Endgame Stabs and Risk/Reward Evaluation

[Josey Wales]

Generally, in my most humble of opinions, anything less than a solo IS a loss. So, I will always look for a stab and expect one coming - not that I can always do anything about a coming stab at times.

In opening moves, Spring 1901, I generally stab someone on the opening gambit - usually to hilarious results in Public Press. However, more often than not it generally works out and sets the theme for the coming game (note I said generally since nothing is ever guaranteed). In a game I am playing right now, engaged in extensive negotiations before S 1901 with everyone but had an general strategy of an immediate stab of my neighbor (2 in fact). Worked out perfectly (so far) and has setup for a strong run for me and my for real ally in this particular circumstance - whom I will be looking to stab mid-to-late game. We are past 1901 at this point.

Not all would favor this approach but I like to make sworn enemies of the rabid, frothing at the mouth variety immediately as they can often be as useful as an ally. When the game mentioned above finishes I think I will write an AAR as it is shaping up to be a really good game and regardless of whether I carry the day or not, the dynamics behind comms/moves/etc will point to whether my strategy is a sound one or not. Generally if a lively Public Press erupts in 1901, then there is a pretty good chance Josey Wales is in the game.

[VGhost]

In the context of a PlayDip ranked game, or a game scored under virtually any other system (even prioritizing centers), I would almost never make the stab, because it's almost certainly risking more than it's probably gaining.

In an unscored game, I'm unlikely to make the stab, unless it involves some nifty tactical possibilities, because the difference between a 3- and 4-way draw is, well, pointless. If the game's definitely ending in a draw, there's no need to add more hostility to the board purely for headcount.

(A solo/loss dilemma would make the choice harder, but positions where those are the possible outcomes seem really rare. If it's solo/draw, then I'm going to - and have - make the stab probably 80% of the time, but it really depends on the relationship with my ally.)

[VerbalKint]

If you want to maximize your score in the situation you describe, you should try to achieve the three-way draw only if you think that the probability of success is above 75%.

On playDiplomacy, the distribution of score points depends on the result of the match, the scores of the players, and the experience of the players. In a hypothetical match in which all players have equal strength and equal experience, the formula for assigning multi-player Elo points transforms into simple draw-size scoring (there are two exceptions: a solo player achieves a bonus, and if two players surrender with one power, they both get the full negative score points. We can ignore these exceptions here).

Assume you are in such a match of equally skilled and experienced players. In this scenario, each player that does not make it into a draw loses a constant number of c score points. The sum of these points is distributed equally among the draw participants. Thus, a 4-way draw will result in 3/4 × c score points for each draw participant, and a three way draw will result in 4/3 × c points each.

For finding out whether your stab will be successful or not, you need to find the correct probability that makes your stab likely to score more points than the 3/4 × c points you have safely in your bag if you stick to the 4-way. Let p be the probability that your stab improves the result of the match from a 4-way to a 3-way draw, and (1-p) the probability that you will lose the game because of that stab. To find the probability that makes your stab successful, you have to solve the following equation for p:

[(4/3)c × p] + [(-c) × (1-p)] ≥ (3/4)c

The result of this operation is p ≥ 3/4, or 75%.

Of course, you will never be in a match with equally skilled and experienced players, but this is the closest estimate you will get.

[DirtyHarry]

I feel kind of dumb right now - what's the "OP"?

And for all those, a draw is a loss people, then why do we get points on this site for a "loss"?

[Damon Huntington]

I feel kind of dumb right now - what's the "OP"?

And for all those, a draw is a loss people, then why do we get points on this site for a "loss"?

I don't think a draw is a loss. Rather, I believe that it is "not-a-win".

Besides, you don't always get points for drawing - sometimes, you lose points if the other players on that board have less Ranking Points than you do.

[boldblade]

I feel kind of dumb right now - what's the "OP"?

Original post or original poster. Meaning the first message of a thread or the one who created the thread.

[David E. Cohen]

I am looking at equations above, and they show the heart of the problem. A point system, in its essence, turns a forum into one all-encompassing, ongoing tournament. In fact, a variant of the original game of Diplomacy. If you want to play that variant, call it what it is and then everyone can move on.

[NoPunIn10Did]

I am looking at equations above, and they show the heart of the problem. A point system, in its essence, turns a forum into one all-encompassing, ongoing tournament. In fact, a variant of the original game of Diplomacy. If you want to play that variant, call it what it is and then everyone can move on.

That's certainly true. Any website with a rating system is essentially a long, ongoing tournament. Any numerically scored game of Diplomacy is effectively a type of variant, but scored games are clearly a popular variant. Players seem to like to have "skin in the game," and scored / rated games provide that.

This is almost necessary for website-based games, where anonymous players can NMR and quit at the drop of a hat, with little or no damage to their reputation. I know I was even guilty of this in the early days of another site: phpDiplomacy, now called webDiplomacy. Back when it was a buggy Facebook app, I got partway through a couple games, encountered some bugs (or just plain forgot about them), and quit. I would never have done this to a group where I was playing by email; at the very least I would have let the GM know to find a replacement.

Even beyond reliability, it's beneficial to the platform to have some built-in incentive for players to try and perform as well as they possibly can; among other benefits, this discourages win-trading behaviors (i.e. metagaming).

So on the one hand, you probably have better Diplomacy played overall when no scores are involved. On the other hand, it's simply not realistic for a web-based platform to sustain a userbase without some form of rating/scoring system. So it really becomes a matter of how to score the games, rather than whether to score the games.

The devil just happens to be in the details regarding how such games are scored, as a scoring system will create intermediary goals that come with tradeoffs. Some of those intermediary goals can conflict with endgame goals as well. People here largely seem to be okay with the site's current scoring/rating methodology; a Draw-Sized Scoring model is applied to an individual game, and Elo rating calculations convert that score to zero-sum rating adjustments based on how you stack up to your opponents.

But here's the tradeoff: it does mean that, on average, a player will net ~70% more points on a 3-way draw than a 4-way draw, even though in an unscored context these two types of draws aren't all that different.

(This is, in part, why I've proposed a considerably different per-game scoring system, based on an existing F2F scoring system, to be provided as a per-game alternative. It won't quite satisfy the desire to have an unscored game, but it should allow players to play a scored game that doesn't inherently encourage draw-whittling.)

[jay65536]

So, let's bring this back to the original reason I made the OP.

In my mind, in the scenario in the OP, almost no matter how you value the 3 different results, the reward is very small compared to the risk, and as such it probably does not make sense to try the stab.

If you value a 3way and 4way as being exactly equal, you have no motivation to stab--and this is true even if you value both of those as equal to a loss. You're either indifferent, or you're risking a loss for what you view as no reason.

But, even if you value a 3way and 4way differently, if you value them according to zero-sum draw sharing, the stab is doing what a gambler would call "laying 3:1"--i.e. risking 3 times the amount you stand to gain. And in that case you need to believe there's greater than a 75% chance the stab won't backfire, before you do it.

It's interesting to me that the only people in the thread arguing that they see value in a stab are openly sidestepping logic and admitting that their reasoning is solely qualitative. It's also interesting to me that the people who would stab for qualitative reasons also equate stabbing more with winning more--and they are the only ones making this argument.

[NoPunIn10Did]

But, even if you value a 3way and 4way differently, if you value them according to zero-sum draw sharing, the stab is doing what a gambler would call "laying 3:1"--i.e. risking 3 times the amount you stand to gain. And in that case you need to believe there's greater than a 75% chance the stab won't backfire, before you do it.

Some of this comes from the perceptual skewing inherent in the zero-sum perspective. While 33% of the points is approximately 33% higher than the 25% available in a 4-way, when you look at the difference in terms of net positive points, the difference from one to the next appears much higher.

Code: Select all

Outcome     Game %  Net %

Loss         0     -14.29
4-way       25      10.71
3-way       33.33   19.04

Particularly if folks are looking back at their score histories and seeing that they earn around double the points (more accurately ~178% of the points) in a 3-way as compared to a 4-way, it's easier to overvalue the smaller draw. The measurement isn't properly considering distance from the loss.