Tuesday 24 May 2016

Roll With It

Last week I watched The Force Awakens again, and one line really got me thinking:
Han Solo: The longer we’re here, the less luck we’re gonna have.
This quote prompted me to rethink "let it ride" and devise an alternative.

"Let it Ride" is an idea that gained traction about ten years ago – if a character successfully makes (for example) a sneak roll then you let all subsequent sneak rolls also pass until you need to make a more difficult roll. This is to stop the "roll until you fail" problem, but I've not been entirely satisfied with the solution.

The problem the rule addresses is that multiple rolls for repeated applications of a skill will cause it to fail eventually. This is easily seen by the following graph which shows how a given % chance for a single check turns into a much lower % chance of passing multiple checks:

The rapid drop off is clear. 70% chance of success becomes 49% chance of two successes – by ten successes it’s dropped to just 3%.
The “Let It Ride” rule however replaces this with a "first check is everything" system:

This means that after you get past the first guard there’s no chance of failing to sneak past the second guard. Han is never going to say his line. What is required is some middle ground…

I went through various solutions which I discarded before settling on a simple rule. (Skip past the next section if you just want to go straight to the actual proposed rule).

Prototype Solutions
My first idea was you roll once, and that roll is reused for each subsequent check except that the roll is reduced by one each time. Thus if you need 14+ to sneak past each guard, and you roll a 17, then you get 17 for the first guard, 16 for the second, 15 for the third, 14 for the fourth, 13 for the fifth. So you fail to sneak past the fifth guard.
This works quite well, except that you will always eventually fail to sneak past a guard (assuming there are enough of them).

Version two is that each time you can also roll to see if you improve the score. Thus if you roll 17, 5, 15, 18, 3 then you get 17 => 16 (better than 5) => 15 (equal to 15) => 18 (better than 14) => 17 (better than 3).
This looks like there might be a lot of book keeping. Also you could improve your chance at a hard task by doing several easy tasks first!

Version 3 is for the DM to roll a D6 each time to see if the roll is decreased. That’s a bit of an improvement but still sounds like a lot of fuss and complicated statistics.

The fourth version is to decrease it by one each time until the roll fails, and then allow the player a second roll. So that’s exactly like the first example, but instead of failing to sneak past the fifth guard you need to roll again. That is, you needed a 14 and got a 17 so you get to pass the first four guards before you roll again.

So how does this look in practice? For a d10:

If you have a 70% chance of success and need ten successes, then the usual rule reduces you to 3% chance of success; let it roll gives you 70%, this rule gives you 35%. So after you’ve got past the first guard you've a 50:50 chance of sneaking past the next 9.

The obvious mechanical concern with this rule is that the effect of it depends heavily upon the dice system in use – the effect of lowering your score by one depends upon what dice you’re rolling! If you switch from d10 to d20 then the drop off is half as steep – 70% only drops to 54. This could be remedied to a certain extent by altering how much you knock off each time – with a d20 system you’d probably knock off two every time.

Final Version - Roll With It.
Hence enter the fifth (and final) version. The roll you make carries over to subsequent checks each time unless you roll a 1 or 2 on a d6 – in which case you reroll it. You roll a 17 for sneaking past the first guard? Then you get 17 for all subsequent sneak attempts until you roll a 1 or 2 on a d6; at which point you roll again.

This gives you a similar outcome to the last version - 

- but this system bypasses the dice system in use – the above graph is true whichever dice system you use. If you have a 70% chance of sneaking past a guard, you have a 27% chance of sneaking past 10 of them. It also removes any need for book keeping – all you need to do is note the roll made. The precise system can be modified according to taste - you could have reroll on a 1 which makes the drop off half as steep.

What Does It Mean In Practice?
The way to validate a system like this is to put some numbers into it:

If you have a 90% chance of passing the first guard, you’ll have 80% chance of getting past 5 guards, and half of the time it’s the first guard that spots you. If you get past the first guard, on average you’ll get past 14 of them.

If you only have a 10% chance of passing the first guard – but you still make it – you're on a roll and the chances are you’ll make it pass one or two more. If you get past the first guard, on average you’ll get past 3 of them.

Keep It Secret
Note that the player may roll a 3 and yay! Keep the roll! But then fail the check (because this check required a higher roll). The player doesn't get the option to reroll – else you would improve your chances of succeeding at a hard task by trying an easier one first.

Hence you must keep the player’s initial roll secret (e.g. via the draw a card method) so they don’t know if they’ll make this harder check or not – there’s always an element of suspense.

Now all I need is to persuade my players they should try sneaking past some guards...