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Making Luck Minisode 43: Money Density

In this episode, Wandering Winder discusses money decks.

No kingdom this week, since it's a minisode.

I really enjoy the analysis you put into your discussions Wanderingwinder.

I am sending my best thoughts and wishes to Adam Horton, his wife, and his family!  Bring on the minisodes 🙂

Looks like WW replied but the forum software ate the reply. I'm reading all of the feedback but it's hard to type when one of my hands is occupied and I'm reading things on my phone 😛

In any case, thanks for your  kind words. The goal is two more minisodes (including the one that will be published today) and then back to normal but I don't want to make any promises yet.

Congratulations Adam!  Great to hear.  No podcasts promises right now, only family commitments.  Enjoy!!!

[Edited to remove erroneous formula]

This comment is actually on the follow-up money minisode that was published this week, but since there isn't a page for that one at the moment (I realise Adam has his hands full!) I thought I'd post it here. It's about the formula WW uses for calculating money density in decks that have cards that draw other cards (Peddler, Lab and Smithy being the main examples he mentions).

WW starts with pure money decks and simply counts the total money and total number of cards, dividing one by the other to get the money density. No arguments there. In this second episode he then takes a trickier example of adding a Peddler to a deck that previously had 13 cards and 13 money. WW’s assertion is that he now effectively has 14 money in 13 cards because the Peddler doesn’t count as a card. That’s very nearly correct, but the problem is that when you draw five cards to start your turn only 1 card in every 14 is a Peddler, not 1 in 13. If you start your turn with 5 cards drawn randomly from your 14 card deck then the probability of getting the extra dollar that turn is only 5/14. So the average money produced in total on your turn is 5 + 5/14, meaning the effective money density is only 15/14 (exactly the same as if you’d added a Silver) rather than 14/13.

Another way to look at it is that the $1 on the Peddler isn't worth quite as much as each $1 on the other cards, because to get the $1 from Peddler you need to draw it in your 5 card starting hand, whereas to get the money from any other card you can EITHER draw it in your starting hand OR draw it with the Peddler.

In this case the difference in average money is minute ($0.027 per turn), but if you add more Peddlers or other cards such as Labs that draw more than one card then the error in the WW formula becomes more significant. Still, the WW formula is very simple and if you’re trying to keep track of the numbers in your head while playing a real game then this is a pretty good approximation if you’re playing a moneyish deck with just a few Actions.

One more point: cards that draw cards miss more shuffles than ones that don’t, so adding a card like Peddler to a money deck will usually be a little worse than what a formula for “effective money density” would imply.