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[Davio]

I think that's an interesting question.

I'm no expert Backgammon player, but the Wikipedia article on Backgammon says: "Although luck is involved and factors into the outcome, strategy plays a more important role in the long run." I think this is true for Dominion as well, but the luck factor may be higher.

In Backgammon, a Doubling Cube is used to offer more strategic choices.

Would 2 player Dominion benefit from such a thing? Why would it? Why not?

[Captain_Frisk]

I'm no expert, but wouldn't you (as first player) just always double - excepting 5/2 splits with on a sea hag board?

[DStu]

I'm no expert, but wouldn't you (as first player) just always double - excepting 5/2 splits with on a sea hag board?

I remember to having read somewhere that the optimal strategy in Backgammon would be to double when your winchance is 80%. If that is correct, and it carries over to Dominion (why shouldn't it?), that would be a lot to early.

[Rabid]

Maybe you could give starting control of the die to player 2.
That might help even up the start player advantage.
Or maybe a no doubling before turn X rule?

[ipofanes]

http://www.bkgm.com/articles/GOL/Jul99/hank2x.htm is a source on how to handle the cube. The reason not to double with a slight lead is that you give your opponent the initiative to redouble.

Due to the snowballing effect of Dominion I would think a doubling cube would shorten a lot of games but not add too much as few matches are swingy enough that they'd allow much redoubling. And on iso games are fairly short so the shortening aspect would not weigh in too much for me.

Also, a cube only makes sense when playing for money or multi-games matches.

Finally, in Backgammon you have double and triple point outcomes (which gave the game its name) without using the cube, so you have the extra subtlety to actually *lose* potential points when offering the double, something you don't have in Dominion.

[Rabid]

Also at what point in your turn would you offer the double?
I guess at the end of your turn, but before drawing your next hand?

[GendoIkari]

Some discussion on this: http://forum.dominionstrategy.com/index.php?topic=2990.msg54683#msg54683

[Davio]

In what situation would using the doubling cube actually be useful?

I mean, I know you should use it when playing Backgammon for money, but couldn't you use points instead?
Is it only useful in matches that are played over multiple rounds?

Let's hypothetically say that Goko is going to include a doubling cube. How would the other aspects need to be formatted to make it useful and meaningful?

[DStu]

Let's hypothetically say that Goko is going to include a doubling cube. How would the other aspects need to be formatted to make it useful and meaningful?

Double Points double the influence of this game on the leaderboard. This is probably too exploitable to implement, but then again...

[DsnowMan]

I think the best time to be allowed to double is after your turn, but before drawing your hand. This is the closest place I can think of that's an analog to right before you roll.

In backgammon, the 2x and 3x rewards for stomping your opponent can create a situation where you are 'too good to double', which wouldn't happen in Dominion. That's ok.

You shouldn't double with a small lead, you are too likely to get redoubled if luck is swingy. The correct time to double is based on match equity, and you can't just throw around any % chance of winning because of all the interdependent factors. It even 'costs' equity to double, in that having the option to double later is worth something. For instance, one province to go, you are up by <6, and you figure your opponent only has a 20% chance to get it, while you have 100%. It's the end of your turn... your probability of winning the game is 80%, but if you double right now, your opponent won't accept, increasing your equity to 1. Lesson: don't just double all willy-nilly at the start of the game.

You should accept a double with a >25% chance of winning. The offer is much more difficult to calculate.

For match play with friends, play to a certain # of points or for money.

For online play, a doubled or redoubled game could count as if you played 2/4/etc games for leaderboard purposes, simple as that.

[PurplePotato]

I play a lot of backgammon, and I think this is a great idea. The doubling cube is my favorite part of backgammon; it's use is 100% skill, and passing over the cube can really give your opponent a headache. As others have pointed out, to make it work you would need to play for money or play a match to a certain number of points, and the latter sounds preferable. Playing a match may not be idea for online play, but should work well IRL. When I used to regularly play backgammon with my dad, we would play to 11 points, and just tally score over how many evenings it took to finish he match.

Having the ability to score two or three points is a big part of what makes the cube interesting, so adding that possibility to the dominion game would be a nice addition. My intuition is that something like this would work: If you win by 12VP or more, then you get 2 points, and if you win by 36VP or more, you get 3 points. These numbers correspond to a clean 5-3 and 7-1 province split, respectively. In backgammon, scoring a double game is difficult but doable, while scoring a triple game almost never happens, and requires quite a bit of luck.

As for doubling cube strategy, you generally want to double when you have a 75% chance of winning. At this point, it a wash for you opponent as whether or not to accept the double or drop. If they accepted during 4 different games, they would win one game for 2 pints and loose three games for 6 points, a net loss of 4 points; while if they dropped during each of these games, they would also loose 4 points total. If you double earlier, you unnecessarily risk the chance of the odds going back in you opponents favor, while if you double later, you will loose points by your opponent dropping. Of course, this often isn't so cut and dry. For example, if you were building a megaturn deck in dominion, you'd likely need to double before the megaturn hits, as doubling afterword would result in a clear drop for your opponent.

And to make it somewhat parallel to backgammon, I would say doubling before playing any cards on your turn would be logical.

[DStu]

Having the ability to score two or three points is a big part of what makes the cube interesting, so adding that possibility to the dominion game would be a nice addition. My intuition is that something like this would work: If you win by 16VP or more, then you get 2 points, and if you win by 48VP or more, you get 3 points. These numbers correspond to a clean 5-3 and 7-1 province split, respectively. In backgammon, scoring a double game is difficult but doable, while scoring a triple game almost never happens, and requires quite a bit of luck.

As always, No to this.  Part of the skill in Dominion is to edge out the 1VP wins via 3-pile endings, and I don't want to see that punished.

Also, you're numbers assume a 8VP Province.

[PurplePotato]

Having the ability to score two or three points is a big part of what makes the cube interesting, so adding that possibility to the dominion game would be a nice addition. My intuition is that something like this would work: If you win by 16VP or more, then you get 2 points, and if you win by 48VP or more, you get 3 points. These numbers correspond to a clean 5-3 and 7-1 province split, respectively. In backgammon, scoring a double game is difficult but doable, while scoring a triple game almost never happens, and requires quite a bit of luck.

As always, No to this.  Part of the skill in Dominion is to edge out the 1VP wins via 3-pile endings, and I don't want to see that punished.

Also, you're numbers assume a 8VP Province.

Whoops, your right, I should have said 12VP and 36VP, I'll edit that. And I don't see how edging out a 1VP win via 3-pilling is punished. You may be less likely to win a double game using this strategy in general, but on a specific board, if 3-pilling is a viable strategy, then someone trying to win via provinces instead will be unlikely to win a double game as a result.

[DStu]

Whoops, your right, I should have said 12VP and 36VP, I'll edit that. And I don't see how edging out a 1VP win via 3-pilling is punished. You may be less likely to win a double game using this strategy in general, but on a specific board, if 3-pilling is a viable strategy, then someone trying to win via provinces instead will be unlikely to win a double game as a result.

Usually it's not 3-piling that's the strategy, it's just the oportunity that you should take. So you build up a megaturn engine, and if the sitatuion arises that you can win by emptying 3 stacks, you should take it.
So say you are building an engine vs. some big money, your engine starts to kick into gear. And you face the descision to either win now with 2 points and 100% certainty, or win next turn with 50 points and 80% certainty by buying some more KCs and Bridges.  Without double/tripple points, you should always just win now, and get 1 "winpoint". With them, you should take the extra turn, and get on average 0.8*3-0.2=2.2 winpoints.
 

[Stealth Tomato]

The problem with a doubling cube in Dominion is that it's an imperfect-information game--there is no point in the game at which one player does not have more information than the other. Therefore, doubling is almost never a good idea except in games that are already a foregone conclusion (in which the opponent will decline and nothing of significant value is added to the game). In games that are not, the opponent will decide based on their hand strength, which is a poor proposition for the doubler--he gets double stakes when his odds are worse than he thinks, and single stakes when they're better.

Whoops, your right, I should have said 12VP and 36VP, I'll edit that. And I don't see how edging out a 1VP win via 3-pilling is punished. You may be less likely to win a double game using this strategy in general, but on a specific board, if 3-pilling is a viable strategy, then someone trying to win via provinces instead will be unlikely to win a double game as a result.

This essentially makes megaturn games worth triple, and Colony games worth double. There are some boards that make a stomp nearly impossible, and some that make it overwhelmingly likely. That would have to be adjusted for somehow to make VP targets viable.

[noon]

I've played Dominion with a doubling cube and I quite like it. The benefits are:

-games are shorter
-gambling
-you have to keep track of both players' decks to make sensible doubling decisions.

[PurplePotato]

Usually it's not 3-piling that's the strategy, it's just the oportunity that you should take. So you build up a megaturn engine, and if the sitatuion arises that you can win by emptying 3 stacks, you should take it.
So say you are building an engine vs. some big money, your engine starts to kick into gear. And you face the descision to either win now with 2 points and 100% certainty, or win next turn with 50 points and 80% certainty by buying some more KCs and Bridges.  Without double/tripple points, you should always just win now, and get 1 "winpoint". With them, you should take the extra turn, and get on average 0.8*3-0.2=2.2 winpoints.

Ah, I see what you mean now. That does warp things quite a bit.

[PurplePotato]

The problem with a doubling cube in Dominion is that it's an imperfect-information game--there is no point in the game at which one player does not have more information than the other. Therefore, doubling is almost never a good idea except in games that are already a foregone conclusion (in which the opponent will decline and nothing of significant value is added to the game). In games that are not, the opponent will decide based on their hand strength, which is a poor proposition for the doubler--he gets double stakes when his odds are worse than he thinks, and single stakes when they're better.

If you doubled before playing your next hand, this wouldn't be as bad of an issue. Your would know your next hand and your opponent would know theirs, so it's imperfect information on both sides. It could be an issue if one side had a strong hand though.

What about if after your opponent finished their buy phase, you stopped them before they drew a new hand, showed them your coming hand, and then doubled? It could stymie the flow of play, but then both sides would have the same information.

[noon]

The problem with a doubling cube in Dominion is that it's an imperfect-information game--there is no point in the game at which one player does not have more information than the other. Therefore, doubling is almost never a good idea except in games that are already a foregone conclusion (in which the opponent will decline and nothing of significant value is added to the game). In games that are not, the opponent will decide based on their hand strength, which is a poor proposition for the doubler--he gets double stakes when his odds are worse than he thinks, and single stakes when they're better.

I think players resigning when they have <20% chance of victory adds a decent amount of value to the game, by removing an uninteresting portion of it.

Assessing whether or not you have a 25% chance of victory is an interesting skill to learn, and you add that to the game as well.

A player may decide to accept or decline based on their hand strength, but as they don't know their opponent's hand strength, it is not always a bad deal for the doubler. If you always assume your opponent has a good hand when they double, it gives them the opportunity to bluff. There's a game called "poker" built on only that mechanism: each player has a  hand only they can see, and players may double the stakes or fold. Poker is fun enough that if doubling-cube dominion frequently devolved into it, then doubling-cube dominion would still be good.

Typically though, when you double someone you do so based the contents of your decks, and what's in the hands is less important.

[KingsSkort]

It even 'costs' equity to double, in that having the option to double later is worth something. For instance, one province to go, you are up by <6, and you figure your opponent only has a 20% chance to get it, while you have 100%. It's the end of your turn... your probability of winning the game is 80%, but if you double right now, your opponent won't accept, increasing your equity to 1. Lesson: don't just double all willy-nilly at the start of the game.

This doesn't seem right unless I'm missing something. Obviously it's better to have the option to double here (equity = 1) compared to not having the option (equity = .8 ), but it's better than either to have already doubled, in which case your match equity is 1.6.

[Dulkal]

It even 'costs' equity to double, in that having the option to double later is worth something. For instance, one province to go, you are up by <6, and you figure your opponent only has a 20% chance to get it, while you have 100%. It's the end of your turn... your probability of winning the game is 80%, but if you double right now, your opponent won't accept, increasing your equity to 1. Lesson: don't just double all willy-nilly at the start of the game.

This doesn't seem right unless I'm missing something. Obviously it's better to have the option to double here (equity = 1) compared to not having the option (equity = .8 ), but it's better than either to have already doubled, in which case your match equity is 1.6.

What you're missing is that equity must be viewed at the point where the double happens. If you double at the start of the game, your match equity is only slightly in your favor AND your opponent has the chance of exploiting the cube to change his later 1.6 to 2.

In other words, an early double is poor because a late double can be good, and with an early double, your opponent gets exclusive access to the late double. You need to put out doubling until your advantage from the double exceeds his advantage from getting control of the cube.

Also, I think doubling cube dominion would be VERY interesting. I think the doubling cube should be offered right before your turn (so you know your hand, but not any draws from tactician, caravan etc.). That way, the unknown information goes both ways. You offer without knowing your opponents hand, but he must decide without knowing yours. You may be able to make him drop a game while you are holding a hand of curses and victory cards.

[DStu]

Also, I think doubling cube dominion would be VERY interesting. I think the doubling cube should be offered right before your turn (so you know your hand, but not any draws from tactician, caravan etc.). That way, the unknown information goes both ways. You offer without knowing your opponents hand, but he must decide without knowing yours. You may be able to make him drop a game while you are holding a hand of curses and victory cards.

Which often is not the worst draw anyway, because the next one tends to be good then.

[Davio]

Okay, here are my thoughts after reading your comments.

A doubling cube in Dominion can be a very interesting addition, but it has to be used in matches over several games or in money games. In a practical sense, it could be used with a leaderboard as a doubled game could double the points gained or lost for a single match. Obviously, this may lead to "gaming" the system, but that's an issue that is very hard to address properly. Still, if there are people willing to go out of their way to be #1 for some silly game on the internet, let them, it's their loss.

Offering extra points for games won or lost by an X amount of VP is a very bad idea. I'm not sure how to deal with ties. I think it's best to let it have no effect on the leaderboard at all, whether the game was doubled or not.

The extra strategy it offers in the sense that players now have to try to judge their own winning chances accurately can offer extra braintainment for high level players. If playing with the cube would be optional (or only available to players with rating > X), beginning players would not be hindered by it.

A player could be able to present the cube after his turn, but before clean-up. This would give the other player an extra advantage since he sees his cards and the offering player does not know what the other player will be able to do this turn (barring hand-revealing attack cards) and what he himself will draw during his clean-up phase. This can be fixed with good cube strategy where you might need a higher percentage to make offering the cube worthwile. On the other hand, if we allow a player to offer the cube after his own clean-up, he gets an advantage and so he might need a lower percentage.
I think the option to do it right before your turn starts is the best one. I mean, you don't know what you'll get from cantrips as well as any duration cards.

Because of the imperfect information, there's a bluffing aspect involved. Let's say there's 1 Province left and I'm behind by 2 points, I've seen that you can only buy a Duchy (which will increase the gap to 5 VP) and before my turn starts I'm offering you the cube. What do you do? Do you think I have $8 and concede? Do you think I'm bluffing, accept and carry on?

I would like to see some real life findings on the use of the cube. Anyone willing to try it out?

[KingsSkort]

It even 'costs' equity to double, in that having the option to double later is worth something. For instance, one province to go, you are up by <6, and you figure your opponent only has a 20% chance to get it, while you have 100%. It's the end of your turn... your probability of winning the game is 80%, but if you double right now, your opponent won't accept, increasing your equity to 1. Lesson: don't just double all willy-nilly at the start of the game.

This doesn't seem right unless I'm missing something. Obviously it's better to have the option to double here (equity = 1) compared to not having the option (equity = .8 ), but it's better than either to have already doubled, in which case your match equity is 1.6.

What you're missing is that equity must be viewed at the point where the double happens. If you double at the start of the game, your match equity is only slightly in your favor AND your opponent has the chance of exploiting the cube to change his later 1.6 to 2.

In other words, an early double is poor because a late double can be good, and with an early double, your opponent gets exclusive access to the late double. You need to put out doubling until your advantage from the double exceeds his advantage from getting control of the cube.

I understand what you're saying, but I think the example given is nonetheless mistaken. Doubling early is bad because you might fall behind and get redoubled. (Even leaving out redoubling, it could be bad because you might fall behind and be playing for double stakes.) Doubling early is not bad because you might get further ahead and lose the chance to force an undoubled resignation.

EDIT: The argument made is equivalent to the following poker argument: You should avoid moving all-in preflop with AA because the flop might come with an A, and in that case, you would want to bet to force the opponent to fold his drawing hand (or call getting bad odds).

[Dulkal]

I understand what you're saying, but I think the example given is nonetheless mistaken. Doubling early is bad because you might fall behind and get redoubled. (Even leaving out redoubling, it could be bad because you might fall behind and be playing for double stakes.) Doubling early is not bad because you might get further ahead and lose the chance to force an undoubled resignation.

I think we're pretty much saying the same thing: Doubling early is bad because it gives your opponent control over the doubling cube.

A doubling cube in Dominion can be a very interesting addition, but it has to be used in matches over several games or in money games. In a practical sense, it could be used with a leaderboard as a doubled game could double the points gained or lost for a single match. Obviously, this may lead to "gaming" the system, but that's an issue that is very hard to address properly. Still, if there are people willing to go out of their way to be #1 for some silly game on the internet, let them, it's their loss.

Offering extra points for games won or lost by an X amount of VP is a very bad idea. I'm not sure how to deal with ties. I think it's best to let it have no effect on the leaderboard at all, whether the game was doubled or not.

I think it is definitely necessary to use it for match play. I think money play with ladder points at risk is too intangible for most players. Very few would really deeply consider whether to resign a game to lose a bit fewer latter points, rather than play on and try to win. They would play on because they want to play, or resign because they don't want to play.

I'm not sure it would fit well within the ISO context.