
I just found this old thread about the cube tower and enjoyed reading it.
An ambiguous randomization system (or mechanism) is a system that gives you a rough idea that the possibility of getting the result A is stronger than the result B but don't let you know the exact probability, unlike rolling dice or drawing cards in most games. I don't know how it's properly called though, since I know pretty much nothing about math (the ambiguousness is called "uncertainty" in this article).
The followings are the examples of the system I know. ・Cube tower (Shogun, Amerigo, etc) ・Upending a bottle (A la carte) ・Coin pusher (Via Appia, Treasure Falls, etc) ・Inserting a card in the middle of a draw pile (the setup of 12 player game of Escape: The Curse of the Temple) ・Your opponent secretly putting some cards into a draw deck from which you draw (does anyone know any games do that?) The last one is different from the others because someone (and the system itself) knows the exact probability though.
So, do you know any other examples of the system? What's your opinion on the topic? Any comments are welcome.
Edit: I deleted the sentence about distinguishing "nonphysical" games from "physical" games, as I realized that the term "nonphysical" is not exactly the same as the term I intended (which is a nonEnglish term I coined that is hard to explain, so I used a more understandable term instead).

Adam Taylor
United Kingdom

There's a interesting take on this in Tank on Tank where, at the start of your turn, your opponent draws a counter from a bag to determine how many actions you get that turn (I think it's 24) but they don't tell you how many you've got. You have to just take actions until they tell you to stop.
It makes for some really interesting prioritising / luckpushing decisions.

Chris Broggi
United States Southwick Massachusetts

DicingWithDearth wrote: There's a interesting take on this in Tank on Tank where, at the start of your turn, your opponent draws a counter from a bag to determine how many actions you get that turn (I think it's 24) but they don't tell you how many you've got. You have to just take actions until they tell you to stop. It makes for some really interesting prioritising / luckpushing decisions.
Waterloo also does that.

Russ Williams
Poland Wrocław Dolny Śląsk

DicingWithDearth wrote: There's a interesting take on this in Tank on Tank where, at the start of your turn, your opponent draws a counter from a bag to determine how many actions you get that turn (I think it's 24) but they don't tell you how many you've got. You have to just take actions until they tell you to stop. It makes for some really interesting prioritising / luckpushing decisions. That seems like an interesting mechanism indeed, but a draw from a bag is nonetheless following a known/calculable probability distribution. I.e. for each possible value N, you know what the probability is that you'll have N actions. Whether your random number of actions is implemented by your opponent drawing a counter in advance and knowing the number actions you'll have before you do, or by dynamically randomizing after each of your actions to see if you must stop now, seems ultimately a mere implementation detail and a red herring.
So to me, this seems fundamentally different from the inherently unfathomable nondeterminism of a cube tower, for which no probability distribution is even known, so you can't do any kind of probabilistic/risk reasoning during play.

Adam Taylor
United Kingdom

russ wrote: this seems fundamentally different from the inherently unfathomable nondeterminism of a cube tower, for which no probability distribution is even known, so you can't do any kind of probabilistic/risk reasoning during play.
Granted. It was more in response to the OP's example of
ffreiheit wrote: ・Your opponent secretly putting some cards into a draw deck from which you draw (does anyone know any games do that?)
Also, I don't know if it's right to say that you can't do any risk reasoning in relation to a cube tower. You can't analyse it mathematically but you can base your decisions on a broad expectation based on what's going in and what's left from previous turns.


Thanks for letting me know the interesting mechanism (now I'm considering to get Waterloo somehow).
But I think Russ is right. If you know how many 2s, 3s and 4s in the bag, you know the exact probability of getting 2, 3 or 4 action points.
DicingWithDearth wrote: Granted. It was more in response to the OP's example of ffreiheit wrote: ・Your opponent secretly putting some cards into a draw deck from which you draw (does anyone know any games do that?) That's a bit different from my example, which is something like this; There's a deck of 3 cards (1 red, 1 white and 1 blue). At this point, the probability of drawing a red card is 1/3. Then your opponent secretly put unknown number of cards (colors are also unknown) into the deck and now you don't know the probability of drawing a red card (you can't examine the number of cards in the deck, by the way).
DicingWithDearth wrote: Also, I don't know if it's right to say that you can't do any risk reasoning in relation to a cube tower. You can't analyse it mathematically but you can base your decisions on a broad expectation based on what's going in and what's left from previous turns. You're right. That's what I meant by "a system that gives you a rough idea that the possibility of getting the result A is stronger than the result B but don't let you know the exact probability".

Roland Sanchez
United States Texas

Couple thoughts here and typing on my phone so no nice links here
I would think the cube tower is not an example of this, mainly because you can count and track how many cubes of each color went in the tower, so you can know the odds of what colors can come out. Unless you factor in that a cube may not come out, but that's not the same as knowing if a cube does come out, what the odds of what color it can be. Or is it?
The Alexander Pfister games Oh My Goods and Port Royal are both games where you cannot count cards because so many of the cards are drawn and never revealed to be used as goods / coins respectively. The card churn is crazy in those, which makes them a lot of fun since it becomes truly random in that respect.
Also, in Fleet, the way cards are used as captains and held under the Tugboat in the expansion also have a similar effect of many cards being played face down and possibly (in the case of the Tug) never being revealed.
Edit  adding proper links

Russ Williams
Poland Wrocław Dolny Śląsk

ath3ist wrote: I would think the cube tower is not an example of this, mainly because you can count and track how many cubes of each color went in the tower, so you can know the odds of what colors can come out. But that's the whole point of a cube tower: you don't know the probabilities, because each cube is not equally likely to come out. Knowing that 3 red cubes and 3 blue cubes are in the tower does not mean that you're equally likely to have red and blue fall out later, because of the (intentionally irregular) internal construction of the tower.
Well, you could pretend that each cube is equally likely, as a very crude simplifying assumption, but I would say that the situation is clearly different from rolling a die or drawing cubes from a sack etc, where the probabilities really are practically equal and you can do easy simple probabilistic reasoning.

Walt
United States Orange County California
In memorium. Bob Hoover died 25 Oct 2016 at 94. In WWII he was shot down in a Spitfire and stole an FW190 to escape. He spent decades at air shows flying Ole Yeller, shown
Please contact me about board gaming in Orange County.

russ wrote: ath3ist wrote: I would think the cube tower is not an example of this, mainly because you can count and track how many cubes of each color went in the tower, so you can know the odds of what colors can come out. But that's the whole point of a cube tower: you don't know the probabilities, because each cube is not equally likely to come out. Knowing that 3 red cubes and 3 blue cubes are in the tower does not mean that you're equally likely to have red and blue fall out later, because of the (intentionally irregular) internal construction of the tower. I agree. The three red cubes could be jammed in corners, never to come out, while the 3 blue cubes could be teetering on the brink, and will come out when someone sneezes.
I approach games with randomness as risk management. Without known probabilities, you can't manage the risk, and the game becomes nearly pure gambling. How can you evaluate the possibility of jammed cubes? There's just no way to assign a probability to it.
So I loathe cube towers, but I understand that some people love them, some because they defeat the efforts of probabilistic risk managers (like me), who usually have an advantage over gamblers in high randomness games.


Roland's examples of card games made me think about the probability of drawing a certain card from a shared draw pile (I wonder why I haven't thought about it).
Is the probability known or unknown like the case of a cube tower?
Example; There is a deck of 30 cards (10 red, 10 white and 10 blue). Four players (including you) draw a starting hand of 5 cards. You don't have red cards in your hand and everyone else's hands are hidden (of course). Now you have to draw a card from the deck of remaining 10 cards. What's the probability of drawing a red card?
I can't answer it. I need some help.

colonial bob
United States Ellk Grove Illinois

The first thing that comes to mind is Biblios (and I'm sure many other games use a similar idea): before play, you remove a certain number of cards from the deck unseen by any player. Therefore, while you may have an idea of the deck composition, it's impossible (EDIT: in practice, though not theoretically) to precisely calculate.

Chuck Harrison
United States Beavercreek OH

ffreiheit wrote: Roland's examples of card games made me think about the probability of drawing a certain card from a shared draw pile (I wonder why I haven't thought about it). Is the probability known or unknown like the case of a cube tower?
Example; There is a deck of 30 cards (10 red, 10 white and 10 blue). Four players (including you) draw a starting hand of 5 cards. You don't have red cards in your hand and everyone else's hands are hidden (of course). Now you have to draw a card from the deck of remaining 10 cards. What's the probability of drawing a red card?
I can't answer it. I need some help. A similar example I was thinking of is the bag of combat VP chits in Eclipse. After a battle you will draw one or more chits from the bag (based on how well you did) choose one to keep face down, and put the rest back. Towards the end of the game there are probably fewer good chits left in the bag, but since you only know what you have drawn, you aren't sure.

Roland Sanchez
United States Texas

ffreiheit wrote: Roland's examples of card games made me think about the probability of drawing a certain card from a shared draw pile (I wonder why I haven't thought about it). Is the probability known or unknown like the case of a cube tower?
Example; There is a deck of 30 cards (10 red, 10 white and 10 blue). Four players (including you) draw a starting hand of 5 cards. You don't have red cards in your hand and everyone else's hands are hidden (of course). Now you have to draw a card from the deck of remaining 10 cards. What's the probability of drawing a red card?
I can't answer it. I need some help.
This is a great example of what I mentioned with the cards.
Also, while I agree with Walt and Russ to a point, another way to look at it is that if a red, blue, and white cube is dropped into a tower, it's not a 1 in 3 chance a given color will come out. It's a 1 in 3 chance that if a cube comes out, it will only either be red, white, or blue. Not orange, not green. Thus you know the odds of what color the cube can be. That's more what I was trying to convey.
Just as you know a single d6 will never roll a 7 or 8 because that is not possible, it will only ever be a 1 thru 6 because you know all the available die faces. Back to the cube tower  if I close my eyes and dump red, white, and blue into the tower, if I hear a cube drop from the bottom, I have a 1 in 3 chance to correctly guess what color may have come out. That's what I was trying to convey, and pose the question  is it the same definition of ambiguous randomization the OP proposes or not? I can kinda see it both ways.
Cool thread

Roland Sanchez
United States Texas

Tineren wrote: ffreiheit wrote: Roland's examples of card games made me think about the probability of drawing a certain card from a shared draw pile (I wonder why I haven't thought about it). Is the probability known or unknown like the case of a cube tower?
Example; There is a deck of 30 cards (10 red, 10 white and 10 blue). Four players (including you) draw a starting hand of 5 cards. You don't have red cards in your hand and everyone else's hands are hidden (of course). Now you have to draw a card from the deck of remaining 10 cards. What's the probability of drawing a red card?
I can't answer it. I need some help. A similar example I was thinking of is the bag of combat VP chits in Eclipse. After a battle you will draw one or more chits from the bag (based on how well you did) choose one to keep face down, and put the rest back. Towards the end of the game there are probably fewer good chits left in the bag, but since you only know what you have drawn, you aren't sure.
50% of the game of Thebes uses this theory and it's Awesome!! Talking about that game makes we wanna pull it out next game night.

Chris Williams
Seattle Washington

I've described Pandemic as being an elaborate randomizer so that the board state on the final round gives you a 50/50 chance of being able to find a clever set of moves which will allow you to win the game. It could be viewed as being similar to the first stages of games like the Rubix cube or a sliding tile puzzle, where you're using the player himself to create a randomized state that needs to be solved.
Theoretically, you're playing against the randomized state of the shuffled deck from the start of the game, but the game play is sufficiently bruteforce that until you hit the point where one of the endgame triggers is going to hit, and you've had a few seemingly unnecessary cards in your hand, there's no real need to truly puzzle out and collaborate on creating an optimal play round. So it's really just the one round where you're doing something other than chilling and pushing cubes around mindlessly  randomizing the board state and which special action cards happen to be in whose hands.

wayne mathias
United States Niceville Florida

I have been trying to see if my approach qualifies as ambiguously random.
The odds to hit are exactly known.
But a hit means a randomly chosen functional unit takes damage (only some units affect combat) and if possible combats remain another round takes place until no further possible combats remain with the new odds each round. And only total damage (not actual units damaged) are known to the attacker.
I think this qualifies. (A pure random overlay with unknown elements of a known odds layer with recursive results)

Walt
United States Orange County California
In memorium. Bob Hoover died 25 Oct 2016 at 94. In WWII he was shot down in a Spitfire and stole an FW190 to escape. He spent decades at air shows flying Ole Yeller, shown
Please contact me about board gaming in Orange County.

By the way, uncertain (uncertainty) is a better description than ambiguous. Uncertain means the result might be this or that. Ambiguous means a given certain result might be interpreted as this or that.
For example, using the blue and red cube tower example. It's uncertain whether a blue cube or a red cube will come out next, but when it does come out, the result is unambiguously blue or red. If a blue and a red cube both come out together, then it's ambiguous which came first.
Uncertain is about what actually happens. Ambiguous is about how you interpret that event.

Kyle
Canada Toronto
Show me something that beats a natural 20 and I'll show you hateful lies.

ffreiheit wrote: ・Your opponent secretly putting some cards into a draw deck from which you draw (does anyone know any games do that?) The last one is different from the others because someone (and the system itself) knows the exact probability though.
That is kind of the Through the Ages event system. There are 2+ players event cards in a deck. Players can play events to the next deck, and when you play one to the future, you draw one from the current. They range from positive, to negative, or goals/penalties based on objectives. Once the current deck runs out, future becomes current.


