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Post by Brian Ború on Oct 2, 2022 14:31:57 GMT
The idea of this thread
When I started playing DBA I soon was fascinated by its easy game mechanics and its underlying mathematics.
Every now and then I will try to examine a part of them here, and I invite you to do the same and discuss these topics here.
Brian
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Post by Brian Ború on Oct 2, 2022 20:34:19 GMT
Shifting possibilities (Part I)One beautiful thing of DBA's combat mechanics is that units of slightly different strength behave very different in combat. This reflects their different way of training and fighting very well. Let's take a look at the following table. It shows the probability (in %) of a unit killing its adversary, holding the ground (no effect) or being recoiled, when both units are of the same type or fight each other with the same combat factor. (The first and second rows CF 0 or 1 are rather hypothetical or rare, but I put them in to complete the picture.) Combat Results Table 1: Units of the same CFCF of two
fighting units | unit kills or
is killed | no effect | a unit recoils | 0
| 25% | 17% | 17% | | 1 | 17% | 17% | 25% | | 2 | 11% | 17% | 31% | 3
| 6% | 17% | 36% | | 4 | 3% | 17% | 39% | | 5 and more | 0% | 17% | 42% |
Let's consider the outcome of two units of Psiloi fighting each other without any advantages. In only 17% of such fights they remain stationary, but each will kill the other in 11% or fight it back in most cases (31%). While the quite low probability of no effect remains always the same, we see one remarkable thing. The better the fighting units (high CF), the harder they are to kill, and the more they tend to recoil each other. Thus (we know it already from our battles) DBA simulates beautifully the pushing and shoving of units in the shieldwall etc. But these possibilities shift slower and slower the better the units are trained, and the outcome can be predicted even less. Will my blades recoil the enemy blades? Quite surely (with about 82%) they will move – but in which direction? Thus the simple DBA mechanics create action and even chaos from order and produce more and more tension.
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Post by Brian Ború on Oct 3, 2022 16:38:37 GMT
Shifting possibilities (Part II)
Now, what about units with combat factors that differ by 1 point? Imagine two units of the same type, e.g. one is uphill or on one side overlapped or Ax fighting Ps.
The next table shows the probabilities of such units killing or recoiling each other. Element A is stronger, element B weaker.
Combat Results Table 2: Units of slightly different CFs| Element A | Element B | A is killed | A recoils | no effect | B recoils | B is killed | | +1 | +0 | 11% | 17% | 14% | 25% | 33% | +2
| +1 | 6% | 22% | 14% | 33% | 22% | | +3 | +2 | 3% | 25% | 14% | 42% | 17% | | +4 | +3 | 0% | 28% | 14% | 47% | 11% | | +5 | +4 | 0% | 28% | 14% | 53% | 6% | | +6 | +5 | 0% | 28% | 14% | 56% | 3% | +7
etc.
| +6
etc. | 0% | 28% | 14% | 58% | 0% |
Table 2 reveals the same tendencies as table 1.
The units of lower level CF tend to kill or recoil each other quite often, so if you want a quick decision in battle, send the lighter troops against each other. But don't be angry if you loose.
The probabilities of killing each other shift slightly and diminish. Recoiling becomes more and more probable, while "no effect" stays always the same, but is slightly reduced to 14% throughout.
It is remarkable that from CFs 4 vs. 3 on and higher the stronger element cannot be killed and recoils always with the same probability of 28%, while the weaker element recoils in 47% of all cases and more.
Now when we think of overlaps and flank attacks between highly trained elements of the same type, the recoil (and kill) results become more probable (about 50% and much more!), and yet they are not inevitable. The overlapped unit may always escape by sheer luck in 28%+14%=42% of such dangerous cases.
Yes, DBA can be cruel sometimes, but you nevertheless still have your chances.
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Post by Brian Ború on Oct 9, 2022 8:57:57 GMT
Shifting possibilities (Part III)
Next we will have a closer look on combat factors that differ by 2 points.
Imagine two units of different type, like Bd and Ax, or two of the same type and one of them double overlapped, etc.
The next table shows again the probabilities of such units killing or recoiling each other. Again element A is stronger, B is weaker.
Combat Results Table 3: Units CFs differ by 2| Element A | Element B | A is killed | A recoils | no effect | B recoils | B is killed | | +2 | +0 | 3% | 14% | 11% | 31% | 42% | | +3 | +1 | 0% | 17% | 11% | 39% | 33% | | +4 | +2 | 0% | 17% | 11% | 47% | 25% | | +5 | +3 | 0% | 17% | 11% | 56% | 17% | | +6 | +4 | 0% | 17% | 11% | 61% | 11% | | +7 | +5 | 0% | 17% | 11% | 67% | 6% | | +8 | +6 | 0% | 17% | 11% | 69% | 3% | | +9 | +7 | 0% | 17% | 11% | 72% | 0% |
Once again the first and the last row of the table may be scarce in gameplay or even hypothetical, but they complete the picture. All in all in these game situations the stronger element almost never is killed directly, but the weaker is very likely to: the lower its CF the sooner. And once again the probability of recoiling the weaker unit becomes more and more probable, from about 1 of 3 to more than 2 of 3 cases, while the probabilities of recoiling the stronger unit or holding it on the spot remain throughout the same with 1 out of 6 and 1 of 10. Considering all these probabilities and the basic game mechanics one must come to the conclusion that although DBA uses dice throwing to a very large extent, the game mechanics nevertheless reduce the possibility of winning by sheer luck to a certain degree. In this way DBA is a quite well balanced game in which the use of the right strategy (i.e. disposition and movement of elements, the use of favorable terrain) becomes decisive.
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Post by stevie on Oct 9, 2022 10:31:28 GMT
Another thing that I discovered when I made my “ Combat Effects Chart for DBA & HoTT” (see:- static.wikia.nocookie.net/fanaticus-dba/images/e/e7/COMBAT_EFFECTS_CHART_for_DBA_%26_HOTT.pdf/revision/latest?cb=20190204191800 )is that giving a -1 to your enemy, from say an overlap, has a better effect on doubling chances than giving yourself a +1, say from being uphill or defending a riverbank. However, the DBA ‘roll-a-single-dice-each’ is rather limited and restricted in its outcome ranges. A mere +1 advantage will effectively double your chances of doubling and destroying the enemy, while a +2 advantage almost triples these chances…and the same if you are the one disadvantaged. Still, this is better than some other rules that require whole buckets of dice. (Honestly, I’ve seen some rules where I swear there were more dice on the table than figures!)But for me the beauty of DBA is that it’s a ‘ positional’ set of rules. The location and orientation of the elements gives you all the information you require to see the tactical advantages and disadvantages, without the need for fiddly time-consuming paperwork, or the need for messy unsightly on-table unit markers cluttering-up the battlefield. That alone for me makes DBA superior to some other rule-sets. And it’s quick to play…and reasonably historical as well (no rules will ever be 100% ‘realistic’). |
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Post by stevie on Oct 9, 2022 11:15:11 GMT
…oh, and as a follow-on to the above, here are my quick ‘in-game-estimations’ when I play:- If you DO have a ‘quick-kill’ = try to have a final combat factor (before dice rolling) of 1 less, or equal, or more than that of the enemy. If you DON’T have a ‘quick-kill’ = try to have a final combat factor (before dice rolling) of at least twice that of the enemy. (Twice the CF gives 9 chances out of 36 of a double,
which is pretty much the same as a ‘quick-kill’)Needless to say, try to prevent letting the enemy from having the above against you!  |
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Post by Brian Ború on Oct 9, 2022 14:32:15 GMT
Hah! Take this, Warhammer and 40K! |
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Post by Brian Ború on Nov 27, 2022 16:42:56 GMT
Quick kill possibilities (Part I): Blades and KnightsToday I want to take a closer look at some rather complex situations: the close combat of Bd and Kn or HCh. Both have peculiar quick kill possibilities. Blades (as Lb or Cb) will kill knights on an even score, while Kn will kill Bd (and any bows) if they get any higher score. The possiblities of killing or recoiling each other are these (depending on their combat factors): | CF Bd | CF Kn/HCh | Bd killed | Kn/HCh recoils | Kn/HCh killed | | +2 | +3 | 58% | 25% | 17% | | +3 | +3 | 42% | 42% | 17% | | +3 | +2 | 28% | 42% | 31% |
No wonder, Bd will very likely be the loser of such a fight. In the second and fourth row of the chart I assume that either Bd or Kn suffer a ‐1 because of an overlap. It is very interesting that if Bd want to meet Kn on even terms (last row, nearly the same chances of destroying each other), they need at least one overlap as a help. And the Bd certainly never recoils from Kn, instead they are ridden over. So what should Bd heavy armies do against Kn? Counter them with longbows, crossbows, light horse and elephants...
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