Steve Lloyd
United Kingdom

Just finished playing the newer version of Britannia (with yellow Romans etc) for the first time and had a blast. Really enjoyed some of the new twists, such as Boudicca, Roman roads and RBs substituting the forts rather than the legions  the last two had already occurred to me to use as house rules with my old AH version, so I'm glad to see my hunch made sense.
One thing that puzzles me reading some of the more recent posts, is how the Roman goes about subjugating the Welsh, the Brigantes AND the Picts, which some players claim to be able to do routinely. In this game just played, the Roman player (who admittedly was new to the game and didn't have the luck of the dice to boot) had a dreadful time with Boudicca and didn't subjugate anyone. The best I've ever achieved is subjugation of the Brigantes and, if I'm lucky, denting the Picts in Alban and Mar, but never enforced subjugation of the latter, and I've never had the resources to do anything but skirmish with the Welsh on the borders.
Does anyone have a killer 1  3 turn strategy for the Romans that, with even luck, achieves all these subjugations?


Ken
United States Crystal Lake Illinois

If you're going to subjugate the Welsh, you're probably going to do it during the MI. You can get to Devon and Gwent on the first impulse, then to Dyfed & Powys on the second. Unless you have really bad dice, that puts the Welsh in a bind  they can either submit or risk losing big population growth & points.
The Belgae are the easiest  just overrun them on your way north. Try to be careful not to let them break your road network when they revolt or you'll end up with major problems getting sufficient force to hit the Picts.
The Picts require a bit of luck and a great deal of planning. To submit them, you realistically must be in Cheshire/York at the end of your MI. If you can get to either Cumbria or Bernicia, that's even better (the latter more than the former). If you've subjugated the Welsh, that sets you up to slam the Brigantes on turn 2 and take a whack at Dunedin to stage for the Picts. Turn 3 allows you to focus strictly on the Picts if you pull that off.
It's not really all that hard. An intractable Welsh player can screw you up, but they risk an immense amount doing so. Bad dice are more likely to be the problem.


Philip Jelley
United Kingdom Hungerford Berkshire

Also try 21 odds to ensure victory, nothing screws up the timetable like a lucky six knocking out a legion.
Philip


Ken
United States Crystal Lake Illinois

Philip Jelley wrote: Also try 21 odds to ensure victory, nothing screws up the timetable like a lucky six knocking out a legion.
I suppose I sort of assumed that, didn't I? I generally try avoiding 1:1 at just about any cost. Particularly if there's a fight in the highlands. I'd far prefer 3:1 there to a 2:1 there and a 1:1 in the clear.


Steve Lloyd
United Kingdom

Thanks Guys. I should say that I missed the extensive thread a bit further down the strategy forum that debates this very topic when I posted this question.
I like the look of the Welsh strategy that says:
 Turn 11, take Devon  Turn 12, put 2 legions on Dyfed and 2 in Powys  Complete the attack in Dyfed  Then have a frank discussion with Green about how you really don't want to hit Powys, as a weak Wales is not in Yellow/Purple's interest, but if he doesn't submit now, thats whats going to happen (pointing out how easy it will then be to hit Gwynedd on the following turn, and how reasonable life under the Roman yoke will be).
I'll have to give that a bash next time we play and see whether it impacts the Brig/Pict schedule. The only fly in the ointment is that I won the last game, and my gaming circle are already always suspicious of any "this really is in both our interests" arguments that I make during games like this. So Green might just play hardball just to spite me.


Ken
United States Crystal Lake Illinois

steelyvoid wrote:  Turn 11, take Devon
I'd tend to add Gwent to this, myself. Then hitting Gwent & Powys in 12 means that there's no retreat possible from Gwent, making it a fight against Romans in the clear. That increases the pressure to submit.
Quote: as a weak Wales is not in Yellow/Purple's interest,
It's not, but it's worth noting that this is more a strategy for the FFG version than earlier ones. Without the Roman roads, penetrating Wales can lock forces into places where you don't want them. I have seen Welsh submissions in the AH version, but nowhere near as often and the Romans almost always end up being forced to pass on Pictish lands/submission.
Quote: So Green might just play hardball just to spite me.
If he does, just watch the Red point totals over the game. Fighting the Romans usually creates opportunities for the Irish in Wales and opens some flexibility for the Saxons.


Steve Lloyd
United Kingdom

perfalbion wrote:
I'd tend to add Gwent to this, myself. Then hitting Gwent & Powys in 12 means that there's no retreat possible from Gwent, making it a fight against Romans in the clear. That increases the pressure to submit.
Perhaps, but I always get the jitters attacking hilands as the Romans turn one. Too high a risk of taking big casualties early on. I'd rather open up routes to Wales's lowlands and use the threat of taking those (with minimal force) as a lever for submission.
Quote: Quote: as a weak Wales is not in Yellow/Purple's interest, It's not, but it's worth noting that this is more a strategy for the FFG version than earlier ones. Without the Roman roads, penetrating Wales can lock forces into places where you don't want them. I have seen Welsh submissions in the AH version, but nowhere near as often and the Romans almost always end up being forced to pass on Pictish lands/submission. Absolutely. I wouldn't dream of trying this strategy without Roman Roads.


Ken
United States Crystal Lake Illinois

steelyvoid wrote: Too high a risk of taking big casualties early on.
Picking a nit  it's no higher than fighting in the clear in terms of suffering a loss. And since you can control the odds before retreats happen, odds of a Welsh retreat from even a 2:1 are pretty good. You stand a 25 in 36 chance of hitting every round to 12 in 36. If he doesn't get lucky round 1 as you miss, I'd bet he runs. And forcing him to run to Powys or Gwent is OK. If he goes for Powys, just move one area north to make submission attractive.


Steve Lloyd
United Kingdom

Sure  the changes of taking a loss in any combat round are the same. The issue for me is the increased likelihood of it going to two or more rounds.
If I were Wales and thinking of toughing it out (having survived the first combat round), I'd be quite tempted on staying put and putting a bit of pressure on the Roman to give up the fight  especially if I'd rolled a 6 on the first round. By contrast, if I'm Wales defending an open space with 1 guy against 2 Romans and get lucky in the first round (killing one Roman without taking a hit myself) I'm still likely to retreat on the second round as the odds are still significantly against me winning the combat overall.


Lewis Pulsipher
United States Linden North Carolina

In tournaments, Romans tend to make a deal to submit the Welsh without actually fighting them much, then rush north. This aggravates the *&*&%^ out of me because it's so ahistorical, so in the new edition you have to beat the Welsh down, not have them withdraw to five and then submit (no one can abandon an area). The Welsh also play after the first half of the Roman invasion, then the Romans play the second half. And they get Caratacus. But for all that, the Romans still do fine, just not as well as in the FFG version.
Lew (the designer)


Ken
United States Crystal Lake Illinois

steelyvoid wrote: ...especially if I'd rolled a 6 on the first round.
Well, now we're in the "bad dice" caveat I had in my first post. And while you want to be as prepared for that as you can (or good dice, if you are the Welsh), planning strategy around it isn't the best of ideas. The events we're talking about now (Romans miss, Welsh hit) are about a 10% likelihood.
But it's worth noting that if this is what you're worried about, getting in to Gwent on the first impulse should be more important, not less. If you only hit Devon and this result occurs, you then are in an evenup fight. If you lose it (or decide to withdraw to come back in greater strength), you can't even get access to Dyfed during your second impulse  submitting the Welsh now requires hitting two highlands or waiting for turn 2.
If I want to be sure submit the Welsh, I'd prefer not to have the 1 in 10 derail the rest of the plan, so I go for the two areas on the first impulse.


Steve Lloyd
United Kingdom

perfalbion wrote: And while you want to be as prepared for that as you can (or good dice, if you are the Welsh), planning strategy around it isn't the best of ideas.
I think this is where we have to agree to disagree. Perhaps I'm just risk averse (alright, I am risk averse), but my aim in all games I play is to make strategy sufficiently luckindependent so that, if disaster strikes on the very first turn of the game, there is a backup plan.
For instance, if I have a disastrous time in Devon in 11 (having lined up 3 legions against one Welshman) and end up with one legion against one Welshman (Wales rolls 2 sixes before I can roll one), then at least I have the option of switching strategy to "don't bother attempting to subjugate Wales  focus my reduced force in 12 on dispatching the Belgae + starting on the Brigs, and just accept the fact that Wales will burn a few forts". Two guys spent on a slightly risky (to my mind) attempt to take Gwent are two guys I desperately need elsewhere, when pressure on Powys might achieve the same end by itself.
Horses for courses I guess.


Steve Lloyd
United Kingdom

lewpuls wrote: (no one can abandon an area)
Interesting  are you saying that, in tournament play, Wales often deliberately abandons areas so that he can submit to the Romans? I agree that that does sound a bit rubbish  I think I'd want to put up at least some resistance to Roman attack if I were Green if only because a few lucky rolls and the Roman will be forced to give up anyway and maintain an uneasy truce on the border.
I have to say I find the FFG rules a big improvement on the AH ones from an historical perspective in this area  I've never seen a Welsh submission in the AH rules despite playing them many times (and surely submission, following the Roman campaign in North Wales that ended with all those druids being slaughtered in Anglesey, was actually what happened).


Ken
United States Crystal Lake Illinois

steelyvoid wrote: I think this is where we have to agree to disagree . Perhaps I'm just risk averse (alright, I am risk averse), but my aim in all games I play is to make strategy sufficiently luckindependent so that, if disaster strikes on the very first turn of the game, there is a backup plan.
I understand. I'm just pointing out that having two attacks where each as a 10% chance of disaster makes it very unlikely that both will become disasters. If you're planning to avoid risk, then my suggestion actually reduces it rather than increasing it.
I certainly wouldn't recommend going 1:1 against the Welsh in the highlands. The odds are simply too good for them to retreat compared to the inevitable followup attack.


Steve Lloyd
United Kingdom

FWIW, I've just been reading up on some of the probability work I did at college and have done some calculations to work out likelihoods of various outcomes
 With 1 Roman against one Welshman in highlands, the chance that the Welshman wins and the Roman dies (or vice versa) is 5/11 (45.45%) with a 1/11 (9.1%) chance of simultaneous annihilation.  With 2 Romans against one Welshman in highlands, the chance that Green will roll a 6 before Yellow does is about 27.47% (25/91). Therefore the chance that the Welshman wipes out both Romans and survives is 25/91 x 5/11 = 12.49%  With 3 Romans against one Welshman in highlands, the chance that Green will roll a 6 before Yellow does is about 18.63% (125/671), so the chance that Green does this and then manages to get the next 6 as well (without reply) is the two percentages multiplied together  roughly 5.1%  and the chance that the Welshman kills them all and survives is about 2.34%
 With 1 Roman against one Welshman in the clear, the chance that the Roman wins (i.e. is alive at the end of the turn with the Welshman dead) is 5/7 (71.43%), the chance that the Welshman wins is 1/7(14.29%) and the chance of a simultaneous annihilation is also 1/7 (14.29%)  With 2 Romans against one Welshman in the clear, the chance that the Welshman kills one of the Romans without being killed himself is 1/19 (5.26%), so the chance of the Welshman taking both Romans out without dying is 1/133 or 0.75%


Ken
United States Crystal Lake Illinois

steelyvoid wrote:  With 2 Romans against one Welshman in highlands, the chance that Green will roll a 6 before Yellow does is about 27.47% (25/91). Therefore the chance that the Welshman wipes out both Romans and survives is 25/91 x 5/11 = 12.49%
There's something about this that isn't adding up. 91 isn't a number I would have expected to see here  it should be a multiple of 6. You'd need to lay this out for me. In any given round, there is a 1/36 chance that the Welsh hit and Romans miss, so your percentage seems awfully high.
And this just flows through to the other math as well. For 2 Romans, there are 216 possible outcomes in the first round, only 25 of which include a Welsh hit & a Roman miss. In contrast, there 55 outcomes where the Welsh miss and the Romans don't.
I'm not saying your math is absolutely, positively wrong. Just that a quick look has me scratching my head wondering how you arrived at these numbers.


Steve Lloyd
United Kingdom

I'm enjoying this exercise  I'll try a few more
 If two Welshmen take on one Roman, the chance that the Roman will kill one Welshman without dying is 25/57 (43.86%). Therefore the chance that the Roman will kill both Welshmen without dying is 25/57 * 5/7 = 31.33%, and the chance that they'll mutually annihilate is 25/57 * 1/7 = 6.27%, which means that the Welshmen will kill the Roman with at least one survivor about 63.4% of the time.
 If three Welshmen take on one Roman, the chance that the Roman will kill his first Welshman without dying is 125/307 (40.72%). Combined the with previous result, the means that the Roman will eventually kill all three Welshmen 12.76% of the time, mutual annihilation will happen 2.55% of the time, so the Welsh should win with at least one piece surviving 84.69% of the time
Considering normal armies fighting one another
 If one Saxon (say) takes on one Welshman, each has a 40% chance of destroying the other while staying alive themselves, with therefore a 20% chance of mutual destruction
 If two Saxons take on one Welshman, the Welshman has a 4/19 (21.05%) chance of killing one of the Saxons without being killed himself. Therefore he has a 2/5 * 4/19 (8.42%) chance of winning outright (and surviving), and a 1/5 * 4/19 (4.21%) chance of mutually annihilating, which means the Saxon should win with at least one piece remaining 87.37% of the time.
Interesting stats. Not sure whether to share them with the rest of my circle though.


Ken
United States Crystal Lake Illinois

Really not seeing how you're reaching your results. For 2 Romans v 1 Welsh in the highlands, there are 216 possible results in a single round.
Welsh hit (1/6) Romans miss (25/36)  25/216 or about 11.5%. Welsh hit (1/6) Romans hit at least once (11/36)  11/36 or about 5%. Welsh miss (5/6) Romans hit at least once (11/36)  55/216 or about 25.5%. Everyone misses (5/6 & 25/36)  125/216 or about 58%.
With that as a starting point, I'm having trouble seeing how you're ending up with your results. Particularly with divisors of 57, 91, and 307 running around.
What method are you using to calculate these probabilities?


Steve Lloyd
United Kingdom

perfalbion wrote: steelyvoid wrote:  With 2 Romans against one Welshman in highlands, the chance that Green will roll a 6 before Yellow does is about 27.47% (25/91). Therefore the chance that the Welshman wipes out both Romans and survives is 25/91 x 5/11 = 12.49% There's something about this that isn't adding up. 91 isn't a number I would have expected to see here  it should be a multiple of 6. You'd need to lay this out for me.
OK  here's the math (though its not going to be very readable using text, I'm afraid). Trust me  I'm an Oxford Maths graduate, so I do know my onions here.
With both armies fighting in highlands, each side needs 6s to win  so any one die roll has a 1/6 chance of killing, and therefore 5/6 of the time a die roll will be a miss.
Therefore, for the Welshman to kill a Roman on the first round of combat without being killed himself, the Roman must miss with both his guys (5/6 squared  i.e. 25/36) and the Welshman hit (1/6). As these outcomes are all independent dice rolls, we can multiply them all together to give 25/216.
For the Welshman to kill his first Roman on the SECOND round of combat without being killed, all three armies must miss the first time round (probability 125/216) and then the Welshman must hit on the second round with the Roman missing twice again (25/216 once again), giving a probability of it happening of 125/216 x 25/216.
For the Welshman to kill his first Roman on the THIRD round of combat without being killed, all three armies must miss on both the first two rounds (so thats 125/216 squared) and then the Welshman must hit on the third round with no reply  i.e. 125/216 x 125/216 x 25/216.
Hopefully you can see the pattern here. This is whats called a geometric series and there is a formula which allows you to take the limit (only works if the quantity you're squaring, cubing etc is strictly between one and minus one, BTW). The formula for the sum
1 + n + (n x n) + (n x n x n) +....
is
1 / (1  n)
(try it out with a calculator and some sample values of n like 1/2 and you'll see this works)
So in our case, we are interested in the sum
25/216 x (1 + n + (n x n) + (n x n x n) +....)
where n is 125/216, i.e.
25/216 x ( 1 / (1  (125/216)) )
= 25/216 x ( 216 / (216  125) )
= 25/216 x ( 216 / 91 )
= 25 / 91
Isn't math cool?


Ken
United States Crystal Lake Illinois

I'd have to go back to a stats book and doublecheck if this is a good way to run the math  too long from my days in those classes. I'd tend to say that while the statistics are good, they aren't an accurate reflection of the way you make decisions in game. At the end of round 1, if nobody dies, the decision the Welsh have to make isn't particularly different than at the end of round 21 if nobody's died. So the pertinent number is the percentages per round. Your method results in inflated numbers for the Welsh in comparison, which I don't think captures the ingame decisions.
I mean, if I knew a fight was going to go 6 round in the first place, that might change my move.


Franz Kafka
United States St. Charles Missouri

The 25/91 has some intuitive appeal. Of 216 possible outcomes, nothing happens on 125 of them, and we're back where we started. If we concern ourselves with only the 91 outcomes where someone actually hits, 25 of them involve only the Welshman hitting. (The Welshman needs a six, and the two Romans both need a nonsix. 1x5x5 = 25.)


Ken
United States Crystal Lake Illinois

JosefK wrote: The 25/91 has some intuitive appeal. Of 216 possible outcomes, nothing happens on 125 of them, and we're back where we started. If we concern ourselves with only the 91 outcomes where someone actually hits, 25 of them involve only the Welshman hitting. (The Welshman needs a six, and the two Romans both need a nonsix. 1x5x5 = 25.)
Right, but 55 of those 91 outcomes involve a Roman hit & a Welsh miss. And the timing of who hits when is critically important. So all that's really changed is the divisor (91 instead of 216). I'm not sure how comparing 25/91 to 55/91 buys you much more than 25/216 to 55/216. The relative odds of either side scoring the first hit hasn't changed at all  it's still 25:55, Welsh:Romans regardless. The Romans are 2.2 times as likely to get a solo kill no matter whether you look at round 1, 3, or 26. And then there's the "both hit" potential, which is 11 out of 91. That's all 91 possible outcomes, but the proportions between them are unchanged relative to analyzing just one round.
I can understand if this is just a matter or preference, but the underlying assumption here is that the Welsh are staying until at least one army dies. I'm not sure that's a good assumption, particularly for the 1st round of the MI. If the Welsh do manage to score that first hit, then it seems far more likely that the Romans withdraw. And that's really the sticky wicket.


Franz Kafka
United States St. Charles Missouri

I do see a point there. It wasn't acknowledging the possibility that the Welsh might decide to retreat if they don't score a hit in the first round of battle.


Ken
United States Crystal Lake Illinois

JosefK wrote: I do see a point there. It wasn't acknowledging the possibility that the Welsh might decide to retreat if they don't score a hit in the first round of battle.
This is another area where hitting Gwent can really help out. If the Welsh can retreat there, now it's 2 defenders in the highlands. Plus, you have to hit at least one other Welsh area and possibly two (another highland) to put sufficient pressure on them to submit. They certainly might stand and fight if you aren't bringing 34 attacking Romans. And 3 is very risky  odds of missing altogether for the Romans are still 125/216, but now the Welsh get at least one hit 11/36 times (and two on one of those results). A disastrous first round is a distinct possibility.
Good discussion!


Steve Lloyd
United Kingdom

Got a few more probabilities for you. In the following list "XvY" means "the probability that X armies will ultimately beat Y armies  i.e. destroy them all with at least one army remaining". "H" means the armies are in hiland, and "R" mean they're Roman. So
2v1H
means the chance of 2 regular armies defeating 1 army defending in hiland.
So, from the examples worked out above
2Rv1H = 851/1001 (85.01%) 3Rv1H = 652921/671671 (97.21%) 1Rv1 = 5/7 (71.43%) 1v1R = 1/7 (14.29%) 2Rv1 = 131/133 (98.5%) 1v2R = 1/133 (0.75%) 1Rv2 = 125/399 (31.33%) 2v1R = 249/399 (62.41%) (not 63.4% as suggested above  slip of the pencil!) 1v1 = 2/5 (40%) 2v1 = 83/95 (87.37%)
A couple more worked out last night
2v1H = 157/232 (67.67%) 2v2 = 2824/6175 (45.7%)
The second of these was a horrendous calculation (because we start with more than one army on both sides, so the number of outcomes in any one round is greater), and its quite possible that I've made an error on that one, but the chance I got (slightly less than half) look right (given that there's always a small chance of mutual annihilation).
(Note, BTW, that the sum of XvY and YvX is not one, because armies can mutually annihilate  i.e. draw. Mutual annihilation is a relative rare outcome though, because to get it, the smaller side has to whittle the larger down to parity in numbers, and then both sides need to hit with all armies simultaneously).
One of the things that surprised me doing these calculations was how good 2 on 1 battles are. My expectation was that 2v1R and 2v1H would be more or less even (they're actually around 2:1 in favour of victory) and that 2Rv1H would be in the Romans favour, but not to that extent (about 6:1 in favour of victory). 2v1 is even better  around 7:1 in favour of victory. That will certainly inform my decision as to whether to retreat from such fights in future!
Of course, one thing to remember is that your "expectation" of a number of wins is the number of battles times the probability of any one succeeding. So if your Roman MI strategy requires you to fight 7 hiland battles with 2 Romans against 1 defender each time, expect to lose one of them.



