Consequences of Precise Probabilities

Pathfinder

I’ve been playing the digital adaptation of the Pathfinder Adventure Card Game lately. Besides the bugs (and dear me there are a lot) it’s a pretty faithful recreation of the physical game – yet I’m finding one aspect of it is making me play very differently: Every time you do something to modify a die roll the game shows you the probability of the roll succeeding and permits you to undo that modification.

Probabilities in Rise of the Runelords

Many of the bonuses in the game are represented by extra dice. At any given point you usually have access to a whole load of these bonuses, but use of them has a very noticeable opportunity cost leading to you seeking to use as few as possible. On a typical turn you might hit into a situation like this:

You’re righting something that needs a total of 22 to beat.
You subtract one from each die rolled.

You can punch at D6 or attack with a sword at D6+D8 or cast a spell at D10+D6+D6+2
You have four blessings which will give you a D6 if you’re attacking physically or a D10 if it’s a spell.
One of those blessings gives two dice instead of one if it’s used for a D6.
You could discard the sword, losing the ability to use it again and get an extra D6
Your mate you shuffle part of his hand into the deck to provide an extra D4+2
You have an item you can discard for a bonus D4 but that applies to all fights this round (Which is at its best if you save your blessings since each blessing could also be used to flip another card and maybe get into another fight if it’s not used here)
One of the other players has a spell that gives +3 to strength rolls so works with the sword but not if you’ve cast a spell.

Computing the probability of success using each combination of bonuses would be a massive headache. Heck even the base combinations would take some doing. But the game does it instantly and displays the number for you.

How does it change the game?

The obvious first degree effects are that it means I make optimal decisions. If I can get a bonus one of two ways and the cost to both is the same then I’ll always pick the bonus that’s best in the situation. That’s not such a big deal, I’d probably have done it anyway most of the time.

The major impact it’s had has been in how I’ve learned the game over repeat plays.

In tabletop I doubt I’d notice the difference between a 91% and 97% chance of success. It’d always be at the point of “I’ve got a big pile of dice and the average expected result is at least twice what I need to roll – it’s gonna be fine.” Yet providing the probabilities makes me sensitive to it. It’s a game that can be won or lost on a single roll – tripling the chance of failure for that roll (from 3% to 9%) is actually a really important difference in those critical situations.

It’s harder to pin down how these things are altering the emotional experience of the game. I’m making better moves, but am I enjoying the game more or less for that? The reaction to a roll seems different – on the one hand I get “Well I decided to stick at 95% and not throw another card in, 1 in 20 chances happen all the time” where I’d have got “That roll is so absurdly below average, I hate you dice.” but on the other hand failing a >99% roll is a worse kick in the teeth than it’d have been if you weren’t aware of just how good the odds were.

There’s also a conflating factor in the game being single player. “Shall I throw in my other characters extra card to squeak an extra 2% chance to win out of this roll” is a fundamentally different question to “Shall I ask Jane to give up her extra go so I can have a 2% extra chance to succeed?”

Overall I think being aware of the exact probabilities sharpens the game. Dice are fickle, but over time, over many rolls, fair. It makes me more aware of smaller changes which in turn means I think about choices that I might otherwise have discarded out of hand. Ultimately it frees me from arithmetic to enjoy what the designers intended the game to be.

What’s the take away for designers?

Games can be more or less explicit about the probabilities of success involved in doing things. A magic computer box that does the numbers is not a necessity: Settlers of Catan dots its pieces to show dice probabilities. It would not be possible to do something for more complex mechanics like the examples shown here – but the mechanics themselves can be streamlined.

It’s also not an all or nothing approach. For instance Race for the Galaxy includes a card that allows you to guess the cost of the top card of the deck and draw it if you were correct. That card contains a little table showing how many of each cost of card are included in the deck. This doesn’t mean you can calculate the probability (I mean you could if you wanted to sit and count the number of cards of each cost currently in play and that you’ve personally discarded) but it makes it less obscure – you have a better idea of what it might be than if you didn’t have the contextual information.

Most games are likely to benefit from giving the players more information and more powerful tools to make decision – if the rest of the game supports that. There are some games that being able to work out the odds of each move *is* the gameplay and these calculations are intentionally on the cusp of human ability – but for more games working out the best move is the gameplay and understanding the odds of various outcomes is a tool in reaching the more interesting factors that define the best move in that particular game.

Dice: Rolls, totals and pools

It’s going to be a mathsy one this week, I’m interested in thinking about different ways to interpret dice rolls and what they mean for game design. It’s not going to be as off the wall as I was in 6, this isn’t about considering stuff like the position of the dice relative to the other dice, but even within those constraints there are still a lot of ways to interpret the number showing on the dice.

snakeeyes

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Don’t tell me the odds

So there’s this cool psychological effect whereby if you ask people “What are your odds of drawing a full house?” you get higher numbers on average than when you ask “What are the odds of drawing a full house?”. People are almost universally aware that the cards drawn off a deck does not change depending on who is doing the drawing, but when asked – on average – will assign themselves higher odds. How do we use that?

cards

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Randomisation Timing

I’ve been playing the new Hearthstone expansion recently and I’ve not had a particularly good time with it. I’ve noted before that I’d enjoy Hearthstone more if they deleted every card with the word “random” printed anywhere on it and this expansion seems to be pushing towards more cards of that nature (A brief aside: There is a difference between “I don’t like this” and “This is bad” – I think this is actually going to be a good direction for the game as a whole). The thing is that there are other games which involve more randomisers than the average game of Hearthstone, because what bothers me isn’t the presence of the random factor, but the timing surrounding it.

epictiming

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Cards and randomness

Cards are a great way to add randomness to a game, they’re incredibly flexible in terms of what you can do with them. You can fix a deck, or part of a deck. You can add things to it without consulting what they are. You can view a few cards and get rid of a few of them selectively. You can put new (or previously used) cards into a deck and they can go on the top, bottom or be shuffled somewhere in between. Cards are magic.

cardmagic Continue reading