HearthSim: Divine Shield Modeling — Part 1

By | July 16, 2014
Let’s take a look at how we might go about modeling Divine Shield.

Recall that the AI scoring function is given by
$$S = S_{\rm b} + \tilde{S}_{\rm b} + S_{\rm c} + S_{\rm h} + \tilde{S}_{\rm h}$$
(see the original post). In particular, for each minion that one has on the board, the score goes up proportionally to the attack and health value of the minion:
$$S_{\rm b} = \sum_{i} (w_{\rm a} a_{i} + w_{\rm h} h_{i})$$
When a minion has divine shield, we expect it to be valued higher than a regular minion. But, by how much?

The essence of divine shield is that it allows the minion to be used (attack) once for “free.” That free attack does not damage or kill the minion, removing the divine shield instead and leaving a regular minion on the board. This observation suggests that we can think of a divine shield as effectively doubling the score of the minion. So, let’s propose to model each minion’s score as follows: for each minion $$i$$ that has divine shield,
$$S_{\rm b} = (w_{\rm a} a_{i} + w_{\rm h} h_{i} + (a_{i} + h_{i}) * w_{\rm ds})$$
where $$w_{\rm ds}$$ is the divine shield weight. When the divine shield is removed, it goes back to the regular minion score. Note that setting $$w_{\rm ds} = 0$$ means that the AI pretty much ignores divine shield, while setting it to a high number (say, 2) means the AI highly values the divine shield and will try to keep it as much as possible.

In real game situations, we don’t expect divine shield to provide us with exactly twice the value that a minion would have without DS. In fact, there are quite a lot of ways in which the opponent can efficiently remove the DS: silence, any battle cry damage, hit it with a weak or almost dead minion, etc. Thus, we should expect the optimal weighting to be somewhat lower than 1, though by how much is a question we can only answer by running some simulations. Part2 will go into some simulation results.

Continues on part 2.