppose if it just blocks LOS, this would work, except for one thing: if you measure from the _top_ of the mini, you're going to get a bad reading, because in actuality the unit is at about ground level (since the miniature is far bigger than the unit -- at least it is in horizontal scale, but does this hold true of vertical too?). Scott Orr ----- [Nope, vertical scale of minis is correct, horizontal scale is off by a factor of a hundred or so. I still think that simply standing behind a wall, that the enemy can get exact laser measured distances to, is a bad ideal. All of these tanks are constantly moving. If you "fire at the gun flashes", you'll miss. -HJC] ------------------------------ From: Chris Camfield Subject: Playing the Odds in Ogre/G.E.V., revisited To: hcobb@slip.net (Henry J. Cobb) Hopefully some (if not most) of you are familiar with the article, Playing the Odds in Ogre/G.E.V., which appeared in the Ogre Book (and, I presume, an old Space Gamer issue). It gives a good summary of the different results produced by for instance one 2-1 attack, as compared with two 1-1 attacks. The 1-1s are better, whether the target is armour, infantry, or an Ogre. However, Roland Parenteau, who wrote the article, basically only considers the single-target situation, where you have several units which can join or separate their fire, but there is only one enemy unit within range. He didn't consider the chances of multiple X results being valuable, which is true when you are fighting a group of enemy units or an Ogre. The following is a few probability tables which include the possibility of getting multiple hits. In calculating these values, I assumed that if one hit disables an enemy armour unit, the next shot will also be at it, to try to get an X. For simplicity's sake, I have just considered armour and Ogre targets. My tables are rougher than Parenteau; the numbers listed are the chances out of 36 of an event occuring. It's still relatively straightforward... the chance of getting 2 X's when rolling two 1-2 attacks is 1/36: you have a 1/6 chance of getting the first hit, and then a 1/6 chance of getting the second hit, giving a product of 1/36. The "E" column deserves a little explanation. It's my version of expected value. I calculated this by totalling all the chances of getting a D *multiplied by 1/2*, together with all the chances of getting an X. 2X got multiplied by 2, X,D by 1.5, and so on. I admit that this is a little dicey; I should perhaps have given D a multiplier of 1/3, and assumed that if you get a D on one unit, your next shot fires at another target. In the final analysis (three 1-1s vs one 3-1), the numbers are chances out of 216. I divided the E values by 6 to make them comparable with the other attacks. What are the results, as compared with Parenteau's? Multiple attacks at low odds are MUCH better than a single attack at high odds. For instance, Parenteau shows gives two 2-1 attacks an 86% chance of X, and 11% chance of D, compared with a 4-1 which has 83% chance of X and 17% chance of D. But my expected value for two 2-1 attacks is MUCH higher than that for the 4-1. This is particularly important when comparing three 1-1 attacks vs one 3-1 attack against Ogres. Parenteau gives three 1-1 attacks a chance of 65% of scoring a hit, and one 3-1 attack has a 67% chance. But he must have gone wrong somewhere, because the odds of getting NE on three 1-1s is not 35%. (The chance is equal to 4/6 times 4/6 times 4/6, which is 64/216 or around 30%. The three 1-1s have a SMALLER chance of missing completely!) The expected value shows that three 1-1 attacks are much better than a single 3-1. Since two 1-1s are better than one 2-1, and three are better than one 3-1, I expect that four are better than one 4-1. What's interesting is how two 1-2 attacks are just about as good as one 1-1 attack. You have a slightly higher chance of missing completely, but gain the opportunity to get multiple hits. If you're in a desparate situation where you need to get rid of 2 targets, 1-2s are not so bad after all. Chris Camfield PS Notice the E values for attacks against Ogres. First, since there aren't any D values to consider, the weighting on the D values can't skew the results. Secondly, the E values of combined attacks sum, since there is no overlap over D results. That is, one 1-1 attack has E=12, two have E=24, three have E=36. That means we should expect four to have E=48, which is barely better than two 2-1s and like the 2-1s much better than one 4-1. vs Armour 2X X,D X D NE E Two 1-2s 1 1 10 8 16 17.5 One 1-1 -- -- 12 12 12 18 Two 1-1s 4 4 16 8 4 40 One 2-1 -- -- 18 12 6 24 Two 2-1s 9 6 16 4 1 45 One 4-1 -- -- 30 6 -- 33 vs Ogre 2X -- X -- NE E % of armor Two 1-2s 1 -- 10 -- 25 12 69 One 1-1 -- -- 12 -- 24 12 67 Two 1-1s 4 -- 16 -- 16 24 60 One 2-1 -- -- 18 -- 18 18 75 Two 2-1s 9 -- 18 -- 9 36 80 One 4-1 -- -- 30 -- 6 30 91 vs Armour 3X 2X,D 2X X,D X D NE E/6 Three 1-1s 8 8 56 40 72 24 8 50 One 3-1 -- -- -- -- 144 72 -- 30 vs Ogre 3X -- 2X -- X -- NE E/6 % of armor Three 1-1s 8 -- 48 -- 96 -- 64 36 72 One 3-1 -- -- -- -- 144 -- 72 24 80 Christopher Camfield - ccamfiel@uwaterloo.ca - 1996 BMath Joint CS/C&O "Do you need a new invention? Are you in the right dimension?" (The Jazz Butcher) ----- [I've added a new column, showing the reduced effectiveness of fire against OGREs (as percentage of effect against armor). Note that the OGRE advantage is more pronounced against multiple small attacks. (It's from calculations based on the smaller attacks that my original OGRE cost formula gave Ogre defense a 50% advantage over normal armor.) -HJC] Henry J. Cobb hcobb@io.com http://www.io.com/~hcobb All OGRE-related items Copyright (c) 1996, by Steve Jackson Games.