Hey all, I am new to this subreddit (and to the game!).

I started some time ago a campaign with u/tree_feared and it's a lot of fun (btw we met through reddit, yay!). We are playing tonight and I had some XP to spend since last session.

Doing so, I realized that my William Yorrick might be low on resources. So I wondered: how much of a second emergency cache will impact my play (I currently have one)?

Instead of working I decided to simulate a bunch of hands and I thought of sharing the results.

You can find the graphs, here: https://imgur.com/q17pBfH.

These are the rules:

• I did the simulations with a 34 cards deck, instead of 33 (my deck is currently 34 for some [spoilery] reason)

• After the first five cards, if no cache is drawn, 3 other cards are redrawn. Why 3? It is arbitrary: there is usually at least a couple you might want to keep. I do not consider here the fact you might draw a weakness in the starting hand.

• I imagine to draw only one card per round, during the upkeep phase where also 1 resource is accumulated. This is unlikely: many things make you draw a card. For one, I play with a bunch of guts, overpower, perception etc. cards.

• A cache is considered spent as soon as it is drawn (which is obviously impossible, as it would be spent at the soonest in the following round). This does not change much the interpretation.

• Of course resource actions and other sources of $$ are ignored.

On the technical side: I simulated (1000 reps), rather than computing, the mean resources under the 1-cache and 2-cache cases. I thought it was faster and more thorough. You can find a super inelegant R code here (https://pastebin.com/AzZNS6v6). The graphs are done in excel because I have a hating/loving relationship with R and its (arguably amazing, but notoriously rebellious) plots.

On the interpretation of the graph(s): You see in blue the 1-cache case and in green the 2-cache case. The dashed lines are the minimum resource possible scenario and the maximum possible scenario. The minimum, that entails not drawing the cache at all in the first n rounds, is shared in the two cases. In the solid lines, you can see the average resources at the end of each round. Averages here need to be interpreted with a grain of salt, since everything is pretty discrete and the resource pool jumps, when a cache is played, rather than smoothly increase.

In the end, again on average, the difference is not striking and the second cache seem not to be justified. In my opinion, the second cache plays a bigger role in two moments, that might eventually justify it in my deck. First, it gives a higher probability of kickstarting the play: having 2 instead of 1 increases the probability of finding one in the first hand (8 cards, as per assumption) from 23% to 37% (this is back of the envelope calculations, but should be correct). This help to early put in play assets that might be useful throughout the whole play. Second, it is useful by the mid-late game. I am worried I simply won't have enough "cash flow" to sustain the cost some of my most powerful cards, when more than one is in play. A second cache elevates the upper bound on total resources.

Talking averages is not that relevant for neither of these two cases, I reckon. If there is interest, I will find a better way to visualize distributions of states of the world.

Edit - Update: Thank you all for your comments! The main point in favor of two caches seems to be the increased consistency for a good kickstart. The second point (that my analysis is more apt to capture) is that two caches relax the upper bound on the total amount of resources available towards mid-late game.

I played yesterday with two caches and it was a good choice. Unfortunately, they were right in the middle of the deck, so I could not use them to equip anything at the get go. More than that: I drew them back to back! What are the odds of that!?!?! (easy: 1/27). In any case I used both of them in a couple of rounds to put down a "Police badge" and be more comfortable with my profligate use of "Lucky!" and "Knife".

As for the analysis: I'll produce some histograms to show different probabilities of given hands later on.