PUTTING YOUR MONEY
WHERE YOUR MOUTH IS:
AN ALTERNATIVE SCORING SYSTEM

by Martin Moore


If youíre 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, youíre 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.

Iíve 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 simplicityís 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:

  • All players would have the same stake in the tournament as a whole, but could vary their stakes in each game as they saw fit.

  • Players who lost a game would lose whatever they risked in that game.

  • Players who won a solo victory would win everything staked in that game.

  • Players who shared in a draw would split the gameís total stakes proportionally based on the amounts they had each wagered. Greater risk should entail greater reward.

After a discussion with some fellow members of the Dipsters group, I arrived at the following rules for a 7x7 tournament:

  1. Each player would start with a stake of 700 virtual ďchipsĒ. They could allocate their chips among the seven games as they saw fit, with the following provisos:

    1. All 700 chips must be wagered over the course of the tournament.

    2. At least one chip must be wagered on each game.

  2. Each player would privately communicate their wagers to the tournament director (me) before the tournament started.

  3. Game assignments would then be made randomly.

  4. The scoring would be done on a pari-mutuel basis; that is, the total amount staked in a game would go to the winner in case of a solo victory. In a draw, the survivors would share the total stakes proportionally based on the amounts of their wagers.

To illustrate the scoring system, letís say that a game had the following wagers:

Power"Chips" Bet
Austria 50
England 100
France 200
Germany 150
Italy 100
Russia 75
Turkey 80

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?

Letís 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 Experiment

Having 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:

  1. The tournament would be anonymous. Players would not know the identities of the other players, or the relationships of powers in one game to those of others, until the last game was completed.

  2. Players would not know how much each player wagered in any game until the last game was completed. However…

  3. At the end of each game, the TD (Tournament Director) would announce the net winnings by each power that won or drew the game, but would provide no information about the amounts lost by the losers.

  4. The TD would also maintain a leader board, with fake player names, that would include the total amount of net winnings by players, but not include their losses.

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 guinea pigs(*ahem*) volunteers were all experienced, skillful no-press players: Scott Ellis, Michael Carter, Arto Hakkarainen, Alidad Tash, Andy Tomlinson, Mark Gregory, and Jonathan Powles. To start things off, each player sent me his wagers, which are shown in Table 1.

Table 1: Wagers by Power
Player
\Country
ScottMichaelArtoAlidadAndyMarkJonathanAverage
Austria 1 185 100 1 150 75 70 83.1
England 150 45 60 1 65 125 50 70.9
France 200 75 150 250 120 200 150 163.6
Germany 1 85 120 146 50 75 50 75.3
Italy 1 95 90 1 135 75 100 71
Russia 150 75 80 1 80 25 180 84.4
Turkey 197 140 100 300 100 125 100 151.7

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:

Table 2: Assignments
Player
\Country
ScottMichaelArtoAlidadAndyMarkJonathan
Austria Game 7 Game 1 Game 2 Game 3 Game 4 Game 5 Game 6
England Game 6 Game 7 Game 1 Game 2 Game 3 Game 4 Game 5
France Game 1 Game 2 Game 3 Game 4 Game 5 Game 6 Game 7
Germany Game 3 Game 4 Game 5 Game 6 Game 7 Game 1 Game 2
Italy Game 4 Game 5 Game 6 Game 7 Game 1 Game 2 Game 3
Russia Game 2 Game 3 Game 4 Game 5 Game 6 Game 7 Game 1
Turkey Game 5 Game 6 Game 7 Game 1 Game 2 Game 3 Game 4

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 wasnít 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:

Table 3: Wagers in Each Game
Game
\Country
Game 1Game 2Game 3Game 4Game 5Game 6Game 7
Austria 185 100 1 150 75 70 1
England 60 1 65 125 50 150 45
France 200 75 150 250 120 200 150
Germany 75 50 1 85 120 146 50
Italy 135 75 100 1 95 90 1
Russia 180 150 75 80 1 80 25
Turkey 300 100 125 100 197 140 100
TOTAL: 1135 551 517 791 658 876 372

Game 1 had by far the largest stake — over three times that of Game 7! What effect did this have on the tournament? Youíll have to read on to find out!

The Tournament

With 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 anyoneís 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:

GAME 1
PowerPlayer (Wager)
Austria Michael (180)
England Arto (60)
France Scott (200)
Germany Mark (75)
Italy Andy (135)
Russia Jonathan (180)
Turkey Alidad (300)
Total stake:1135

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 wasnít 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:

GAME 3
PowerPlayer (Wager)
Austria Alidad (1)
England Andy (65)
France Arto (150)
Germany Scott (1)
Italy Jonathan (100)
Russia Michael (75)
Turkey Mark (125)
Total stake:517

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 1ís 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:

GAME 2
PowerPlayer (Wager)
Austria Arto (100)
England Alidad (1)
France Michael (75)
Germany Jonathan (50)
Italy Mark (75)
Russia Scott (150)
Turkey Andy (100)
Total stake:551

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 Ė and it appeared that the defenders didnít 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:

  • England: (1/251) x 551 = 2.20, minus wager of 1, net profit of 1.20
  • Russia: (150/251) x 551 = 329.28, minus wager of 150, net profit of 179.28
  • Turkey: (100/251) x 551 = 219.52, minus wager of 100, net profit of 119.52

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.

GAME 4
PowerPlayer (Wager)
Austria Andy (150)
England Mark (125)
France Alidad (250)
Germany Michael (85)
Italy Scott (1)
Russia Arto (80)
Turkey Jonathan (100)
Total stake:791

In this game, Turkey got off to a good start and eventually overwhelmed his neighbors. But as is so often the case, he couldnít 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:

GAME 5
PowerPlayer (Wager)
Austria Mark (75)
England Jonathan (50)
France Andy (120)
Germany Arto (120)
Italy Michael (95)
Russia Alidad (1)
Turkey Scott (197)
Total stake:658

In this game, Germanyís 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) didnít 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.

GAME 6
PowerPlayer (Wager)
Austria Jonathan (70)
England Scott (150)
France Mark (200)
Germany Alidad (146)
Italy Arto (90)
Russia Andy (80)
Turkey Michael (140)
Total stake:876

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:

GAME 7
PowerPlayer (Wager)
Austria Scott (1)
England Michael (45)
France Jonathan (150)
Germany Andy (50)
Italy Alidad (1)
Russia Mark (25)
Turkey Arto (100)
Total stake:372

This game was reminiscent of game 4, featuring a Turkish solo try. But as in that game, Turkey couldnít 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 Up

The following table shows the final results:

††† ††† ††† ††† ††† ††† ††† ††† ††† ††† ††† †† ††† ††† ††† ††† ††† ††† †††
Final Results
PlayerTotalResults
[ A E F G I R T]
Score
Scott 1458.77 L 2 W L L 3 5 7.23
Andy 36.52 L W L L L L 3 2.33
Michael 16.12 L 3 L 4 5 L 2 1.98
Jonathan -308.33 L 5 3 L L L 4 -1.52
Alidad -344.67 L 3 4 L L L l -2.92
Arto -426.86 L L L 5 L L 3 -3.27
Mark -431.54 5 4 L L L L L -3.85

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. Itís interesting that the players would have finished in exactly the same order under either system!

Final Thoughts

Scott 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 didnít work out so well for him because he didnít have much success with the powers he favored. Wagering strategy doesnít 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 wasnít worth the trouble. On the other hand, it unquestionably rewarded effective wagering, which was the whole idea in the first place.

Itís also true that the total stakes varied greatly among the games; game 1ís stake was more than three times as much as game 7ís. This meant that some games were more important than others in the final result. Iím 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, Iím 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!



Martin Moore
(mooremar@gmail.com)

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