# Random but bounded game lengths

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jwarrend
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Joined: 08/03/2008

Games like "Lowenherz" have a game end that is triggered randomly, and this can be appealing because it prevents end game "cashing in your chips" effects. In my GDW game "Sands of Time", and now in my new game based on the Thirty Years War, I'm trying to explore ways to have the game ending, and/or the onset of scoring rounds, occur randomly but with some predictability.

I have come up with one idea that may work, but I hope that others will chime in in this thread with solutions they've come up with to similar challenges (not necessarily to help me out, but just for the sake of discussion).

In my idea, there are sixteen cubes, four in each of four colors, green, yellow, red, and black. The colors correspond to four phases of the game, first, second, third, and fourth, respectively. The idea is that each turn, one cube will be pulled from the cup. But at first, only the four green cubes are thrown in the cup. Each turn, a cube from the next phase is thrown in to the cup as well. When you pull a cube from the next phase, a scoring round is triggered, and you now begin adding cubes from the subsequent phase.

So for example, initially there are the four green cubes in the cup. At the end of turn 1, you pull a cube (suprise, it's green!) and then add a yellow cube to the cup. You do the same thing in the next turn, and the next, until you pull a yellow cube. At this point, you evaluate scoring and then begin throwing in red cubes. And you keep going until you pull a red cube, at which point you score again and beging throwing in black cubes. When you finally draw a black cube, the game ends.

There are a few variants to this; one possibility is that a phase doesn't end until all four of its cubes are out (instead of ending the first time a cube of the next phase appears). This is nice because it gives a fixed game length (16) but slightly variable timing of the different phases.

I want to have something like this in my game because I would like to have various points in the game where the Emperor dies, and a succession begins. But I also think I'd like to tie the overall game length to the number of imperial elections; eg, when the fourth emperor is elected, the game ends. This could in principle lead to a wildly varying game length, but concepts like these could be a way to keep it reasonably consistent from game to game.

-Jeff

rellekmr
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Joined: 12/31/1969
Random but bounded game lengths

Caylus has a varying but player-controlled game and section end mechanism which I found interesting.

jwarrend
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Random but bounded game lengths

rellekmr wrote:
Caylus has a varying but player-controlled game and section end mechanism which I found interesting.

Thanks for the tip; I haven't had a chance to play Caylus yet, but reading a quick review of the game, it does seem like an interesting mechanic. But, it isn't exactly what I'm looking for in this thread; I am interested primarily in a game end that is triggered by a random event, such as a card flip or a die roll, but whose ending is somewhat controlled (so that the game-to-game fluctuations are limited).

-Jeff

rellekmr
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Joined: 12/31/1969
Random but bounded game lengths

You could use a hidden timer.

jwarrend
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Random but bounded game lengths

I suppose, but that seems more appropriate for a party game than a strategy game; I'm more interested in a way to trigger the game end internal to the game's components and mechanics.

Although there definitely is some potential to the idea of just playing for a fixed length of time; that means that the more efficiently players play, the more they can accomplish, but the total game length is identical from game to game. I wonder why that hasn't really been tried before; it's an interesting idea.

-Jeff

rellekmr
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Joined: 12/31/1969
Random but bounded game lengths

I think Icehouse uses a hidden timer.

rellekmr
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Random but bounded game lengths

This could be paired with a "hot potato" kind of mechanic that penalizes the last player to act. This would encourage quicker play.

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Joined: 04/23/2013
Random but bounded game lengths

Wow it's amazing how quickly a misunderstanding of the problem at hand can get the whole thread off track.

Jeff,

In my probably never to be finished game Wreck Ashore, I wanted the game length to be between 12 and 18 turns, with an obvious average of 15 turns. As you recall, each turn a single shipwreck was revealed and placed. 12 of the 18 possible wrecks had a shipwreck icon on it. As soon as the 12th wreck with the wreck icon was revealed, it triggered the game end.

Now I know your game has several scoring rounds, so it might not be applicable, but perhaps it will give you some ideas as to what to try. Personally, I like the idea you already suggested and have mentally filed it away as something to possibly try in the future.

-Michael

Kreitler
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Joined: 12/31/1969
Random but bounded game lengths

Hey Jeff,

I've implemented a "random game end" mechanic for Mors Atlantis. In that game, players try to cast permanent spells to achieve victory. Most spells have an elemental aspect (earth/fire/air/water), but some are "black arts". When someone casts a black spell, he must draw and immediately play a from a deck of cards. This deck contains 3 blank cards per player, plus 3 face cards (Ares, Hades, and Hecate). When all three face cards are played, the game ends immediately.

The black cards have special powers that help players achieve victory more quickly, but each time players use them, they drive the game closer to a premature end.

I have only playtested this solo currently, so I don't know how well it works in practice.

Mark

rellekmr
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Random but bounded game lengths

Darkehorse wrote:
In my probably never to be finished game Wreck Ashore, I wanted the game length to be between 12 and 18 turns, with an obvious average of 15 turns. As you recall, each turn a single shipwreck was revealed and placed. 12 of the 18 possible wrecks had a shipwreck icon on it. As soon as the 12th wreck with the wreck icon was revealed, it triggered the game end.
If the goal is to avoid game-end cash-out strategies, this method would often fail if the non-icons all came up early, signaling to the players that the game would definitely end on the 18th turn.

johant
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Joined: 12/31/1969
Random but bounded game lengths

Pallazzo came to my mind, as soon as the "fifth tile" from the third and last pile has been drawn the game ends.

The mechanic used in Caylus is a good example of how the players could force the game to end earlier.

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Joined: 04/23/2013
Random but bounded game lengths

rellekmr wrote:
Darkehorse wrote:
In my probably never to be finished game Wreck Ashore, I wanted the game length to be between 12 and 18 turns, with an obvious average of 15 turns. As you recall, each turn a single shipwreck was revealed and placed. 12 of the 18 possible wrecks had a shipwreck icon on it. As soon as the 12th wreck with the wreck icon was revealed, it triggered the game end.
If the goal is to avoid game-end cash-out strategies, this method would often fail if the non-icons all came up early, signaling to the players that the game would definitely end on the 18th turn.

The chance of this actually happening is 1 in 6 with the above scenario. It would be even less if you increase the turn variance. For example, If you wanted the game to go between 10 and 20 turns, it would happen 1/10 of the time. But you're right, it is a matter of timing of when the non iconized tiles come out. As you stated, if they come out too early, it's just a matter of counting the remaining tiles. I think this would be extremely rare however, especially with a greater variance in turns. In my game, it works well because the game ended thematically by the onset of the hurricane season, something the players should be able to forsee somewhat...

-Darke

Xaqery
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Joined: 07/26/2008
Random but bounded game lengths

If three of you showed up at my door tonight, after I helped solve some board game design emergency, I would suggest we all played Tikal. Of all my games itâ€™s the game I want to play the most now that my board game playing time is at a premium.

One of the reasons I like Tikal is the random but increasingly predictable scoring rounds / end of game.

When you know there is not going to be a scoring round you can play very differently than if there might be one very soon. Tikal has both of these types of moments. This forces you to switch gears and at all times be thinking about your short term goals and your long term goals.

- Dwight

Nando
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Joined: 07/22/2008
Random but bounded game lengths

EDIT: I got nothing.

IngredientX
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Random but bounded game lengths

I suppose the most extreme example of this is High Society, when the fourth red card comes out. This could mean that a game could end after the fourth card draw (though this is rare).

It's not so much a problem in High Society, which is a 15-minute filler game, but I think you're planning for a heavier game. So the second method you mentioned, when all the cubes of a certain color (or perhaps X cubes of a color) have been pulled have been pulled, will probably give you the predictability you need, while still making the actual timing fuzzy.

One thought is to have the mechanic that inserts cubes into the cup under the player's control. Offer them a certain number of VP, or some other benny, to toss a cube in. This could help certain players and hinder others. You probably wouldn't want to make it so that it would be an obvious play every turn, so that a constant number of cubes are going in every round anyway.

There are lots of ways to go with this one...

jwarrend
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Random but bounded game lengths

Thanks to those who have chimed in so far. Tikal is a great example of what I'm talking about. And indeed, that and the example from Wreck Ashore are nice because the "game clock" is integrated into the existing mechanics and componentry of the game. With my "colored token" idea, it would, at the moment, be a separate phase and a separate system, which is less elegant.

I do think, though, in a different game, it could work well as a well-integrated mechanic. For example, perhaps in an exploration game, there are four areas that you can explore, you start in the "green" region and work your way out, and the tokens correspond to the timing of which regions score when. Maybe there are even specific flags that you uncover that instruct you to pull a token, or to add one to the mix. This would sort of be like Betrayal at House on the Hill, where the game switches phases when a certain number of icons of a specific type have been revealed.

I could also see it working with Gil's suggestion to allow player control over what tokens go into the cup. It would be a bit like Age of Mythology, in which players have some control over what scoring avenues are most heavily rewarded. Only in this case, players would be governing the relative timing at which the different payouts were to occured. Again, this could be a spatial thing (eg, which region will score next, red or green?) or it could be a set of commodities that everyone has (eg, what will score next, red (apples) or green (grapes)?)

Definitely some potential that I can see; hope it will find its way into one of my games at some point.

Thanks again for some good input!

-Jeff

Epigone
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Joined: 12/31/1969
Random but bounded game lengths

Darkehorse wrote:
In my probably never to be finished game Wreck Ashore, I wanted the game length to be between 12 and 18 turns, with an obvious average of 15 turns. As you recall, each turn a single shipwreck was revealed and placed. 12 of the 18 possible wrecks had a shipwreck icon on it. As soon as the 12th wreck with the wreck icon was revealed, it triggered the game end.

This actually doesn't work. The game will end in 12-18 turns, yes, but here are the probabilities:

18: 17C11 / 18C12 = 0.66667
17: 16C11 / 18C12 = 0.23529
16: 15C11 / 18C12 = 0.07353
15: 14C11 / 18C12 = 0.01961
14: 13C11 / 18C12 = 0.00420
13: 12C11 / 18C12 = 0.00065
12: 11C11 / 18C12 = 0.00005

The average turns out to be just about 17.5 turns rather than 15; in fact, a game will last 15 turns or less only about 1 in 40 times.

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Random but bounded game lengths

Epigone wrote:
Darkehorse wrote:
In my probably never to be finished game Wreck Ashore, I wanted the game length to be between 12 and 18 turns, with an obvious average of 15 turns. As you recall, each turn a single shipwreck was revealed and placed. 12 of the 18 possible wrecks had a shipwreck icon on it. As soon as the 12th wreck with the wreck icon was revealed, it triggered the game end.

This actually doesn't work. The game will end in 12-18 turns, yes, but here are the probabilities:

18: 17C11 / 18C12 = 0.66667
17: 16C11 / 18C12 = 0.23529
16: 15C11 / 18C12 = 0.07353
15: 14C11 / 18C12 = 0.01961
14: 13C11 / 18C12 = 0.00420
13: 12C11 / 18C12 = 0.00065
12: 11C11 / 18C12 = 0.00005

The average turns out to be just about 17.5 turns rather than 15; in fact, a game will last 15 turns or less only about 1 in 40 times.

You may be right, but I have no idea what your calculations mean. I was basing my assumptions on common sense. Perhaps you could explain your reasoning in laymans terms.

-Darke

Sebastian
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Joined: 07/27/2008
Random but bounded game lengths

Darkehorse wrote:
Epigone wrote:
Darkehorse wrote:
In my probably never to be finished game Wreck Ashore, I wanted the game length to be between 12 and 18 turns, with an obvious average of 15 turns. As you recall, each turn a single shipwreck was revealed and placed. 12 of the 18 possible wrecks had a shipwreck icon on it. As soon as the 12th wreck with the wreck icon was revealed, it triggered the game end.

This actually doesn't work. The game will end in 12-18 turns, but the average turns out to be just about 17.5 turns rather than 15; in fact, a game will last 15 turns or less only about 1 in 40 times.

You may be right, but I have no idea what your calculations mean. I was basing my assumptions on common sense. Perhaps you could explain your reasoning in laymans terms.

Imagine that you are revealing the shipwrecks from a stack which has been shuffled randomly. Consider the tile at the bottom of the stack. There are 12 out of 18 tiles which are special. If it is special, then you will have to draw all 18 tiles to end the game. So there is a 67% chance that you will have to draw all 18 tiles to end the game. So it's very likely that the game will end around turn 17 or 18, giving an average of about 17.5

Epigone
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Random but bounded game lengths

Sorry. Here's how you can find the chance the game will last 18 turns: to last 18 turns, the 18th card must be a shipwreck card. Pretend you peeked at the last card before the game started. How often will it be a shipwreck card? 12/18 times. So 66.7% of the time it lasts 18 turns. Similarly most of the remaining probability goes toward the game lasting 17 turns. To last only 12 turns, you'd have to flip up 12 shipwreck icons in a row.

The general method is to say that in order for the game to last exactly K turns, a) the Kth card must be a shipwreck card, and b) the other 11 shipwreck cards must have turned up somewhere before the Kth card.

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Random but bounded game lengths

Ahh that makes perfect sense. So how would one go about making a game last between 12 and 18 turns with an average of 15? Is there a simple way to do that?

BTW, any one of you probability guys up to doing a probability FAQ?

-Darke

rellekmr
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Random but bounded game lengths

Beginning in the 12th round, have them draw one tile out of seven. one tile ends the game. the others don't. that will give you the desired probability.

Gogolski
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Random but bounded game lengths

Back on topic:
My 'Meteor-Cargo-Race' has a variable timer/counter for each phase (race).

As soon as the first person arrives on the arrival planet, the other players have 2 turns to arrive there also or else they loose VP's. Last night, one race turned into a cargo-shipping-frenzy. Every player was roaming the board and earning money without focussing on arriving first.

I will now add a second timer/counter at the side of the board that has a maximum number of rounds that a race may last. You will still have to arrive withing a number of rounds after the first player arrives or loose VPs, so there's a little more presure on the kettle. The earlier you arrive, the more bonus-VPs you earn...

Basicly: 2 timers, you use the one that indicates the shortest time that a race may last.

Cheese!

Brykovian
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Joined: 07/21/2008
Random but bounded game lengths

I'll chime in with a couple things -- first an idea of how to adjust the (very cool) cubes-in-a-cup system that jw mentioned, and, second, I'll just describe the system I'm using in a strategy political/war game that I'm working on (as just another example of something similar, which may or may not be helpful).

First: What if you had 20 cubes -- 4 each of 5 different colors. You want 4 phases that each end with a scoring round. You could put all 20 in the cup to start with and have players draw a cube out after each turn (or round). Once *any* color has all 4 cubes drawn for it, the phase ends and scoring is done. Once the 4th *color* has been completed, the game is over. This would likely cause the first phase to be much longer than the last couple of phases, which might give a nice acceleration-towards-game-end feel.

Second: I'm working on a game that I've mentioned to a few people here through the chat room ("Uncivil" for Nando, Seth, Xaq, et al). It's a strategy game that attempts to put a balance between military and political conquests, and is set in a small country that is attempting to convert over to a democracy.

The main driver of the game is a deck of cards that, among other things, each have a number from 3 through 7 on them. There are more 3's and 4's in the deck than 5's and 6's, and 7's are quite rare. The game is timed by a "political steps track" that shows the progress of the people in the country at fulfilling a step-by-step process. There are 9 steps along the track.

After each player's turn, that player flips over the next card from the draw deck. If that card is the right number, then the marker on the track is moved on to the next step. The first 4 slots require a 6 or 7 to be drawn from the deck. The middle 3 slots require a 5, 6, or 7. And the final 2 slots require a 4 or better.

While it seems like the chances of moving on to the next step should increase greatly toward the end of the game, there are a number of factors that will make it less and less likely for the larger numbered cards to be in the draw deck toward the end of the game, so I'm not exactly sure how it's going to play out. (I have solo-tested it about halfway through the political steps track as I try to shore-up the other systems in the game. I do hope to get a local playtest with other testers in on this one ... and I hope to bring this one to Protospiel with me. ;-D)

-Bryk