|
If you’re like most players, you do better with some powers than others. If you salivate over the prospect of a solo with Germany or feel that Turkey gives you an easy draw but Italy sends you home early, you’re not alone. So have you ever played a tournament with all seven powers and wished that your game as France counted more than the one where you got stuck with Austria? Yeah, me too. I’ve been known to play a game of poker now and then; in poker, you bet more when you have stronger cards. Suppose you could do something similar in Diplomacy — that is, have a bigger stake in the games with your favorite powers. This line of thinking led me to try and come up with a tournament scoring system that would let players do just that. For simplicity’s sake, I focused on how to manage it for a simple 7x7 tournament — one with seven players who each play one game with each power. I started with a few basic criteria:
After a discussion with some fellow members of the Dipsters group, I arrived at the following rules for a 7x7 tournament:
To illustrate the scoring system, let’s say that a game had the following wagers:
This game has a total stake of 755. If France solos, he wins the whole pot; subtracting his own wager of 200, he makes a net profit of 555. Everyone else loses their wagers. That case is pretty simple; how about a more complex one? Let’s say that EGT draw. The losers (AFIR) each lose their wagers; again, that part is pretty simple. The survivors split the total pot of 755 proportionally. EGT wagered 330 among them (100+150+80), so E wins (100/330) x 755 = 228.79; G wins (150/330) x 755 = 343.18; and T wins (80/330) x 755 = 183.03. Subtracting their original wagers yields net profits of 128.79 for E, 193.18 for G, and 103.03 for T. A greater amount risked leads to a greater profit, in accordance with the initial criteria. Setting up the ExperimentHaving gone this far with the thought experiment, the next step was to do some actual play testing. I found seven volunteers willing to play a no-press 7x7 under this system. After some more discussion, we hammered out the following additional rules:
The last two rules were a compromise that was done to limit metagaming while still allowing players to have some idea of where they stood as the tournament progressed. The seven
As you can see, there was a divergence in wagering strategy among the players. Scott and Alidad took the strategy to extremes; they wagered only 1 in some games and loaded up in others. At the other end of the spectrum, Arto was the least "variant" bettor, with all of his wagers between 60 and 150. Which of these strategies would turn out to be the best? France and Turkey were clearly favored over the other powers. France had an average wager of 163.6, where 100 would be the nominal average wager. Turkey was close behind with an average of 151.7, but in a couple of ways it was the most favored power: it had no wagers less than 100 and also had the highest single wager in the tournament (300 by Alidad). France and Turkey were also the only two powers that had no 1-point wagers, while Austria and Italy, perhaps unsurprisingly, had such wagers by two players. Next, powers were assigned as follows:
The variation in wagering caused some games to have larger total stakes — and therefore more importance in the tournament — than others. (The actual distribution is shown in Table 3.) This seems like an obvious consequence in hindsight, but it wasn’t something I had foreseen before starting. More about this later… Finally, the total number of "chips" bet in each game was calculated to determine the overall stake:
Game 1 had by far the largest stake — over three times that of Game 7! What effect did this have on the tournament? You’ll have to read on to find out! The TournamentWith the preliminary arrangements underway, the games began. Starts were staggered one week apart. Remember that the players did not know any information about the total stakes in each game or anyone’s wagers other than their own. A web page for the tournament, with links to maps and summaries for all games, can be found at: http://www.floc.net/observer.py?login=7x7twist&other_public=&page=login Game 1 was the first to start and the first to finish:
The total stake was 1135, making this the most heavily weighted game in the tournament. Scott raked it all in with a well-executed French solo that really wasn’t in much doubt after the first few years. Subtracting his wager of 200 from the total, he netted a cool 935 for the win. With Game 1 in the books, Games 2 and 3 were both reaching the endgame. Game 3 was the next to finish:
In this game, England (Andy) used a beautifully timed stab of his ally France to claim a solo victory. But with a much lower total stake in this game, his net winnings of 452 were much smaller than the reward for game 1’s solo. At this point, there had been two solos in two completed games. Game 2 was also in its endgame and looked like it might follow the trend:
England had swept the western half of the board, and by the end of 1915 he had Tunis and Munich locked up. He needed only to gain Berlin (and hold onto Munich) to ensure the solo – and it appeared that the defenders didn’t have enough armies in the right places to stop him. However, a critical misorder at just the wrong time, combined with some inspired defense by Russia, caused the opportunity to slip away. The game ended in a three-way ERT draw, and the survivors divided the total stake of 551 as follows:
So just missing cost Alidad a bundle; the solo would have given him the whole pot of 551, for a net profit of 550. Instead, he gained just over one measly point — far less than his partners in the draw received. In fairness, though, they were risking a lot more in the game, and one of the tenets of the format was that greater risks should yield greater rewards. This brought out another unforeseen aspect of the format: If you have a small stake in the game, the difference between a draw and a loss is fairly insignificant; but if you have a large stake, the difference is significant. As such, a small wager encourages playing all-out for a solo even at the risk of a loss, while a large wager encourages playing more safely and perhaps not risking a safe draw to go for a solo.
In this game, Turkey got off to a good start and eventually overwhelmed his neighbors. But as is so often the case, he couldn’t get past the 17th center, and the result was a four-way EFGT draw. This resulted in net winnings of 51.56 for England, 103.13 for France, 35.06 for Germany, and 41.25 for Turkey. The next two games finished on the very same day:
In this game, Germany’s solo try was thwarted by a four-power coalition. Nobody was willing to risk whittling the draw further, so the result was a five-way AEGIT draw. This result was notable in that it was the only game in which Austria (the power, not this Austrian player) didn’t lose. As you might expect, having so many survivors meant that nobody got a particularly large share. The net winnings: Austria 16.90, England 11.27, Germany 27.04, Italy 21.41, and Turkey 44.39.
This game looked like it was heading for a three-way EIT draw, but Michael realized that Italy could be whittled out without much risk — so he proceeded to do just that! The resulting two-way draw, in a game with a higher than average total stake, netted a nice payoff for the survivors: 303.10 for England and 282.90 for Turkey.
The final game combined low wagers from several players, with the result that its total stake was the lowest in the tournament:
This game was reminiscent of game 4, featuring a Turkish solo try. But as in that game, Turkey couldn’t get past that 17th center, and the result was a three-way EFT draw. The net winnings were 11.75 for England, 39.15 for France, and 26.10 for Turkey. Wrapping it All UpThe following table shows the final results:
Total is the player's score under the system used for this tournament. Results are the player's results in power order (AEFGIRT). Score is the score that would have resulted using a standard scoring system where winners/survivors gain (7/N) -1 points. It’s interesting that the players would have finished in exactly the same order under either system! Final ThoughtsScott won the tournament by a huge margin because he placed his wagers with remarkable effectiveness: he wagered 1 point each in the three games he lost, while his wagers in the four games he won or drew were 200, 197, 150, and 150. In his case, the strategy of loading up on his favorite powers was highly effective. However, Alidad used the same strategy and it didn’t work out so well for him because he didn’t have much success with the powers he favored. Wagering strategy doesn’t help much without results on the board. One interesting note: although England had the lowest average wager of all powers, it was actually the most successful power in the tournament! It had one solo, one 2WD, two 3WD, one 4WD, one 5WD, and only one loss. (And it might have done even better if not for a critical misorder in game 2.) The real question is: was the scoring system a success? On one hand, it yielded the same order of finish that a standard system would, which seems to imply that it wasn’t worth the trouble. On the other hand, it unquestionably rewarded effective wagering, which was the whole idea in the first place. It’s also true that the total stakes varied greatly among the games; game 1’s stake was more than three times as much as game 7’s. This meant that some games were more important than others in the final result. I’m not sure if this is a detriment. On one hand, it seems inherently unfair; but is it really? The whole point was to allow players to bet the most on the powers in which they had the most confidence. Going back to the poker analogy, you bet more with strong cards (in this format, the powers you perceive as your strongest) than with weak ones. Random variation means that some pots will be larger than others; sometimes there will be multiple players with stronger hands than average, other times there will be multiple players with weaker hands. In this tournament, Game 1 was the equivalent of a poker table full of straights and flushes, while Game 7 had at best a few small pairs. One idea that comes to mind is to try and normalize the total amounts bet in each game; however, I’m not sure whether this would be desirable or even possible without completely negating the main objective. And finally, the play test led to a mini-tournament with seven well-played, interesting games by seven good players. In my opinion, that has to count as a success! Any comments or suggestions will be received with interest. Thanks for reading!
If you wish to e-mail feedback on this article to the author, and clicking on the envelope above does not work for you, feel free to use the "Dear DP..." mail interface. |
