This article describe how to build up theoretical standard to judge Push or Fold.
Hi all. Thank you for checking this website!
Before going to the main topic, let me share today’s astonishing Haipai: starting hand
Result of this hand ? Well, Let’s go back to the main topic…
I was 4th at East 4, had 2,000 Tenpai against dealer Riichi. Push or fold ?
In this case first you should calculate how dangerous this tile is. Good way to calculate is to count Suji, like 14m 25m… There are 18 Suji (6 for circles, 6 for bamboos, 6 for characters), and in this case, 7m, 9p, 9m, 4m, 4s, 2p, 8s didn’t hit. So you can regard 14m, 47m, 69m 14s, 47s, 58s, 25p, 69p is safe (Actually, Riichi’ wait especially at early turns may not be Ryanmen, or may be Honor tile. This is a kind of simplification) . So there is 10 remaining Suji, and this 6s will hit both 36s and 69s. So possibility that this tile hits is roughly calculated as 20%: 2 Suji/10 Suji.
Next question is if this hand is worth pushing 20% hitting tile. Well, you can calculate that ! I refer to the data of the book below, written by famous, great Mahjong data analyst, Miinin.
「統計学」のマージャン戦術 (近代麻雀戦術シリーズ) みーにん https://www.amazon.co.jp/dp/4801911803/ref=cm_sw_r_tw_dp_U_x_znQgEbXJS1CHA
According to this book, when you have 2,000 points hand and push against dealer’s Riichi at 8th turn, if you discard 0% hitting tile: safety tile your EV is -400, and if you discard 10% hitting tile your EV is -1,100. So when you discard 6s: 20% hitting tile, EV is calculated as -1,800: -1,100-(-400-(-1,100)). This is because EV decrease -700 with every 10% risk increase. This seems to be too simplify the problem, but this way of calculation is also authorized by Miinin. (you will find the table which covers many cases and this description on page 92-95).
As you have seen, EV is negative even if you discard safety tile. So must we fold this hand ?
No. You should compare this to the EV when you fold. If you fold, there is no chance that you increase your point, and you have to wait opponent win or Ryukyoku: exhaustive draw. So EV when you fold is negative and it is -1,700 when dealer Riichi. So when you compare this -1,700 and EV when you push: -1,800 and know this is the borderline of Push or Fold. Now your point is below 25,000: starting point. In this case value of your win increases, so you can push this tile.
I hope this will be of some help to you!