Feast for Odin Starting Draws

I was procrastinating at work and reading Steph’s weekly blog about board games, when I came across her criticism of A Feast for Odin‘s starting occupation cards:

I wanted to start off by saying I really don’t think the starting cards are all that balanced, and I know that is mean of me to say but I could really feel it in this game. Ron was constantly getting material goods for free from the forests every time he visited a specific section on the board while I got a terrible 1 time bonus when I collected 4 sheep for milk and a couple wool tokens. I’m sorry but it really pissed me off. I don’t know what I am going to do about the starting cards for future plays, perhaps we will get 2 and keep 1 or just go through and remove the “lesser valued” ones.

I’ve been playing and loving A Feast for Odin quite a bit lately and I wondered if drawing two and keeping one would alleviate the problem. For instance, let’s assume that the cards can be distilled to an arbitrary power between 0 and 10. There’s a scenario where I draw a 5 and you draw a 7. Okay, that’s a slight power advantage for you. But if we do “pick two, keep one” and my second draw is a 2 and yours is a 10, then the difference in power goes from 2 (7-5) to 5 (10-5).

Being a game design teacher and all-around nerd, I decided to see if I was just cherry-picking an edge case. This upcoming analysis based on some assumptions that may not be true; specifically, that cards have an objective static value.

Anyway, I ran an Excel simulation at 1,000 repetitions based on three cases: each of two players draws one card with value 0-10, each player draws two cards with value from 0-10 and keeps the highest, and each player draws three cards with value 0-10 and keeps the highest. I then calculated an average power for each case and an average difference in power for each case. I then ran that simulation 1,000 times for one million total repetitions.

Remember that we are giving every card a score between 0 and 10 and assuming a flat distribution. Thus, we should expect that the average power in a “draw 1, keep 1” scenario to be pretty close to 5 after a million draws. This will be our sanity check to make sure we are doing this correctly. There shouldn’t be much variation after a million repetitions.

Here are the results:

Draw 1 Draw 2 Draw 3
Avg. Power 4.998 7.149 7.973
Avg. Difference 3.641 2.636 2.095

In the rules as written, you get an average power of 5, but the difference between players is, in my opinion, significant. Going to “Draw 2, Keep 1” cuts the difference between the two players by 27.6%.

However, I think the real benefit is not the reduction in difference but the increase in average power. Taking the higher card of the two means that players will both (1) feel better due to getting something more useful (which would not happen if you just went in and removed the lesser valued cards) and (2) feel a greater attachment to the occupation they choose to keep because they chose it. This is likely related to a number of cognitive biases such as effort justification.

Additionally, this is also likely affected by relativity effects. We are likely okay to have a gap in power between us as players as long as we feel like we have something to work with. This means the situation of a 1 vs. 4 feels worse than the situation of a 7 vs. 10.

Here is a histogram of one of the 1,000 run simulations of the number of times a player ended up with each power level:

screen-shot-2016-11-01-at-1-00-16-pm

In the Draw 2, Keep 1 system, you will see the junky numbers 1-4 just as often, but you are less likely to be stuck with a pair of them. In fact, the most likely scenario is that you end up with a card from the highest power decile.

I think I’ll try the Draw 2, Keep 1 next time we play.