We wished to find some way to block the effect of $$H$$. By introducing $$Y_0$$ we've made an observable control for us to use to mitigate $$H$$. $$Y_0$$ and $$Y_1$$ are connected because they are not independent events. The direction points to $$Y_1$$ because $$Y_1$$ contains $$Y_0$$, i.e., $$Y_0$$ contributes to $$Y_1$$.

Observable Controls in Selection Diagrams

With events created using functional constraints.

University of Michigan - Ann Arbor

We know, given the nature of the problem that 
$$Y = H \vee (X \land B) $$
This can be reframed as a more concrete counterfactual :
$$PS_{01} = P(Y_1 = 1 | Y_0 = 0 )$$
Where $Y_1$ is the event $H \land B$ and $Y_0$ is the event $H$. 
$PS_{01}$ is the probability that a death is caused by Russian Roulette alone.
Now let, 
$$PS_{10} = P(Y_1 = 0 | Y_0 = 1 )$$
By definition, since $Y_1$ contains $Y_0$, $PS_{10} = 0$
The law of total probability gives us : 
$$P(Y_1 = 1) = (1 - PS_{10})(P(Y_0 = 1)) + PS_{01}(1 - P(Y_0 = 1)) $$
We can then solve for $PS_{01}$ to get :
$$\frac{P(Y_1 = 1) + P(Y_0 = 1)}{1 - P(Y_0 = 1)} = \frac{1}{6}$$
Now we use the equation derived from the law of total probability and plug in values for NYC, to get the estimated mortality rate as $20.8%$

Thus using the structural diagram(s) and functional constraints, we've managed to solve this problem using only the two assumptions we began with.

Using Functional Constraints

Cinelli, Carlos, and Judea Pearl. “Generalizing Experimental Results by Leveraging Knowledge of Mechanisms.” Technical Report - UCLA, 10 Dec. 2019.

https://ftp.cs.ucla.edu/pub/stat_ser/r492.pdf

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