A quiz based on a real game.
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The_Bishop wrote:
I'm in a hard situation, my opponent holding 5 cards and I have 4, with a set which I can turn in, but I do prefer not to. I would like to be able to break his small +1 region with my 3-troop reinforcement.

See image (click to show)

So there are three options: I can attack the yellow region (Wilsonville) from the North, with 4 troops against 2; or I can attack from North-West with 5 troops against two enemy territories having 2+1 troops; or, attack from the South with 6 against three enemies having 2+1+1 troops.

First option, second or third, which one is best and why?
«God doesn't play dice with the World» ~ Albert Einstein
Blagoje_Jovovic wrote:
If you play against me then the best option is to resign :)
dough_boy wrote:
If you owned any I would have cashed.

Personally I would go from south. Slightly better odds and I believe would take down to 3 reinforcements.
The_Bishop wrote:
Well in fact cashing would be the 4th option, but I excluded it: if I am sure he cannot win at his next turn, then I do prefer to cash right after him, so bringing back everything Jovovic could take from me; plus the cards are increasing and 2 troops more is better than 2 troops less. I don't know the answer for sure, I just know what my sense and my maths suggested me to do, and it worked very well really... Unfortunately then I lost the game but I believe to have made the right move in that round.
«God doesn't play dice with the World» ~ Albert Einstein
The_Bishop wrote:
Which way did you go?
I'll tell, but not immediately. First I would like to listen to everybody's thought.
«God doesn't play dice with the World» ~ Albert Einstein
The_Bishop wrote:
Well, I don't see much participation in my riddle...
For now Blagovic's answer is the worst ever: resigning!! ^^
Dough_boy's is second for suggesting to turn in, it's clearly better to wait the next round.

I can make it simpler. What I actually did first was to calculate the odds for breaking his region with the 3 options mentioned above (see the image for clarity). So I got:

-- attacking from North: 4 vs 2 = 65.6%
-- attacking from West: 5 vs 2+1 = 56.3%
-- attacking from South: 6 vs 2+1+1 = 47.1%

I certainly wanted to damage him as much as possible, but in the end I decided for the third (and hardest) option: attacking from South, with only a weak hope of breaking his region (actually less than 50% chance).

Why I did so?
«God doesn't play dice with the World» ~ Albert Einstein
dough_boy wrote:
You didn't provide ANY information around cards, turn in value, what you owned, etc. I was making a comment that there could be more than what you presented.

How did you determine the odds? 6v2 is one, then 5v1 is one, 4v1 is one.
The_Bishop wrote:
I have 9 territories (Blue) and my opponent has 14 territories (Red).
+3 reinforces for me, +5 to him if I do nothing.
He holds 5 cards and I hold 4.
Next turn-in value: 8 troops.
Domination: 20 territories

I checked the odds on GamesByEmail.com
N.B. you have to input the active troops of the attacker i.e. one less than what you have on the territory.
«God doesn't play dice with the World» ~ Albert Einstein
sfclimbers wrote:
I started a response explaining why I would not try to break his region at all, only to then realize that this is a Domination game. I've never played Domination, so will instead lurk quietly, hoping to learn the nuances that you guys consider when playing this format.
The_Bishop wrote:
Well, inhead-to-head there's not a great difference between between Domin and DM:
more-or-less the win in Domination mode occurs when it's the time to surrender in Death-Match mode.
«God doesn't play dice with the World» ~ Albert Einstein
sfclimbers wrote:
Based on the premise that you would not be cashing in your cards...

I would not attempt to break his region. Even if successful, it would not be worth the losses, IMHO. Rather, I would put all 3 troops in Newberg2, for a total of 5. I would then attack Newberg1 for essentially a guaranteed card with minimal expected losses. If not having suffered any losses, I would move a total of 1 troop to Newberg1, leaving 4 behind. Otherwise, I would divide my forces between Newberg2 and Newberg1 and end the turn.

If not having suffered any losses, I might risk a 1 troop loss of the remaining 4 in Newberg2 to attack Dundee, moving a total of 1 if successful.
Depending on losses, I would either fortify with 1 troop from Newberg2 to Newberg1, balancing between the 2, else from Donald to Newberg1, thereby leaving me a situation of:
- Having acquired my own 1 point city bonus (and possibly entire region), with defenses as strong as any other on the board (2 troops at each border)
- Having reduced his holdings to as few as 12 from 14, with minimum loss, thereby pushing him further from domination
- Somewhat forcing his hand into addressing me in my region, rather than attempting to clear out all my other holdings
- Having, at my next turn, all the the same attack vectors described in your original post (subject to whatever he conquers)

Another option might be to put them all in N. Sherwood, attempt to take S. Sherwood, moving all troops, and end the turn there. That would again
- Gain me a city bonus
- Leave me with some level of defense at the border
- Isolate his two singles in the blue region

I think that I would prefer the acquiring the blue region approach better (i.e. first scenario), since it allows me to leave 1's behind without fear of paratroopers wiping me out behind my main lines, as would be the case in the second scenario.
The_Bishop wrote:
No sorry sfclimers, I don't think your answer is correct.

You are not taking into account the fact that your opponent (mine actually) has 5 cards and will begin his next turn with 13-troop reinforcement. There's actually no bonus you can hold against that, not even close. If the idea is to <try> to hold a small bonus then you should turn in, but he will turn in immediately after you, getting 2 troops more than you, so being normally able to break your bonus, unless he gets horrible dice.

Who turns in second here has an advantage. As my situation is already quite bad, I prefer to grab that advantage instead of gambling on protecting regions which I cannot reasonably protect. Another small advantage could come from decreasing his reinforcements, so for example reducing his territories from 14 to 11, which is hard, or just breaking that small bonus he holds, which is feasible and that's what I propose to do.

I think however you said something correct and really important so that if you only focus on the three options I proposed you'll probably chose the right one. At least, let's say, the one which I suppose is right.

The fact that it was a Domination game and not a Death-Match should not be considered as part of the riddle. I might have done some mistakes on that matter, i.e. I considered like probably I could take 2 territories off my enemy, so he could not win conquering 8 territories at his next turn (12+8=20) but really there's some chance he could do that. This would change the scenario but likely not enough, so I think I would always do the same move, I am not sure though.
Let's assume it was just a normal Death-Match to keep things simple.

Plus, let's remain bound to one of the 3 options for now. Which one do you think is the best and why?
«God doesn't play dice with the World» ~ Albert Einstein