Paper-based prototyping: simulating real time

I was messing around with this game idea where players race along a dangerous road in trucks to deliver their cargo. As they travel along the road (especially if they decide to go at speed) they will run into dangers: landslides where they must dodge/clear terrain, fog so they can't see the cliff sides etc.

I'd love to try this out 'on paper' first with some friends. However I'm not sure how to simulate a real time experience of driving the trucks at various speeds. The most simple solution I have come up with is rolling dice to move however many grid squares; wherever you land you roll again to see if a randomised disaster occurs. To measure speed I could add a modifier, such as if they're going an 'above average speed' they get a +1 to the amount of grid squares they cover but also a +1 to the chance of a disaster happening.

However, in a video game I'd be simulating acceleration (by holding down a key for example) and changing gear for speed. It also would not be turn based and they would have free control of the truck's movement and could accidentally plummet off the edge.

I guess the game can track when a player leaves and enter a new square in the grid and, after so many, roll to see if a disaster occurs. However, I don't think my current idea would really reflect the real time game experience/dynamics I'm trying to create in the video game. Am I looking at this the wrong way?

Many thanks

It's a bit hard to imagine how a pen-and-paper-and-dice version of a game should actually convey the impression of real time at all. And admittedly, I doubt that this paper version will provide valuable feedback in regard to the implementation of a real-time game. However, if you think that it may be helpful (maybe just to get a rough idea about the events and variables that are involved, and their effects on e.g. the likelyhood on accidents), there may be some options.

The first one that came to my mind was: Derivation. As you probably know (or as you should know when you want to implement such a game)

• Velocity is the first derivative of position
• Acceleration is the first derivative of velocity (and the second of position)
• Force is acceleration times mass

So instead of allowing the player to control the movement, you could only allow them to control the velocity (or maybe only the acceleration, or maybe even only the force)

Note that this is actually pretty close to what you would implement in the real game: The player can not directly move his truck, say, 10 meters forward. He can only press a key to indicate that he wants to accelerate, and release the key (and press another one) to indicate that he wants to decelerate (or brake). In reality, one actually contains further derivatives. Namely, the force via the gas pedal (and even further: How fast one is pressing down the gas pedal etc.)

This could be modeled in a pen-and-paper game as well: You would keep track of (at least) the position and velocity. The player can change the velocity (and maybe the direction, by steering), and the new positions are computed from the velocity in each turn.

I hope that some ASCII-art will be enough to make the idea clear: Imagine the track to be modeled as a sequence of fields. The player starts, with a velocity of 0, facing right:

 __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __
|0>|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|
|  |  |  |                 |  |
|__|__|__|                 |__|
|  |
|__|
|  |
|__|


Then he can either actively decide to increase the velocity, or roll a dice to decide how much he wants to accelerate. Let the result be an increase of velocity of 6. This means that the next two rounds would be

 __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __
|6>|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|
|  |  |  |                 |  |
|__|__|__|                 |__|
|  |
|__|
|  |
|__|


and

 __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __
|  |  |  |  |  |  |6>|  |  |  |  |  |  |  |  |  |  |  |  |  |
|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|
|  |  |  |                 |  |
|__|__|__|                 |__|
|  |
|__|
|  |
|__|


Now, he could decide to keep his current speed, or maybe brake or accelerate further. Let him keep the current speed, then the next step will be

 __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __
|  |  |  |  |  |  |  |  |  |  |  |  |6>|  |  |  |  |  |  |  |
|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|
|  |  |  |                 |  |
|__|__|__|                 |__|
|  |
|__|
|  |
|__|


Now, some predefined event could happen, which is always to happen at the third time step: A landslide XX fills one field!

 __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __
|  |  |  |  |  |  |  |  |  |  |  |XX|6>|  |  |  |  |  |  |  |
|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|
|  |  |  |                 |  |
|__|__|__|                 |__|
|  |
|__|
|  |
|__|


Fortunately, the player is already past this obstacle! A player that only had accelerated by 5 in each step would now encounter this situation:

 __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __
|  |  |  |  |  |  |  |  |  |  |5>|XX|  |  |  |  |  |  |  |  |
|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|
|  |  |  |                 |  |
|__|__|__|                 |__|
|  |
|__|
|  |
|__|


And he'll probably crash into the obstacle, because he can't brake and steer and take the detour to avoid it.

However, the fast player may now decide to decelerate, because he's heading for a corner. So he decelerates to 5

 __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __
|  |  |  |  |  |  |  |  |  |  |  |XX|5>|  |  |  |  |  |  |  |
|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|
|  |  |  |                 |  |
|__|__|__|                 |__|
|  |
|__|
|  |
|__|


giving

 __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __
|  |  |  |  |  |  |  |  |  |  |  |XX|  |  |  |  |  |5>|  |  |
|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|
|  |  |  |                 |  |
|__|__|__|                 |__|
|  |
|__|
|  |
|__|


then decelerates to 2, giving

 __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __
|  |  |  |  |  |  |  |  |  |  |  |XX|  |  |  |  |  |2>|  |  |
|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|
|  |  |  |                 |  |
|__|__|__|                 |__|
|  |
|__|
|  |
|__|


and

 __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __
|  |  |  |  |  |  |  |  |  |  |  |XX|  |  |  |  |  |  |  |2>|
|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|
|  |  |  |                 |  |
|__|__|__|                 |__|
|  |
|__|
|  |
|__|


Now turn the steering wheel, to avoid rushing out of the track, giving

 __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __
|  |  |  |  |  |  |  |  |  |  |  |XX|  |  |  |  |  |  |  |2 |
|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|v_|
|  |  |  |                 |  |
|__|__|__|                 |__|
|  |
|__|
|  |
|__|


and

 __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __
|  |  |  |  |  |  |  |  |  |  |  |XX|  |  |  |  |  |  |  |  |
|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|
|  |  |  |                 |  |
|__|__|__|                 |__|
|2 |
|v_|
|  |
|__|


Of course, there may be rules, e.g. like

"Changing the direction is only possible with velocity smaller than X"

or

"Changing the direction will take X turns when the velocity is X"

All this also depends on how exactly you want to model the track and the directions in the paper version. One can imagine generalizations of this, e.g. by using tracks that are 5 fields wide, and 8 directions (including diagonal movement). But I think that it will allow to model some behaviors that are similar to that of a real-time game:

"Oh sh..! I'm to fast for this curve! I should have braked earlier..."

• Absolutely excellent answer. Thanks so much. This has really helped and also improved my thought process on how the game will work with derivation in mind. I'm very new to game design so I'm attempting to try different approaches and get into a good design and testing mindset.My goal really with prototyping it on paper is to have some very low-tech , low-cost way to measure how fun the dynamics of the game could actually be and getting some friends to try it out. This and some other feedback I've received elsewhere is going to be immensely helpful. Thank you!
– Mark
Aug 22, 2015 at 12:19