How much a win costs when the AI played it: pay by moves

The Audamir game pays for a win in Principalities^[1] and in free play by score. The score measures the difficulty of the setting, not the time, and therefore, according to the time model of the analysis, an hour of duels pays an average player 431 XP, while an hour of games with eight players pays only 121. My proposal of 30 October 2026 was to pay for the rounds of the player, as Colony already does, and to add an AI that may play at any time, but only the rounds the player played are paid. The analysis measured it on AI opponents and on one saved game of a real player, and 15 questions were decided at once. Today only half of it is built: the share of the AI and the three classes of game (step X1) and the rule written as data (step X2). The payment by rounds itself is not yet connected to any game.

Why pay for rounds: the score does not know time

Principalities, free play and the daily challenge pay the score, which is the sum of the points of 25 settings (98 values in the table). Points are eight times the drop in log-odds, that is the logarithm of the ratio of the chances of winning and losing, which was measured on AI opponents (the principle is in the article on the calibration). Golden Dice are paid in the same number as experience. As a measure of difficulty the score is reasonable, as a measure of time it is not, and the article on the score by the length of a game fixed only free play: Principalities stayed outside the effort factor, because their prices feed the economy of the Golden Dice. The analysis of 30 October 2026 showed three things:

1. An hour of duels pays 3.6 times more than an hour of games with eight players. An average player (in the measurement of an AI of level 2) wins a duel in 50.2% of games after a median of 9 rounds, and the win pays 97; an eight-player game is won in 14.6% of games after 21 rounds, and the win pays 122. With a game time of 2.2 + 0.49 minutes per round it is 431 XP per hour against 121.
2. The bonus for a quick win is not a bonus. The norm against which speed is measured is 24 to 38 rounds, while the median win is 9 to 22. The bonus therefore pays almost every win (×1.16 to ×1.23): a hidden +21% in the price.
3. The difficulty matrix is good for one change and bad for a mix. The correlation of the points with the measured difficulty is 0.80 across 191 settings, but the error is ×1.95 for one change and ×4.3 for a random mix. The setting r16 (six opponents, fixed reinforcements, peace, an ally) is valued by the matrix against Principalities with four players at +17 points, the measurement at −28 (the AI wins it in 91.7% of games).

The rule: the player's round, the base, the cap and the multiplier

Colony (article about the game) pays for moves: 0.5 XP per move × 0.5 / 1 / 2 depending on the level of the AI, so a win against a Normal AI brings on average 30 XP in 5.8 minutes. The analysis proposed this for Kastgard:

XP    = zaokrúhli( 5 × ( min(kolá hráča, strop) + 6 ) × m )     pri výhre
        × 0,6 pri výhre na body, 0 pri prehre aj pri remíze
minca = XP                                                       (Zlaté kocky v aréne)
strop = min( 100, 1,5 × typické kolá výhry )

Why a round. From my 20 recorded games with the time of the start and of the end comes minutes = −0.50 + 0.322 × rounds (R² 0.66), that is a round of about 19 seconds, and minutes = −1.21 + 0.069 × attacks (R² 0.77), that is an attack of 4 seconds. From the gaps between games in the history, including the menu, a round is 0.49 minutes. It is one player and 20 games, so a scale, not a law. An attack would describe the time better, but the round is in every line of the history.

The base of 6 rounds gives the game a minimal price (the menu and the closing card cost about 4.5 rounds of time). The cap of 1.5 × typical rounds prevents a stretched game from being paid without end; for Principalities it is 14 / 20 / 23 / 24 / 29 / 33 / 32 rounds for 2 to 8 players, it cuts 9 to 16% of wins and takes 2 to 13% of the reward. Stretching was measured (four players, AI of level 2) with an AI that could make at most 2 attacks per move: it wins only 18.0% of games against 23.5%, but a win lasts 31.9 rounds instead of 15.6. If the player plays such a round in 7 seconds, they earn per hour without a cap 2.5 times more (449 against 179 XP), with the cap 1.8 times more (320 against 179); at a round of 15 seconds with the cap 1.15 times, at a normal round (29 seconds) 0.69 times. One attack per move does not win, so it does not pay.

**The multiplier m** pays a harder game more. If m = 0.25 / the chance of an average player to win, the expected reward of a game (chance × reward) is proportional only to the number of rounds, that is to the time. Principalities have a table of seven numbers, set so that an average player earns the same per hour at every number of players:

The mix of player counts that is played (8 / 17 / 40 / 15 / 10 / 4 / 6%) gets by rounds 110.1 XP per win against today's 112.2 (−1.9%), so the economy of the Golden Dice does not move on average. It shifts between player counts: a duel pays 45 XP instead of 97, an eight-player game 198 instead of 122. It is the most visible change for a player of Principalities, and the closing card should explain it in one line.

Free and daily play have too many settings for a table (up to 1.5 × 10¹³ combinations), and therefore m is derived from the chance of an average AI at the start of the game: 24 simulations of finishing from the first position, the same ones that the analysis of the game makes for the first point of its chart. A measurement on 40 random settings in 12 maps gave a deviation of the reward of ×1.8 (80% of settings within ×1.5 of the ideal), while today's score gives ×3.5 (35%).

The default setting of free play would pay 136 instead of 96, because the AI wins it in 30% of games in 27 rounds; opponents with aggression 4 (chance 3.7%) ×10.9, an alliance of two ×0.48. The points of the matrix remain as the score of the leaderboard. All this is decided and measured, but not built (steps X3 and X4).

The AI and the 90/10 rule

The function "Let the AI finish" (decision of 21–22 October 2026, DESIGN §42) lets the AI play the side of the player to the end of the game. Such a game was to remain forever invalid: without reward, achievements, record and statistics. The proposal of 30 October 2026 changes that: the AI may be used at any time, only the rounds of the player are paid, and if the AI only finishes the game (it plays about its last tenth), the player should get the full reward, even with achievements. "About the last tenth" must be changed to a rule that the player knows in advance. The analysis tried three readings:

Why not C. The chance was counted after each move by 24 simulations. It reaches 90% after 0 to 5 moves of the player, and then the AI needs another 7 to 16 rounds, which is 65 to 91% of all rounds of the game; not one win fitted into the tenth limit. As advice in the dialogue the chance is fine (an AI of level 2 or 3 wins 92 to 100% of such positions, a weak one only 24 to 69%), but it must not determine the reward.

The tenth in rounds. The game of Principalities lasts a median of 9, 13, 15, 16, 19, 22 and 21 rounds for 2 to 8 players, so a tenth is one or two rounds. Table: the share of games in which handing over t moves before the end still gives the full reward (games won by conquest, 114 / 156 / 114 games, 40 simulations per cell, with 8 players 30):

With f = 1/9 (the exact tenth) "finishing" means practically only the last move, with f = 1/4 the last two to three. In the ROADMAP (ch. 27) my answer of 30 October 2026 is recorded: "I agree with everything you proposed", so the quarter applies, and two numbers of the original proposal were replaced: the tenth by a quarter of the moves of the player (with the AI roughly a fifth of the game), and the prices of the AI 5,000 / 20,000 / 100,000 Golden Dice by the prices 7,000 / 30,000 / 110,000. The reward is not paid by a jump: a player who handed over three moves before the end at f = 1/9 would get 67% of the reward in a duel, with four players 75%, and with eight 85%.

The move is counted at its end. The analysis proposed counting the move at its start. During the construction it turned out that the game is saved at the end of the move and after Continue it is played again, so the same move would be counted twice after a restore. The move is therefore counted to the one who ended it (DESIGN §90.2).

The three classes of the game and what the player learns

When a game ends in which the AI played, the class is determined from the counters and the result (Autopilot.classOf, X1, version 0.64.1):

Example from DESIGN §90.1: the player played 12 moves and the AI 5. The AI played 29% of the rounds, the limit at 12 moves is 20% (3 rounds allowed), so the player gets 71% of the reward; with a win for 97 XP it would be 68 (calculated as round(full × share)). Edge classes: own (the AI took the seat, but the game ended before it played a move) and void (a game saved under the first rule, nothing is counted).

How the player learns of it. The dialogue of the button states, before the click, the permitted number of rounds (the Slovak text of the game, translated here): "The AI may play at most 3 more rounds for the full reward." and "If the AI loses, nothing is paid and your record does not change." The closing card has three messages: "The AI finished the game and it counts as yours: full reward.", "The AI played 29% of the rounds (the limit is 20%), so you get 71% of the reward." and "The AI lost the game. Nothing was paid and your record was not changed." Not built are the lines of the dialogue "the AI needs about N rounds, in 9 cases out of 10 at most M" and "Your chance now: P %": they want the simulations of the analysis with a budget, and they are advice, not a rule (DESIGN §90.6).

What can be abused

My request was to check for abuse:

One place the analysis does not name as abuse, and it follows from the rule: class L leaves the record of the player clean, whoever played the last move. Whoever sees that they will lose the position can let the AI in at least one move before the game ends, and the loss does not show in the streak or in the count of losses. It applies only to the record (L pays nothing); it is a reasoning from the code, not something tried in the game.

What is built and what is only decided

Check of the code as of 31 October 2026 (version 0.65.6): Xp.moves and the module Pay are called by no file in js/, index.html and sw.js do not include js/data/pay.js, and Principalities still pay by score. The function "Let the AI finish" is offered by Autopilot.MODES = ['classic', 'free'] to everyone from the first game, without a level or a purchase; Colony and Lines do not have it.

Proof for X1 (tools/core/pay-migration.js): a game without AI leaves the profile byte for byte the same as the old code, and games with AI (30 classes F, 30 P and 16 L) pay exactly by the rule (DESIGN §90.8).

Shop. From level 10 (2,500 XP, 4.2 hours at 594 XP per hour) three permanent purchases open, the Weak, Normal and Strong AI: in Kastgard for 7,000 / 30,000 / 110,000 Golden Dice (11.8 / 50.5 / 185.2 hours of play at 594 per hour), in Rokgard^[2] for 3,700 / 15,000 / 57,000 Golden tokens (12.0 / 48.7 / 185.1 hours at 308 per hour). The original proposal of 5,000 / 20,000 / 100,000 is 8.4 / 33.7 / 168 hours in Principalities, but in the campaign only 1.5 / 5.9 / 29.3, because the campaign pays 6.1 to 6.5 Golden Dice per XP (a run of 3,020 – 4,531 dice against 495 – 692 XP). Watch a game, according to the addendum of 30 October, shows only from the level of the slot and offers only the bought levels of the AI.

Tasks. A daily task costs 2 × the reference game of the realm (208 XP in Kastgard at reference 104, 60 in Rokgard at 30), a weekly one 7 × (728 and 210). Whoever only clicks the AI on one daily and three weekly tasks would, without a cap, get 520 XP per day, more than an active hour (300 to 500). The cap 28 × REF per week per realm (2,912 XP in Kastgard, 416 a day, that is 42 minutes of Principalities) limits it; a task above the cap still counts toward the streak and the achievements, but pays nothing. Lines (see three in a row and the length of a line) should pay by the same rule, with a deduction for small boards (ROADMAP ch. 28); about realms there is a separate article.

What could not be verified and what remains

• None of the payment by rounds was played with people. All the chances are chances of the AI, and the only human data is my own save (20 games with the time of the round).
• Two numbers on stretching. The analysis writes in several places that the cap limits the gain from stretching to "about ×1.5", but its table gives, at the cap of 1.5 × median and a round of 7 seconds, 320 against 179, that is ×1.8; the article has the numbers of the table. Four attacks per move give at a normal pace +26% (225 against 179), so the "round" slightly favours the style that takes more rounds.
• Time on a phone was not measured and the chance at the start was not built in the game (X4). The campaign by rounds is not measured for Threat 0 – 2; rounds explain only 11% of the time of a mission, so it stays on its own table.
• The tempo of Colony is 308 XP per hour of wins, four-player Principalities by rounds 643, so a click task in Rokgard would be a third smaller. Texts in nine languages with an estimate and a limit were not tested at 375 px width.
• Documents. docs/PAY-BY-MOVES.md still says "Analysis only; nothing is built", part 1.6 describes the AI from before X1, and my answers are in ROADMAP ch. 27, not in it. Row R4 in the table of phases of the ROADMAP ("a game that a bot finished counts for nothing") contradicts ch. 27.

Sources and notes

• Analysis and measurements: docs/PAY-BY-MOVES.md (30 October 2026, version 0.62.3), chapters 1.2 to 1.4, 3.1 to 3.4, 5.2, 6.1 to 6.3 and 10. Measurements M1 to M8 come from scripts outside the repository and were not run while writing.
• Decisions and state: docs/ROADMAP.md ch. 26 to 28 (row R4, the block "Decided" in ch. 27); the code js/realms/kastgard/games/stacks/core/autopilot.js, js/core/profile.js and js/data/pay.js at version 0.65.6 of 31 October 2026.
• Commands run on 31 October 2026: node tools/core/pay.js --check (passed) and --profile on the backup of 23 October 2026: 38 games of Principalities, 35 wins, 19 with time; 594 XP per hour by score, 549 by rounds.
• Own calculations: ratios and seconds from the numbers of the article (for example 19 seconds per round is 0.322 × 60). Reading class L as a way to hide a loss is a reasoning from the code, not the text of a document.

What could not be verified: the payment by rounds is not connected in the game, the numbers of the analysis were not recalculated (except by the tool pay.js), and the claim about class L is derived from the code.