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Roll or Draw: Basic Probabilities in Board Games

Posted Monday, 27-Jul-2015

 

Contributed by Andrew Knighton

Most board games contain an element of chance, whether from rolling dice, spinning a dial, drawing a card or pulling tokens from a bag. Understanding the difference between them is the most basic step in understanding the probability of games, and so winning more often.

Dice Have No Memory

We all have superstitions about our dice. This one is cursed and always rolls 1’s, that one is lucky, never touch someone else’s dice, and so on. Beyond very small imperfections in the way the dice are made, these superstitions are just jokes.

There’s no point using the dice that rolled well for you last time, or the ones that rolled badly because they’ve “used up most of their bad rolls”. Dice, unlike their owners, have no memory of what’s come before. A red Zombie Dice dice has a one in six chance of rolling a brain every time, no matter what.

 

Each die roll in Zombie Dice provides you with the same amount of chance.
Each die roll in Zombie Dice provides you with the same amount of chance.

 

The same is true for spinners. Unless there’s a crease in the cardboard that makes your Escape From Atlantis spinner stop on the same monster every time, the odds are the same no matter what came before.

Cards Carry Their History

Cards, and other blind draws like taking tiles from a bag, are a different matter. Whatever emerges this turn is now less likely in future turns.

Imagine you’re playing Doomtown Reloaded and you’ve stacked your deck with as many 4’s as you can. In the first shoutout you have a nearly one in three chance of each card being a four, making it easier to draw a great hand. But if your poor no-bullets shooter somehow draws five fours, you’ve used those up – each card has only a roughly one in four chance of being a four next time.

 

As opposed to dice, cards actually have memory -- and the player using them should as well.
As opposed to dice, cards actually have memory — and the player using them should as well.

 

Each time you draw the card, tile or token you want, the odds of it coming up again drop, at least until the deck is reshuffled or the bag refilled.

Knowing When to Count

If you put effort into keeping track of random results, will it help you predict future outcomes? Not for dice, but definitely for cards. As with history, card draws doom those who don’t learn from the past, and favor those with a good memory.

Published by BoardGamePrices.com



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