Game Theory: Probability moves

Probability and I have a long and complicated relationship. In my early years I loathed mathematics with my entire being, and my old math teacher still uses me as an example on how you should definitively not solve math equations.

As with so many other things it took a hobby to finally unlock the secrets of probability, and today I’m going to try and pass on the secrets of using them to your advantage.

Playing the odds

A game a Warmahordes is one long string of decisions and probability, which keeps influencing the following probabilities, which means that once you get the ball rolling it’s easier to keep it rolling, while a mistake early on can send you tumbling down a difficult path.

This is something most people figure out early on in their miniature wargaming careers, but using the knowledge actively is something else entirely.

odds

They’re… pretty bad…

Some people actively ignore probability, because they feel knowing the odds it’s somehow detrimental to their game, but these people rarely end up in upper echelons of tournament ranks, so let’s ignore them and talk about making an informed decision instead.

If you need help with the actual numbers, the old Dice Math article here is worth a read.

The probability of moves

There are the moves which are statistically likely to succeed, like trying to roll three or more on two dice, or even moves which don’t involve any rolls at all like movement. These high probability moves are statistically likely to succeed, but are also (usually) less powerful moves.

On the other side we have the low probability moves, which are statistically unlikely to succeed but have a huge impact on the game if they do. These are moves like rolling fourteen or more on three dice, in order to neutralize a significant threat to your game. In between the two extremes is where it gets tricky, so let’s consider an example.

You have a RAT 6 and POW 10 ranged attack available, with two possible targets. One target is defense 12 and armor 14, while the other is defense 14 with armor 12 and five boxes. The first target is low priority and the second is high priority.

Target 1: Here we have roughly 70% chance of landing the hit, and 85% chance of killing the target once we do. This in turn becomes a 60% chance of successfully killing target 1, and I refer you to the aforementioned article if this confuses you.

Target 2: Here we have roughly 40% chance of landing the hit, and 60% chance of killing the target once we do. This in turn becomes a 25% chance of successfully killing target 2, and I again refer you to the aforementioned article if this confuses you.

These are very rough numbers but that doesn’t matter much, and it makes it a lot easier to do the math in your head. If you decide on doing this consistently, you’ll find yourself not actually doing the math after a couple of games, but simply ‘feeling’ the odds.

Returning to the example above we face a decision. We can go for target 1 with a solid probability of success, or we can go for target 2 with a low likelyhood of success. If we decide on target 1 we most likely score the kill and gain a slight edge, but we leave target 2 alive to inflict all kinds of nasty on us the following turn.

If we go for target 2 we will most likely fail, which leaves target 2 alive to hurt us, but now also leaves target 1 alive to act against us because we opted for the high risk play. If on the other hand we succeed at our high risk move we gain a significant edge in the game.

I can’t teach you what the consequences is, or even tell you what you should do in an insanely complicated game, but I can tell you what the different types of play lead to.

High probability players

I’m a high probability man myself, which means I usually opt for the high probability kill instead of the low probability gamble. This means that I slowly inch my way towards victory, instead of leaping and bounding towards it, but it also means that if I’m not a better player than my opponent I’ll lose.

Playing the high probabilities also means that you’re predictable, which allows a really good player to manipulate and bait you. I’ve been in some grueling games with some of the worlds best players, where I’ve lost simply because they figured out that they could depend on me going for the safe options every time.

High probability moves lead to slow paced attrition games, as a caster kill is almost never a high probability move until the game is decided anyway. In my opinion the best players are high probability players who know when to switch gears and go for the low probability attacks.

Low probability players

Low probability players take a lot of chances. They risk throwing their main heavy away on the low odds that it can roll significantly above average and take out your main heavy, because if it does they’re going to be way ahead in the game.

These players are often frustrated and feel like their dice are deserting them, when in reality it’s simply cause and effect. If you open the game with low probability moves you’ll soon be forced into even more low probability moves trying to catch up (unless of course you’re low probability moves succeed, in which case you’ll be steamrolling the opponent in no time).

Low probability moves lead to fast paced and sweat inducing games, where casters are in mortal danger every turn because there’s no probability to low for the opponent. I’ve lost games to low probability players simply because I couldn’t for a second imagine them betting the game on a 10% assassination, but they did and it worked.

Balancing the probability

There are two types of game states you can end up in, which is ‘optional’ and ‘forced’. Evaluating the right move is extremely dependent on which type of game state you’re in, and now it becomes a wee bit complicated.

The flowchart of moves

Forced moves are moves your opponent forces on you. A forced move is what happens when your opponent runs a model at you, which will kill you if you don’t kill it, or forces you into a zone to avoid losing on scenario.

Optional moves are all about evaluating the consequences of a given move, and then only taking the low probability moves that won’t negatively impact your game in a manner which you can’t come back from (Do or die is bad!).

Expanding on our two target scenario from before, we now place them in two different situations. In one situation the high priority target is unlikely to ruin your game on the following turn (optional), and in the other it’s almost guaranteed to happen (forced).

Scenario 1. The high priority target needs to roll 11+ on 2d6 in order to ruin your game. It could happen but it’s unlikely, and if your opponent attempts it he’ll hand you the high priority target for free

Scenario 2. The high priority target needs a 5+ on 2d6 in order to ruin your game. It will most certainly happen unless the dice gods intervene, and it will make it very hard to win the game.

In scenario 1 I would send my ranged attack at the low priority target, as the risk of getting my game ruined is just over 5%, which means that I have a 95% chance of getting that high priority target served up on a platter if he tries his extremely low probability move.

In scenario 2 I would certainly take my shot at the high priority – but low probability – target, which will most likely ruin my game if it survives. I will most likely miss, and it will most likely cost me the game, but if those dice come up my way I’m back in the game.

Conclusion

You might already have known this, and you might use it in every game, but if this is news to you then welcome to a whole new world.

In the beginning you’ll find it a slow and cumbersome system, doing math and deciding between options, but before long you’ll find yourself doing it on fingerspitzengefühl (intuition).

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