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Luck Mitigation in Board Games

Luck can often play a large part in board games. From the very first games, using dice and pawns, to now more complex games with decks, luck mitigation has always been an important part of the board game culture. It is an essential part of game theory, and an even more important in the world of modern board games. Take it from me – luck mitigation is a really cool thing.

Okay, so this may be nerding out a bit – however, believe it or not, statistics and numbers form a core part of board gaming. This is evident when we look at the analysis behind games, something we like to do a lot here at Start Your Meeples. This board game blog was founded on the concept that gaming can be broken down into mathematical parts and process, and today we are going to look at some of the fundamental concepts surrounding board games – luck, probability, and mitigation.

There are various types of luck mitigation that can take place when playing games, and we will be looking at three core types today within this article. There is saturation model of luck mitigation, the alteration method, and the supplementation method of mitigation (those may not be the technical terms – if you know the technical terms please let me know in the comments below).

Understanding luck mitigation in games can help develop strategies in how to play them. If you are new to board games, or new to the concept of luck mitigation, then this article may give you some ideas. If you are a veteran on the gaming scene, then this article may simply confirm things you already know, but I hope you find it interesting anyway.

What are Luck and Luck Mitigation in Board Games?

Okay, so this may sound like a bit of an odd question – but before we go any further – humour me. Let’s take a closer look at luck and luck mitigation within games. What do we mean when we talk about both?

Well, Luck is the simplest thing to define, as it literally has a solid definition. Luck is:

Success or failure apparently brought by chance rather than through one’s own actions.

That is the definition according to the Google Rich Snippet when you type in the term “definition luck”. I know, it’s a scientific method. Good ol’ Google never fails.

Side Note: Google actually takes its definitions from https://www.lexico.com which is powered by Oxford University. 

There is, however, one key word in that definition that we need to pull out:

CHANCE

What this means, when we talk about chance, is we are talking about various mathematical concepts surrounding the idea of chance – namely, we are talking probabilities.

“To mitigate”, on the other hand, has the definition of:

Make (something bad) less severe, serious, or painful.

So, in essence, “Luck Mitigation” as a term means to lessen the effect of luck or bad probability within gaming. Simple, eh?

Now we have stated that – let’s move onto the different forms of luck mitigation we’ll be talking about in this article.

The Deck Saturation Model and Removal of Negatives Model of Luck Mitigation

Have you played Gloomhaven? If not then have you played deck building games like Legendary or Tyrants of the Underdark? All of those games use decks where the decks are pretty dire to begin with yet which you can improve over time. In Gloomhaven we are talking about the attack modifier decks of each character (read more here). In Legendary and Tyrants of the Underdark, talking about decks is just talking about the main part of the game.

In all games where you build decks, or modify pre-existing decks, you always want to improve your odds of getting the cards you want. Bad luck, for instance, is (in Gloomhaven) drawing the -2 card when you are trying to deal damage. In Legendary: Marvel, you want to avoid your rubbish cards clogging your deck up, and don’t really want to draw the Agents of Shield once you get to a certain point of the game. They’re just not good enough. The same for some of the basic Drow card in Tyrants of the Underdark. You want better cards, and you want to draw those more frequently.

This is where the saturation version of luck mitigation can come in. Paired with the removal of bad cards (ie. remove bad cards and the odds of drawing a bad card reduce…for obvious reasons), it is possible to increase your odds of drawing a good card, by decreasing your odds of drawing a bad. By adding cards to your deck, you can improve your odds of drawing a better card.

Let’s take Gloomhaven as an example. The Gloomhaven attack modifier deck is drawn from whenever an attack is taken. You do base damage, and then apply the result. If, for instance, I have ATTACK 2 and I draw +2, then it becomes ATTACK 4. If, however, I draw -2 then the attack fails. No damage is done.

Now, when you modify your deck in Gloomhaven you can remove a certain number of negative cards – like how in Tyrants of the Underdark you can sacrifice cards you don’t want; however, you can only do that a set number of times. Then, what do you do?

So, first, let’s look at what the simple removal of bad cards means for luck mitigation. As an example, let’s say you start with a deck of 30, with 15 bad cards in it. First, you remove as many bad cards as you can. Let’s say, you manage to remove 10 of the 15 bad cards.

Luck Mitigation - Negative Removal

Looks good, doesn’t it? But you’ve now removed all the negatives you can. How do you decrease the odds of drawing bad cards even further

From here, one way you can improve your luck in this case is via saturation. You add more cards to the deck (preferably good ones, otherwise what is the point?) to reduce your odds of drawing a dud card.

Let’s say, as an example, you now have a deck of 20 cards, of which 5 can’t be removed and are causing you a pain in the neck. Those cards are bad cards (it just occurred to me that this is especially important for those who enjoy the game Friday by Friedemann Friese) make your odds of drawing a bad card 0.25 or 25%.

Adding cards to the deck; however, will improve the odds of not drawing a rubbish card.

Luck Mitigation

As you can see, if you have a set number of negatives in a deck, then by saturating the deck with neutral or good cards you can seriously decrease the odds of you pulling a rubbish card. As noted before, it is important to remove negatives where you can as well, just to reduce the odds even more.

This is also why blessings are so good in Gloomhaven. Not only do they add benefits, but they make it less likely to draw negatives. Score!

Okay, a bit of a sweeping visit through luck mitigation through removal of cards and saturation of goodness into a deck. This can get a lot more complex as you remove and add cards at carious different times, and we’ll cover it at some point in another article, but for now let’s move onto the next method of luck mitigation.

The Alteration Method of Luck Mitigation

Very closely related to the above, the alteration methods of luck mitigation also incorporates aspects of the saturation model; however, it goes further than that.

Okay, so let’s take Dice Forge as an example. In Dice Forge, you play the game with two dice. You then, as the game progresses, change the sides to those dice, and thus conduct a sort of dice version of the deck saturation model. This is not the kind of alteration we are talking about, and that kind of works the same as the above.

Instead, when we talk about “alteration” we are talking about physically changing results, and this is mainly the case with dice.

The first is very very simple, and can be seen with the Focus symbol in Star Wars: Destiny. What it allows you to do is physically change a dice face to whatever you want it to be. Easy, eh? There’s not a huge amount that can be said about that other than it costs a dice to change a dice. You want a Blaster symbol, you can have a Blaster symbol, so long as you have the Focus on another dice.

The second, however, is cooler as it is something we come across literally all of the time – rerolling.

Rerolling or re-drawing is a form of luck mitigation that is vital in a lot of games – most notably tabletop war games like Age of Sigmar or  Shadespire. If you reroll, you increase the chances of getting what you want. Other games we are looking at Star Wars: DestinyDice Masters, and Dice Forge (again).

The big question is – how does this work? Well, although it sounds simple, the mathematics is actually quite complex.

If you roll one D6 dice the odds of getting any singular face is 1/6 (let’s say a 6 on a D6), which results in a 5/6 chance of not getting the face you want. If you are allowed a reroll then we actually multiply the failures by themselves – so if there is 5/6 chance of failure then, if you are allowed a reroll, you get a 5/6*5/6 chance of failing. This keeps multiplying based on the number of rerolls and in each case we subtract the result from 1, to provide us with the positive chance of getting the number we want.

What this means is the graph ends up looking like this –

Luck Mitigation - Rerolls

Pretty neat, eh? So if you have 10 rerolls on a D6 you have almost a 90% chance of getting the number you want.

Naturally enough this can be extrapolated. What if you want one of two numbers of a D6? Well, in that case we use the failure of 4/6, and the graph looks a bit like this –

Luck Mitigation - Rerolls 4.6

You get the idea. Rerolls are a great method of luck mitigation through providing an additional chance to get the number you want.

The Supplementation Method of Luck Mitigation

And so, as we journey through the Chasm of Chance and around the Peninsula of Probability, we come across our final stop off at the Sea of Supplementation.

Supplementation is probably the easiest concept we’ll be covering in this article and it is this –

You can make your luck better by having automatic passes on checks.

What does this mean? Well let’s take Game X as an example. Game X is a real life example by the way, but it is a legacy game, so I don’t want to give away too much whilst needing to talk about the mechanic. In Game X, you take checks based on stats and those determine the number of dice you get to roll for a check. There are, in Game X, also methods of adding on instant successes to certain rolls.

This means you may take a check with ten dice, but can add on instant success to make that easier.

Luck Mitigation - Supplementation

It makes sense when you look at it that way. You could also put it as percentages, reversing the Y axis, multiplying it by 10, and calling it “success percentage needed from dice”.

Supplementation is really that simple. Off the top of my head, right now, I can’t think of a game other than Game X that uses it, but my brain is a little bit mathematically frazzled right now. You get the idea though.

So, there we have it – three different methods (four if you count the top method as two) of luck mitigation in board games. As you can see, in includes a lot of maths, a little bit of game theory, and a lot of patience with trying to get Excel to format my freaking graphs correctly (seriously Microsoft – get it together!).

What are your thoughts? What methods haven’t I included? What methods do you like the best. Let me know in the comments below.

1 Comment »

  1. Enjoyed the post Luke! Of course, you’ve left out the simplest method of luck mitigation available, that doesn’t require any knowledge of probabilities at all – cheating! Sadly, I think I tend to lose most games ’cause I’ve failed to master either luck mitigation or cheating, but as long as I enjoy the game it doesn’t matter!

    Like

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