## Is Getting Robbed a Good Thing?

Well no. It’s not. First, I should clarify my distinction between getting stolen from and robbed.

Getting *Robbed* is when a 7 is rolled and you have more than 7 cards, forcing you to discard half of them.

Getting *Stolen From* is when the Robber is put on your hex and the opponent gets to steal a card from you. This isn’t what I’m talking about.

So again: *is getting robbed a good thing?* No. It means you lose cards. In the strictest sense of the definition, getting robbed is simply spending cards and getting nothing tangible in return. It’s spending resources on nothing. More precisely, it’s spending resources for the convenience of holding those resources. So, in that sense of it, if at any time you find yourself holding more than 7 cards in your hand, you are essentially gambling half of them. We’re gambling against the *roll distribution*.

Here’s a little math lesson for you. Anyone who has taken some basic probability classes will be able to teach this lesson, so bear with me if this sounds like a class you took freshman year of college. Basically, there’s a set probability of rolling each number, shown by the graph below: So, we know there’s about a 17% chance of rolling a 7 at any given time. The thing that gets a lot of attention in Settlers is that 7 has the highest probability of being rolled. It’s a scary idea to know that at any given moment, the most probable roll means blocking a resource and getting to steal a card from someone, all-the-while some other player could be getting punished for holding too many cards. Scary right?

I don’t look at it like that. I look at the complement of rolling a 7 – that is, the probability of *not* rolling a 7. It’s 83%. That means that when we “gamble” against the roll distribution by holding too many cards in our hand, we win 83% of the time. Those are pretty good odds if you’re into betting. Let’s say I have too many cards in my hand, and I am deciding whether or not I should spend them or take my chances on a 7 being rolled in the next round. In a 4 player game, it’s about a 47.5% chance that the 4 rolls will go by 7-less. In a 3 player game, it’s a 57% chance. So do you hold them or not? That’s up to you – you’ve got the numbers and get to make your own decisions.

Ok, now that we’ve established the frequency (or lack thereof) of getting robbed, let’s look at the consequences. We all know what they are: discard half of your resources. This seems pretty steep – half of your liquid assets are taken from your possession. The worst-case scenario is being left with only 4 resource cards. When you consider that your resource cards are not (or had better not be) the most valuable assets in your possession (anything you buy/build is worth multiple resource cards), this doesn’t seem so bad. Collecting cards gives me more freedom per turn to react by extending my *longest road*, buy Development Cards, or trade with others. Also, collecting cards is a natural result of doing well – if I have more Settlements or Cities on the board, I’m going to naturally end up with more cards in my hand. This means I have a high income. I also like to take into consideration the advantages of picking which cards to discard. I can throw away the cards of least worth, minimizing the effect of the 7 on me. Not too bad at all!

I like to consider being robbed as a parallel to being taxed. Every now and then the rich get taxed. Does this mean I should stockpile up to 20 cards in my hand? No, there’s no reason for that. What it means is that if I have 8 or 9 cards in my hand and I’m not happy with what I can do with them right now, I don’t have to panic and spend them or lower my trade value for them simply to lower the number of cards I hold – I can take my chances (which aren’t bad) and leave room for developing something that I know is valuable and will directly help me. I shouldn’t waste 2 cards or more when the worst-possible outcome is wasting 4 about 50% of the time. I’ll take my chances.

So, for me, getting robbed is by no means a good thing, but it’s really not that bad of a thing.

Insightful!

Dude you probably were smoking weed in your probability classes. Subsequent rolls are not related in any way and you cannot calculate probability of throwing/not throwing any number in a row. Probability of getting rolled 8 is higher than getting 7, you can figure out why yourself. All your “math” is crap.

It’s been a long time since I’ve done anything with this blog, but I felt like I should respond for other people that might stumble on this. I’m hoping this comment is just someone trolling.

If not, though, then I think you have some serious misconceptions on what’s going on here.

1. You’re absolutely right in that subsequent rolls are not related in any way. You’re wrong, though, about calculating the probability of throwing certain numbers in a row. Since rolls are independent, the probability of any two numbers being rolled consecutively can be found using the multiplicative property of independent events — P (A and B) = P(A)*P(B). This is actually ONLY true for independent events. So it’s strictly because of the fact that rolls are independent that we are able to do this.

2. The probability of rolling two dice and having the numbers sum to 8 is definitely not higher than 7. This is super easy to do. We can just count the combinations of numbers from 1 to 6 that sum to 8 and 7 respectively.

8: 2+6, 3+5, 4+4, 5+3, 6+2 (5 different combinations where order matters)

7: 1+6, 2+5, 3+4, 4+3, 5+2, 6+1 (6 different combinations where order matters)

Out of the 36 different combinations of two numbers, then the probability of rolling 8 is 5/36 and the probability of rolling 7 is 6/36 (or 1/6).

The math here is pretty basic. Looking back at this project several years later, there are definitely some areas that could have been done better…some of the analysis is pretty bare-bones. But this section holds up, since it’s just relying on some basic probability facts.

Alex, if you still have questions about this, feel free to comment more. I’d be happy to clarify.