[Deadline] 1 Page, 24 Hours

[knicknevin]

Well, I wrote a game in a day yesterday: from initial idea to final document actually took me about 8 hours (including a trip to the cinema to see V for Vendetta, which is fantastic by the way!) so the game itself is very short and sweet.

The basic idea is that players take turns to choose dice for their actions, like so:
Quick Actions: The character does something now, on the spot, for instant results: the player rolls 1d6 and multiplies the result by 1 minute. A success earns 0.5 Goal points.
Slow Actions: The character takes their time & is methodical, for more certain results: the player rolls 1d8 and multiplies the result by 3 minutes. A success earns 1 Goal point
Long Actions: The character goes off on a mini-quest to acquire the resources they need: the player rolls 1d10 and multiplies the result by 5 minutes. A success earns 1.5 Goal points.

The target for success is to roll greater than 4, but there is a session Clock and the time you take is added to the time on the Clock; when the Clock reaches the deadline set by the GM, the game4 ends and the winner is, broadly, the player with the most Goal points. There are more tactical decisions to be made by the players, but the choice of actions and their consequences is at the heart of the system.
I did some very rough maths, based on 1 player using 1d8 for all his actions, and came to the conclusion that it would take him about 4 Hours to achieve 8 Goal points just on his own; since other players will also take actions in that time, then he can expect to get less than this, but the time allowed for the by the Deadline is likely to be closer to 8-12 Hours.

OK, so... any breaks in this? Do any of the actions have a clear, tactical advantage over the other two, such that the players will always pick the same action and ignore the other choices? Or are there situations (e.g. Player A has 4 Goals, Player B has 1 Goal and there is 1 Hour left on the Clock) where there is a definite tactical advantage to taking one course of action? Its a little beyond my ability with statistics to figure it all out, so I'd appreciate any constructive comments.

[Selene Tan]

The average results for a d6, d8, and d10 rolls are 3.5, 4.5, and 5.5 respectively. Multiplying each by the time for the action, you get 3.5 minutes, 13.5 minutes, and 27.5 minutes. Divide the Goal points earned by these times to get average Goal points per minute:

Quick actions: 0.14 gp/min
Slow actions: 0.074 gp/min
Long actions: 0.054 gp/min

In other words, there's no reason to take anything other than Quick actions. You'll have to take more of them, but on average you'll earn about twice as many Goal points as Slow actions in the same amount of time.

One solution is to increase the Goal points earned for Slow and Long actions. 2 GP for Slow and 4 GP for Long will make the gp/min values close to even, but slightly favor Slow over Long and Long over Quick actions. (To be almost exactly even, it should be 1.93 for Slow and 3.93 for Long.) But if you want nice, round numbers for GP earned and minute multipliers, you'll have to accept some unevenness in the results.

You could also change the minute multipliers, although if that's all you change, the time difference between the actions will be very small.

Another possibility you might consider is to change the number and type of dice used for quick, slow, and long actions. e.g. quick = 1d6, slow = 2d4, long = 3d3 or 3d4. Rolling more dice makes results stick more closely to the average. So in my example, longer actions will take a more predictable amount of time.

[knicknevin]

Does that model take into account the target needed to actually earn a Goal point? For example, 3.5, the average for a d6 roll, is 1.5 below the amount needed to succeed, therefore on average you will get 0 Goal points on such an action. You will only succeed 1/3 of the time with a d6 and will need to do so twice to earn 1 whole Goal point; with a d8, you will succeed 1/2 the time and earn 1 whole Goal point each time you do so.How does that effect the statistics?

[Walt Freitag]

Apparently, Selene's model doesn't take the success threshold into account.

Here's what I get:

quick: .048 gp/min
slow: .037 gp/min
long: .033 gp/min

But the question remains, what makes the decision of quick vs. slow vs. long actions tactically interesting? Often in games like this a higher maximum payoff is balanced by a higher risk (that is, a broader flatter probability distrinbution with a lower average expected payoff). But in this case, even though the quick action succeeds less often per action, it also allows more attempts per minute, so the risk per minute invested is actually less. Even if you were to adjust the formulas so that the gp/min were the same in all cases, making quick actions would still actually be the "safe" option because over time, making seven quick actions (approximately, on average) instead of one long one, the chance of ending up with no points at all would be very small (about 6%), while the chance of getting no points at all with one long action is 40%.(It's actually a bit more complex than that, because the attempts that fail also take less time, especially for the slower options. But even so, the game is clearly optimizable in an "if you're X many points behind, and there's Y much time left, your best chance is to do Z" way.)

One more thing... why fiddle with the halves of goal points? Why not make the goal point payoffs 1, 2, and 3?

- Walt

[Walt Freitag]

Oops, I completely overlooked an important factor in the analysis. There's only one clock, and the players take turns rolling. So when a player's action uses up time, it uses up time for everyone.

That changes everything. It actually makes the gp/min pretty much irrelevant. What's important is the gp per player's turn. If they're taking turns, in the end everyone is going to get approximately the same number of turns (within 1 more or less) regardless of what happens with the clock.

quick: .167 gp/turn
slow: .5 gp/turn
long: .9 gp/turn

So, long actions are the only sensible option. Using more time is no downside at all, if it uses up my opponents' time too.

- Walt

[Selene Tan]

I thought the success roll was separate from the how-many-minutes roll, which was why I didn't include it. I might have been wrong. :)

Anyway, the numbers obviously could use some tweaking. It might be helpful to set up a spreadsheet so you can put in new numbers and immediately see the results.

[knicknevin]

That's interesting, thank you.

One more thing... why fiddle with the halves of goal points? Why not make the goal point payoffs 1, 2, and 3?
- Walt

Well, the Goal requirement (i.e. how many points your 'team' [see below] needs to win) is tied directly to the number of hours allowed by the Clock, e.g. if the Deadline will be reached in 8 hours, then your team needs 8 or more Goal points.

So, long actions are the only sensible option. Using more time is no downside at all, if it uses up my opponents' time too.
- Walt

Generally that is true and encouraged by the game; the complication is that you don't know whether the other players are on your team or not.
At the start of the game, each player secretly picks an agenda:
Success: You are on the team trying to save the day.
Glory: You are a loner who cares only about yourself.
Sabotage: You are on the team supporting/causing the crisis.

When the Deadline passes, players reveal their agendas:only if the combined Goal points of your team equals or exceeds the Goal requirement can you, as a player, win by having the highest individual score. If neither 'team' wins or if they tie, then the Glory player with the highest individual score is the winner.

Players can also take part in conflicts to steal Goal points form each other and force players to miss turns; in addition, each character has strategic options like 'Suddenly...' which means their action takes places concurrently with someone elses, or 'Then...' which allows you to see another player's agenda but advances the Clock 15 minutes and so on.

[knicknevin]

If they're taking turns, in the end everyone is going to get approximately the same number of turns (within 1 more or less) regardless of what happens with the clock.
- Walt

I just had a thought; what difference would it make, if any, if each player had their own Clock? That is, instead of one big clock counting down, each player manages the time taken by their own character... say that each round carried on until all players had taken at least 1 hour, so that some might get to take more actions than others.

Spinning off from the idea, what if players actually bid time for their actions instead of rolling? The highest bidder in each round got 2 Goals, the next 1, the next 0.5 and the rest none; if each player had a Time fund, they would be limited on what they could bid... Well, its just an idea, needs some working out.

BTW, meant to write 'Meanwhile...', not 'Suddenly...' on the prior post; my brain is on the fritz.

Thanks for the constructive feedback Walt & Selene! It always helps to get a fresh perspective on things. :-)

[knicknevin]

But the question remains, what makes the decision of quick vs. slow vs. long actions tactically interesting? Often in games like this a higher maximum payoff is balanced by a higher risk (that is, a broader flatter probability distrinbution with a lower average expected payoff).

After mulling this over for a while, I came up with this alternative:

- At the start of each round, each player makes a secret bid of 1 to 12; whoever has made the lowest unique bid earns 1 Goal and the player to their left starts the round proper.
- On your turn, you choose from the three actions as before, but they are now implemented as follows; for all actions, you roll 1d12 and your result must be equal to or lower than the bid you made at the start of this round in order for you to succeed.
Quick Action: Add 1 to your roll for success, gain 1 Goal point if you succeed; add your bid and your roll together and multiply the result by 1 Minute.
Slow Action: Add 2 to your roll for success, gain 2 Goal points if you succeed; add your bid and your roll together and multiply the result by 2 Minutes.
Long Action: Add 3 to your roll for success, gain 3 Goal points if you succeed; add your bid and your roll together and multiply the result by 3 Minutes.

- The end game now works as follows:
If the 'Success' team meets the Goal requirement, then the winner is the player on that team with the highest score.
If the 'Success' team did not meet the Goal requirement by the time the Deadline was reached, then the 'Sabotage' player with the highest score is the winner.
If however, in the above case, the 'Sabotage' team did meet the Goal requirement, then the winner is the Glory player with the highest score.

Hopefully, this model rewards high risk play more than the low risk whilst still keeping prices in line with risks. Also, it encourages Success players to preserve Time in favour of getting Goals, whilst Sabotage players want to waste Time and avoid getting Goals; Glory players will alternate between gaining points when they think they are behind and wasting time when they think they are ahead.

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