Monday, August 15, 2016

Star Wars Rebellion: Opposing Odds

I have become slightly obsessed with a board game that Adam taught me before WBC this year: Star Wars Rebellion. It's an asymmetric card driven 2 player wargame with a great theme. The game starts a little before the original Star Wars trilogy and goes through all three movies. One player is the rebel alliance which is trying to convince the galaxy to go into full on rebellion. The other player is the empire which is trying to find the hidden rebel base and eliminate them.

Even though the mechanics are basically the same for each side they play very differently which makes the game particularly interesting for me. Ostensibly the game is about the empire trying to find the rebel base so you'd think the rebels would have a game based on staying hidden, but that's really not the case. The length of the game depends on how many objectives the rebels can manage to achieve so really the rebels are trying to score as many objective points as they can while hoping the game mechanics keep their base safe. But then the empire could focus on denying objective points and just assume they'll stumble into the base eventually... But that probably means giving up on outproducing the rebels militarily, so then the rebels could just try to earn extra time with military actions...

As an aside, each game round you get to take one action per leader and generally speaking each side has the same number of leaders, and that number increases as the game gets longer. So on the first turn each side takes 4 actions but by turn 5 each side is taking 8 actions. Often you can spend a leader to try to counter the opponent's action instead of taking one of your own, but that's guaranteeing you lose an action to just have a chance of costing them an action. So unless the action you're giving up isn't very important or the odds are very good it just doesn't feel very good to do it.

One thing I found while playing as the rebels was there were two actions I wanted to take every single turn if I could. I always wanted to make an alliance with a region (which lets you produce units and is a criteria of many missions) and I always wanted to do some spy work to manipulate the objective deck. This lets you draw two cards and put one on top and one on the bottom, which accomplishes two things... It lets you end up with objectives you're likely to succeed at based on the current game state by burying hard ones and it lets you draw cards from the bottom of the deck. (The deck is pseudorandom in the sense that there are 3 tiers of 5 cards each, and the lower tier cards are just better.) But even though those actions seemed critical to my game plan regardless of the game state, my opponent would almost never contest them. And then when I finally played a game as the empire I kept finding other things to do instead of contesting those actions, even though I know how valuable those actions are for the other side.

This leaves me with a bit of an issue. Are all my actions as the empire equally valuable? Is my evaluation of how useful those two actions are for the rebels off? Are the odds of succeeding at an opposition really bad? Unless one of those three things are true I really need to change my empire strategy to put a premium on opposing those two actions.

I think it's pretty clear the first statement is false. All empire actions are not equally valuable. Each card can only be played once per turn, and each fleet can only be moved once per turn. Different actions will change in value based on the game state, so I'm not saying different actions are strictly superior or anything. But I am saying that on a given turn you will have an action that is worth less than another.

How about the odds of opposing an action? The way that works is all missions have an associated stat and each player rolls a die for each point their leaders have in that stat. So Chewbacca is really good at opposing a punching mission (he has 3 points in punching) but really bad at everything else (he has 0 points in the others). A die is worth 0, 0, 1, 1, 1, or 2 successes. The player who took the action needs more successes in order to have the action happen. Note that this means the opposer wins ties, and with small numbers of dice and small values on those dice, ties will actually happen pretty often. Andrew was saying he thought that meant even numbers of dice would be 60-40 but my intuition has that as being too favorable for the initial actor. Which means opposing would really be something worth considering! But let's work out the actual odds for differing numbers of dice...

1 2 3 4 5 6 7 8 9 10
0 67% 89% 96% 99% 100% 100% 100% 100% 100% 100%
1 31% 61% 80% 91% 96% 98% 99% 100% 100% 100%
2 13% 36% 58% 75% 87% 93% 97% 98% 99% 100%
3 5% 19% 38% 57% 72% 83% 91% 95% 97% 99%
4 2% 10% 23% 40% 56% 70% 81% 88% 93% 96%
5 1% 5% 13% 26% 41% 56% 69% 79% 87% 92%
6 0% 2% 7% 16% 28% 42% 55% 67% 77% 85%
7 0% 1% 4% 9% 18% 30% 42% 55% 66% 76%
8 0% 0% 2% 5% 11% 20% 31% 43% 55% 66%
9 0% 0% 1% 3% 7% 13% 22% 32% 43% 54%
10 0% 0% 0% 1% 4% 8% 14% 23% 33% 44%

What we have here is a table with the number of dice being rolled by the initial actor across the top and the number of dice being rolled by the opposer down the left. Typically you'd be looking at numbers between 0 and 3 but occasionally there will be lots of leaders in one spot working on a single action (trying to turn Luke to the Dark Side, for example). It turns out Andrew's initial guess was actually pretty good, with a 60-40 split when you're rolling 4 against 4, but at lower numbers of dice it gets better for the opposer at even strength.

Throwing a leader in just to 'make them roll' (an unopposed action doesn't have to roll dice) feels like it doesn't make much sense at anything except maybe 1v0. In that 1v0 case you're basically getting a third of an action. Is your worst action that bad? I doubt it, but I guess it might be. But if you have a good leader back then going in 1v2 is 87% of an action. Is your worst action worth 87% of their action? Yeah, yeah, that seems pretty good. I like 1v3 and 2v3 also. So leaving a good symbol leader back feels like something I need to encorporate more into my game.

What about trying to capture a leader? The empire can lock a leader up with a card that requires only a single punch symbol to start up. Capturing a leader means they can't take actions again until they get saved and opens up some powerful torture related actions for the empire, so it's pretty powerful. It's non-trivial to rescue a leader, but even if the rebels have one of the 3 cards that do it and succeed in it on the next turn, you're looking at a 1v0 roll being 2/3rds of costing them 2 actions and 1/3rd of doing nothing. That's going to cost them more actions than the one you're spending, so a 1v0 roll actually feels pretty good. You don't want even dice numbers being rolled, but any positive number of dice is probably a good idea.

The last thing to consider is some of the cards get 2 guaranteed successes if the correct leader runs the action. How good is that in terms of the odds?

1 2 3 4 5 6 7 8 9 10
0 100% 100% 100% 100% 100% 100% 100% 100% 100% 100%
1 94% 98% 99% 100% 100% 100% 100% 100% 100% 100%
2 71% 86% 94% 97% 99% 100% 100% 100% 100% 100%
3 46% 67% 81% 90% 95% 98% 99% 99% 100% 100%
4 26% 46% 64% 78% 87% 93% 96% 98% 99% 100%
5 14% 29% 47% 63% 75% 85% 91% 95% 97% 98%
6 7% 17% 32% 47% 62% 74% 83% 89% 93% 96%
7 3% 10% 20% 33% 47% 61% 72% 81% 88% 92%
8 1% 5% 12% 22% 34% 47% 60% 71% 79% 86%
9 1% 3% 7% 14% 24% 35% 48% 59% 70% 78%
10 0% 1% 4% 9% 16% 25% 36% 48% 59% 69%

Opposing these cards is a lot worse. You need to roll 2 extra dice on opposition to barely get better than 50-50. Now, some of these character specific action cards are so powerful you may want to take your 31% chance at stopping them (10v10 with +2, like when the Emperor is trying to turn Luke to the Dark Side) but in general, getting 2 free successes is pretty absurd for the odds.

What does this all mean? I think I need to try opposing more actions!

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