Sunday, May 20, 2018

Understanding the Dice

Hello again, today I am going to talk math. Dice are an important part of Guild Ball, and make for an exciting yet random outcome. Casinos always win by stacking the odds in there favour, doing the same techniques we can position ourselves better to win at guild ball. If we are able to use the power of math to understand the dice, we can choose better targets which leads to forming better plans.

First lets delve into the math around kicking. Players that roll more dice are better at kicking the ball, right? That assumption is correct but the difference between rolling 4 dice compared to 5 dice isn't noticeable (93.8% compared to 96.9%). Using the chart below, we can know the percentage for success for scoring a goal (or completing a pass)

  # of dice  normal TN      Tap In     + 1 TN
1 50 66.7 33.3
2 75 88.9 55.6
3 87.5 96.3 70.4
4 93.8 98.8 80.2
5 96.9 99.686.8
6 98.4 99.991.2
If you want to do your best to ensure the goal, stacking more dice will raise the certainty of a successful goal. The best way to raise the certainty of a goal is by reducing the TN, and to defend against a goal you want to try and increase the TN while reducing their dice pool. Most of the time I aim my dice pool to be between 3-5 dice when shooting a goal because I can live that high of a percentage for success. If I am in a position where missing the goal will put me in a bad spot, I try to get as many dice as possible. If you are getting behind in a game, taking a two dice shot is still a great option for getting back into the game.

The dice math for attacking is more complex, but I look at it with a more simple approach. 

TN                 Percentage
6+ 16.7
5+ 33.3
4+ 50.0
3+ 66.7
2+ 83.3

Looking at the percentages for successful outcomes at each defense value, we can predict the amount of success we should get. 
Lets look at an example of this. Honour is TAC 6 so she is rolling 6 dice for an attack against Tapper who is a 3/1. On those six dice she rolled two-thirds (66.7%) so Honour should get four dice being higher than a 3, but we have to take away 1 success because of Tappers arm. So Honour is left with 3 net successes.  
So if we take the Player we are using to attack TAC and multiply is by the percentage of expected outcomes, we are given an idea of what our player can do. Certain players have efficiencies built into there playbook to help boost there output if they can reach a certain part of there playbook. Fillet, Tapper, and Veteran Decimate are great examples of this.

Fillet really wants to attack a bleeding target. If no one on the other team is bleeding, she has to do it herself (usually the scenario on turn 1). In a classic butcher v fish, fillet kicked off which brought Sakana forward to retrieve the ball. So with only that one target to go for, Fillet goes in. At TAC 8 attacking a 4/1, Fillet should get 4 success, which leads to 3 net hits which is short of her blood rain to bleed Sakana. If she rolls slightly above average Fillet gets her blood rain and is happy, but we don't like to be in the position when odds are not in our favour. If Fillet charges she has a dice pool of 12, which would result in 6 successes which is 5 net hits which gets us our blood rain. However, if Sakana uses defensive stance to a 5/1, Fillets 12 dice should result in 4 successes, which again puts us outside where we want to be. This was a bad example to look at because with tooled up Fillet should hit her Momentous 2 up to 3 every time, which will takeout Sakana without the blood rain.

Tapper, like all brewers, wants to wrap on his first attack for commanding aura and a knockdown. His charge can be the difference between him setting up the team or getting a take out. So lets look at Tapper attacking Brick. Tapper charges because he wants to have the most dice to get him to his Knockdown and commanding aura. Taps has a dice pool of 10 attacking a 2/2. He should only get around 8 successes for 6 net hits which leaves him short of getting commanding aura and a knockdown. The Masons player should ensure that this doesn't happen by using defensive stance to make Tappers activation less efficient.

Veteran decimate is the new hotness, that has turned a few heads. Having knockdown and stagger on the same playbook result can swing the dice heavily. Given bag of quaffers on Decimate to bring her up to Tac 7. Attacking the game average of 4/1 defensive stats on a charge, decimate will get 5 to 6 success on average which will get her the KD+stagger. Now that 4/1 player is effectively a 2/0 model to decimate, which will give her about 33% more success on the following two attacks and for the rest of the brewers.

Playing with an idea of what to expect from every model should give you an advantage. But, dice are random and can roll higher or lower than you expected at any point. Using the expected results of the dice can help you put your opponent in a position where the odds are stacked against them. When you use this information to help form a plan on the pitch you should plan pessimistically. This means that if the dice math says you should get a certain outcome, you should plan that you will fall short on an attack. For example if a player is on 4 hit points and you have a model with 2 damage on three hits, plan that you won't hit the two damage a couple times rather then he should hit his two damage every time. It is better to play where the dice do not matter and that you can guarantee an action on the pitch.

Controlling tilt caused by dice is another key to success. Attacking in this game is binary, the dice roll is either a success or a miss. If our player has a defense of three, and the opponent rolls all sixes for his successes. The result being a six doesn't change that it was a hit. In my last game against a local practice partner, tower counter attacked Jaecar rolling 4 sixes and a one so we just cheered out Yahtzee. Never blame dice for anything that happens, there is always a different option that could have been taken throughout the game that may have given you a better opportunity or given the opposition more difficulty. 

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