Make Me Think! (Decisions Per Minute)
Sheamus Parkes
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(First, let me be clear that this is just an exercise for fun and thought stimulation. I don't think any of the "math" in this list is right. It's all just subjective calculations to stimulate some fun chatter on the geek. So, on with the fun

After inundating myself into modern boardgame culture for over a year, I think I've come a long way towards identifying what I like. I've had the same three things listed in my profile for quite awhile:

1. Fun I'd better be smilin' or yellin' by the end of it.
2. Meaningful decisions I like to make important choices turn after turn.
3. Quick Playing / No Downtime I like my games to keep moving at a brisk pace.

The biggest item, fun, is a very hard item to pin down. I think it mainly comes from the people you are playing with. I play with a great group of folks in Indy, my own family, and most importantly, my beautiful wife. All of these people contribute to making games fun.

Beyond fun, my other main requirements are a little more objective. I can measure how many important choices I make and how much idle time is involved. I thought I should combine those together and make a new metric:

Decisions Per Minute or DPM

I thought I should analyze some of my favorite games and try and guestimate which games give me the highest DPM score.

Yes, these calculations are subjective. No, there is no right answer. Yes, please do add more!
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1. Board Game: Through the Desert [Average Rating:7.05 Overall Rank:435]
Sheamus Parkes
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Est DPM:
2-Players: 2.15
3-Players: 1.23
4-Players: 0.85
5-Players: 0.68

And lets start off with my favorite game. The pastel camels are strong in the DPM. I am always amazed how quickly my turns come around and how I feel that each camel I place is a meaningful choice. There are just enough subtle rules tweaks to preserve the game play at any number. You can see my estimated DPM does still tail off with more players. That's going to happen for almost any game I imagine.

For TtD, the DPM drops because you get to place less and less camels over a longer period of time.

I think the DPM is very high because there are so many incrementally positive things you can do each turn. Players can generally settle on a play that satisfies them in very little time.

Just to stimulate thought, here's my rough calculations. They assume that one color runs out and the other four colors end at about 75% exhaustion.

2-Players: 5 Leaders plus half of 76 Camels over 20 minutes.
2-Players: 5 Leaders plus a third of 96 Camels over 30 minutes.
5-Players: 5 Leaders plus a fourth of 116 Camels over 40 minutes.
5-Players: 4 Leaders plus a fifth of 116 Camels over 40 minutes.

I really do just love this game!
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2. Board Game: Notre Dame [Average Rating:7.38 Overall Rank:216]
Sheamus Parkes
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Est DPM:
2-Players: 0.75
3-Players: 0.60
4-Players: 0.50
5-Players: 0.42

I think the biggest appeal to Notre Dame for me is just how many decisions it fits in such a short amount of time. The number of decisions tends to stay the same no matter how many players there are, but the play time does increase.

Card drafting is probably among my favorite mechanics. Probably because it does a great job of blending hand management and simultaneous action selection without introducing the chaos of "6 Nimmet" style games. I get to evaluate a hand of cards and make a play choice at the same exact time every other player is. And yet it doesn't turn into rock-paper-scissors due to the reduced interaction of the actions.

Not all the decisions in Notre Dame are meaningful though. For example, I only count about 1.5 decisions per draft. Choosing between 2 cards is only meaningful maybe half of the time.

I find the bribing interesting most of the time. I went ahead and counted 9 decisions, but it could be a little less there. Of course, moving the carriage or the donation size to Notre Dame were left out, so it probably evens out.

Here's my rough calculations:

2-Players: 9 Drafts with 1.5 Decisions Each; .5 Decision on which card not to play 9 times; 3 Decisions where to send your Advisor; 9 Decisions on who to bribe; 40 Minute Play Time
3-Players: Same, but 50 Minute Play Time
4-Players: Same, but 60 Minute Play Time
5-Players: Same, but 70 Minute Play Time
 
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3. Board Game: Wits & Wagers [Average Rating:6.97 Overall Rank:501]
Sheamus Parkes
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Est DPM:
Any Number of Players: 0.70

Ah yes, my party game of choice. It gives me real choices, and it does it in a very rapid format. Every guess is meaningful, and the bets doubly so. Especially under the updated rules. This is another game where simultaneous action doesn't degrade into chaos.

Also, I just *love* the economics of it. On average, a group knows way more than you think they know. The more people you ask an obscure question, the closer the median will get to the real answer. It's often times down right scary how many times the middle answer turns out to be right in Wits & Wagers. Math and economics are beautiful!

Rough Calc:
7 Answers and 7 Bets in 20 Minutes
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4. Board Game: Puerto Rico [Average Rating:8.06 Overall Rank:15]
Sheamus Parkes
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Est DPM:
3-Players: 0.46
4-Players: 0.36
5-Players: 0.28

Well, we can see where I get disillusioned with Puerto Rico. Now, some people are going to argue with my definition of "decision", but I only considered the following to be meaningful:

1. 75% of your Role Selections. This is the driving force of the game. It really is the meat and potatoes. But occasionally the choice is obvious.
2. 12 Building Choices. I estimated about 12 times would you be offered the option to build and the choice would be very deep and meaninful.
3. About 3 plantation grabs. The rest of the time you'll take what you can get or it just doesn't matter.

So what do I consider an autopilot decision:

1. Colonist Placement: 95% of the time, it's going to be obvious.
2. Choice of what to Ship / Trade: Almost always there is a "right" answer.

So in the end, there's just not enough to engage me for how long Puerto Rico takes. I'm sure many other people will contest this one. But the formula below is subjective to your own belief obviously.


3-Players: 12 Builds, 13 Meaningful Role Selections, 3 Meaningful Plantation Grabs in 60 Minutes
4-Players: 12 Builds, 12 Meaningful Role Selections, 3 Meaningful Plantation Grabs in 75 Minutes
5-Players: 12 Builds, 10 Meaningful Role Selections, 3 Meaningful Plantation Grabs in 90 Minutes
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5. Board Game: Race for the Galaxy [Average Rating:7.77 Overall Rank:48]
Sheamus Parkes
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Est DPM:
2-Players: 1.45
3-Players: 0.86
4-Players: 0.60

So this one is complicated. How long does the game actually last? How many "Governor Rounds" and how often is each phase chosen? I used a uniform estimate of each phase being performed 8 times. But then I said that about a third of the phase choices would overlap. That means about 55 phases would be chosen in aggregate for each game.

Then for hand management, I thought about half of the explores and 75% of the develop and settle phases would generate meaningful decisions.

The game length does seem to stay pretty stable without too much increase with each additional player. You just get to choose less and less of the total roles though.

This is definitely a subjective calculation, but the resulting numbers do seem reflective of my experience. A little higher DPM than Notre Dame. But it blows Puerto Rico out of the water.

I think the key is the very contained play time. So much of this game is done simultaneously, it really is a thing of beauty. The idea that there really isn't a turn order for such a deep economic game is really unique I think. Are there any other games that compare?

Very Rough Calc Below:

For any number of players:
8xExplore
8xDevelope
8xExplore
8xConsume
8xProduce

40 Total Phases
55 Phases Chosen

Chance of Decision:
Explore: 50%
Develop: 75%
Explore: 75%
Total: 2X

2-Player: Half of 55 Phases Plus 16 Hand Management in 30 Minutes
3-Player: One Third of 55 Phases Plus 16 Hand Management in 40 Minutes
4-Player: One Fourth of 55 Phases Plus 16 Hand Management in 50 Minutes
 
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6. Board Game: Ra [Average Rating:7.47 Overall Rank:134]
Sheamus Parkes
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Est DPM:
3-Player: 0.94
4-Player: 0.73
5-Player: 0.58

This one is an absolute Mess. Just what is a meaningful decision? I think that it's meaningful if you have to consider calling Ra on your turn. I also think it's meaningful if you have to consider to bid. I think about 30% of the pulls are borderline, and about half of the auctions make you consider. Man is this one ever subjective. I think I'm over estimating the DPM on this game some, but it still is a great game. No matter how you slice it. Maybe someone else has a better view on this game.


I think it maintains the high DPM by severely limiting your choices on each turn. Sometimes this backfires and leaves you with no meaningful decision (I'm estimating that to happen on 70% of the pulls and half the bids) But the rest of the time it gives you a meaningful choice that you should still be able to work through in a very short period of time.

Also, the great push-your-luck Ra track introduces a very large unknown. You just aren't going to be able to calculate the "right" answer.

Very VERY Rough Calc:

30 Ra Tiles
150 Other
15% Ra Call
30% Borderline Pull
50% Bid choice

3-Players: 24 Ra Tiles
137 Draws
20 Ra Calls

137 * .3 + 20 = 61 Turn Choices and 44 * .5 = 22 Bid Choices
One third of 61 Turn and all of 22 Bid Choices in 45 Minutes

4-Players: 27 Ra Tiles
155 Draws
24 Ra Calls

155 * .3 + 24 = 71 Turn Choices and 51 * .5 = 26 Bid Choices
One fourth of 71 Turn and all of 26 Bid Choices in 60 Minutes

5-Players:
30 Ra Tiles
172 Other
26 Ra Calls

172 * .3 + 26 = 78 Turn Choices and 56 * .5 = 28 Bid Choices
One fifth of 78 Turn and all of 28 Bid Choices in 75 Minutes
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7. Board Game: Himalaya [Average Rating:7.00 Overall Rank:912]
Sheamus Parkes
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Est DPM
3-Player: 0.78
4-Player: 0.58
5-Player: 0.47
6-Player: 0.39

Himalaya is actually one of my favorite "Family Games". I really like this game. I notice that my number of decisions doesn't really change with the number of players. And the play time really isn't too bad to scale either. Its a real shame that this game as become hard to acquire. It's also a real shame that the author left the Stupas as the first elimination step. It really sucks to know you've lost with a third of the game left. I much prefer my inverted elimination scoring:

http://www.boardgamegeek.com/thread/222146

Each turn, I probably choose about 2.5 key points. Roughly 2 places to trade and maybe where to end up or how long to wait. Also score roughly 7 times during the game. And probably 5 of those are meaningful choices of which influences to increase.

Rough Calcs:
3-Players: 12 * 2.5 Plans + 5 Scores in 45 Minutes
4-Players: 12 * 2.5 Plans + 5 Scores in 60 Minutes
5-Players: 12 * 2.5 Plans + 5 Scores in 75 Minutes
6-Players: 12 * 2.5 Plans + 5 Scores in 90 Minutes
 
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8. Board Game: Advanced Squad Leader [Average Rating:7.95 Overall Rank:209] [Average Rating:7.95 Unranked]
Harald Torvatn
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A 7 turn scenario with about 16 pieces for each side takes 4 hours=240 minutes.

Each of these turns have many phases, but the most decisions happen in the movement phase. The movement phase is organized in the following way: One player moves his pieces, one by one, or stack. Each time he moves a piece/stack, the opposing player may choose to fire. After seing the result of that fire (if any), he may fire more, but he has a limited pool of total defensive fire to use. Based on which defending units fire, the moving player may continue moving that piece/stack, which may posibly be subject of more fire as it moves on. So the two players continously throws decisions at each other.

Assuming that eight units move each movement phases, and each movement gives the moving player about three decisions and the other player five, that is 64 decisions each movement phase. Over 14 movement phases, that is 896 decisions.

Moreover, those 8 units which did not move each required one decision to not move, which is 112 more decisions. As number of units not moving decreases through the scenario (some die) we set this mumber to 80.

Morever, each of a players unis require one decision in the advance phase. The number of units able to advance also decline, assuming the average is 10, that is 140 more decisions. There are some more, but these are the main ones.

The total, for both players, is 1116. For each player, that is 558. Per minute, it is: 2,3.
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9. Board Game: Pit [Average Rating:6.40 Overall Rank:1351]
Twinge
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Decisions per minute: TWO! TWO!! TWO!! ... THREE? THREE!!!
 
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10. Board Game: Galaxy Trucker [Average Rating:7.46 Overall Rank:128]
Twinge
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Playtime: 100 minutes.

* You fill 3 spaceships with tiles, but they may not always be full, so about 70 tiles total.
* 1 in 4 tiles is probably taken from what other people turned face up, the rest from your own blind draws.
* You probably only keep about 1 in 3 of your blind draws
* Sometimes it's obvious what to throw away, so I'd say about 50% of the total tile choices are meaningful.

* After ships are built, you run them through the cards. There are 36 cards total you go through in 3 rounds.
* Maybe 3 in 4 of those cards end up giving you a choice.
* Most of those choices are at least fairly meaningful, though sometimes it's obvious, so I'd say 67%.

17.5 choices to grab face up tiles, 157.5 blind draws, 50% meaningful = 87.5 decisions, plus 18 decisions during the flights.

1.06 meaniful decisions per minute. I actually expected this to rate ridiculously high (instead of just 'very high') due to the real-time element, but I suppose the breathing time between building sessions evens it out a bit.
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