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3 Offbeat South 4 Puzzles

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The final rounds of a mahjong game often contain the most interesting decisions. In the east round of an east-south mahjong game, we play relatively straightforward, balancing the reward of winning our hand with the risk of dealing in to an opponent’s hand. On ladder, where only placement affects the payouts of the game, the final round can encourage some more polarized strategies. We may want to feed a player’s hand to protect a first place. We may want to hold back tiles to avoid feeding a competitor. We may need to meet a certain point requirement to escape 4th place, forcing us to build for value. Understanding each player’s incentives should influence our strategy. The final round also has the most consequential decisions. In this post, we’ll assume a normalized reward system of [2, 1, 0, -3] for 1st through 4th place. While a mangan win in East 1 moves our expected reward by around 1 point, it could be a swing from 4th (-3 pts) to 2nd place (-1 pt) for 4 pts in all last....
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How to Measure Mahjong Luck and Skill

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Every Game of Mahjong Is A Dice Roll Imagine you are playing a 4 player game of mahjong against 3 clones of yourself. The probability that you get 1st, 2nd, 3rd, or 4th place is 25% - you're all equal in skill and playing the same strategy, so there's no reason any clone would have an advantage. The average placement you would achieve is 2.50. If you were playing against weaker players and had an average placement of 2.40, we would say that you have some edge , or advantage. Now suppose you were playing perfect mahjong against competent opponents. How much edge is possible? One estimate of the maximum possible edge would be the results of the AI LuckyJ, who has the best performance of any person or AI in the Tokujou room on Tenhou. Over 1145 games, LuckyJ's spread of placements is 31.5% 1st, 27.5% 2nd, 24.1% 3rd, and 16.7% 4th. Its average placement is 2.26. There is some selection bias in estimating the edge of perfect play using the best performance we've seen...
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Push Fold Fundamentals: Keiten

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If you haven't already, check out the first post in the push fold fundamentals series. What is Keiten? The term keiten refers to a tenpai hand with no yaku. Although these hands rarely win by ron or tsumo, they can gain points if a round goes to exhaustive draw (a.k.a. Ryuukyoku, rkk). In this post, we will analyze the EV of pushing dangerous tiles against 1 riichi with 5 or fewer draws until rkk. In the context of push/fold within 5 turns of rkk, we will incorrectly use the term keiten to refer to tenpai hands with or without yaku. There is a practical reason for this: if we decide that we should push a tenpai hand with no yaku, it follows that we would push the same hand if it had a yaku. Data Sources The main chart we will analyze in this post will be from this Mahjong Math post , which uses the nisi simulator to estimate EV. If you find this post helpful, consider supporting the Mahjong Math group by purchasing the post for 500 yen, which will give you access t...
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Push Fold Fundamentals: Winrate/Dealinrate

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Shoutout to hue for recommending Japanese resources and proofreading this post. Introducing The Win Dealin Ratio Your opponent declares riichi. Do you push a dangerous tile, or fold? Some players may refer to a flowchart (push good wait with X han), or a chart of expected values (EVs) to answer this question, but I think there’s a deeper understanding to be had. What is the math underlying these charts, and how can you modify your answer if parameters such as value, dealinrate, ability to fold/maneuver, or position change? I'm going to propose a heuristic that will help you answer push fold problems in a variety of circumstances. This is a concept that I borrowed from poker and modified for riichi mahjong. It’s a concept that is so important that I think about it in every game of mahjong that I play, and one that I wish I was formally taught as a beginner. It starts with a very simple idea: if I push, what percentage of the time will I win, and what percentage of the ti...
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