12 个大盲时,9 人桌的 Nash 全下范围是:UTG 7%、MP 12%、CO 23%、按钮 34%、小盲 63%。这是纯推弃开始让位给「加注—弃牌」的筹码档——图里能看清哪些牌最先掉出去。
| 位置 | 全下比例 | |
|---|---|---|
| UTG | 6.9% | 91 个组合 |
| MP | 12.2% | 162 个组合 |
| CO | 23.3% | 310 个组合 |
| BTN | 33.8% | 448 个组合 |
| SB | 63.0% | 836 个组合 |
| AA | AKs | AQs | AJs | ATs | A9s | A8s | A7s | A6s | A5s | A4s | A3s | A2s |
| AKo | KK | KQs | KJs | KTs | K9s | K8s | K7s | K6s | K5s | K4s | K3s | K2s |
| AQo | KQo | QJs | QTs | Q9s | Q8s | Q7s | Q6s | Q5s | Q4s | Q3s | Q2s | |
| AJo | KJo | QJo | JJ | JTs | J9s | J8s | J7s | J6s | J5s | J4s | J3s | J2s |
| ATo | KTo | QTo | JTo | TT | T9s | T8s | T7s | T6s | T5s | T4s | T3s | T2s |
| A9o | K9o | Q9o | J9o | T9o | 99 | 98s | 97s | 96s | 95s | 94s | 93s | 92s |
| A8o | K8o | Q8o | J8o | T8o | 98o | 88 | 87s | 86s | 85s | 84s | 83s | 82s |
| A7o | K7o | Q7o | J7o | T7o | 97o | 87o | 77 | 76s | 75s | 74s | 73s | 72s |
| A6o | K6o | Q6o | J6o | T6o | 96o | 86o | 76o | 66 | 65s | 64s | 63s | 62s |
| A5o | K5o | Q5o | J5o | T5o | 95o | 85o | 75o | 65o | 55 | 54s | 53s | 52s |
| A4o | K4o | Q4o | J4o | T4o | 94o | 84o | 74o | 64o | 54o | 44 | 43s | 42s |
| A3o | K3o | Q3o | J3o | T3o | 93o | 83o | 73o | 63o | 53o | 43o | 33 | 32s |
| A2o | K2o | Q2o | J2o | T2o | 92o | 82o | 72o | 62o | 52o | 42o | 32o | 22 |
| AA | AKs | AQs | AJs | ATs | A9s | A8s | A7s | A6s | A5s | A4s | A3s | A2s |
| AKo | KK | KQs | KJs | KTs | K9s | K8s | K7s | K6s | K5s | K4s | K3s | K2s |
| AQo | KQo | QJs | QTs | Q9s | Q8s | Q7s | Q6s | Q5s | Q4s | Q3s | Q2s | |
| AJo | KJo | QJo | JJ | JTs | J9s | J8s | J7s | J6s | J5s | J4s | J3s | J2s |
| ATo | KTo | QTo | JTo | TT | T9s | T8s | T7s | T6s | T5s | T4s | T3s | T2s |
| A9o | K9o | Q9o | J9o | T9o | 99 | 98s | 97s | 96s | 95s | 94s | 93s | 92s |
| A8o | K8o | Q8o | J8o | T8o | 98o | 88 | 87s | 86s | 85s | 84s | 83s | 82s |
| A7o | K7o | Q7o | J7o | T7o | 97o | 87o | 77 | 76s | 75s | 74s | 73s | 72s |
| A6o | K6o | Q6o | J6o | T6o | 96o | 86o | 76o | 66 | 65s | 64s | 63s | 62s |
| A5o | K5o | Q5o | J5o | T5o | 95o | 85o | 75o | 65o | 55 | 54s | 53s | 52s |
| A4o | K4o | Q4o | J4o | T4o | 94o | 84o | 74o | 64o | 54o | 44 | 43s | 42s |
| A3o | K3o | Q3o | J3o | T3o | 93o | 83o | 73o | 63o | 53o | 43o | 33 | 32s |
| A2o | K2o | Q2o | J2o | T2o | 92o | 82o | 72o | 62o | 52o | 42o | 32o | 22 |
| AA | AKs | AQs | AJs | ATs | A9s | A8s | A7s | A6s | A5s | A4s | A3s | A2s |
| AKo | KK | KQs | KJs | KTs | K9s | K8s | K7s | K6s | K5s | K4s | K3s | K2s |
| AQo | KQo | QJs | QTs | Q9s | Q8s | Q7s | Q6s | Q5s | Q4s | Q3s | Q2s | |
| AJo | KJo | QJo | JJ | JTs | J9s | J8s | J7s | J6s | J5s | J4s | J3s | J2s |
| ATo | KTo | QTo | JTo | TT | T9s | T8s | T7s | T6s | T5s | T4s | T3s | T2s |
| A9o | K9o | Q9o | J9o | T9o | 99 | 98s | 97s | 96s | 95s | 94s | 93s | 92s |
| A8o | K8o | Q8o | J8o | T8o | 98o | 88 | 87s | 86s | 85s | 84s | 83s | 82s |
| A7o | K7o | Q7o | J7o | T7o | 97o | 87o | 77 | 76s | 75s | 74s | 73s | 72s |
| A6o | K6o | Q6o | J6o | T6o | 96o | 86o | 76o | 66 | 65s | 64s | 63s | 62s |
| A5o | K5o | Q5o | J5o | T5o | 95o | 85o | 75o | 65o | 55 | 54s | 53s | 52s |
| A4o | K4o | Q4o | J4o | T4o | 94o | 84o | 74o | 64o | 54o | 44 | 43s | 42s |
| A3o | K3o | Q3o | J3o | T3o | 93o | 83o | 73o | 63o | 53o | 43o | 33 | 32s |
| A2o | K2o | Q2o | J2o | T2o | 92o | 82o | 72o | 62o | 52o | 42o | 32o | 22 |
| AA | AKs | AQs | AJs | ATs | A9s | A8s | A7s | A6s | A5s | A4s | A3s | A2s |
| AKo | KK | KQs | KJs | KTs | K9s | K8s | K7s | K6s | K5s | K4s | K3s | K2s |
| AQo | KQo | QJs | QTs | Q9s | Q8s | Q7s | Q6s | Q5s | Q4s | Q3s | Q2s | |
| AJo | KJo | QJo | JJ | JTs | J9s | J8s | J7s | J6s | J5s | J4s | J3s | J2s |
| ATo | KTo | QTo | JTo | TT | T9s | T8s | T7s | T6s | T5s | T4s | T3s | T2s |
| A9o | K9o | Q9o | J9o | T9o | 99 | 98s | 97s | 96s | 95s | 94s | 93s | 92s |
| A8o | K8o | Q8o | J8o | T8o | 98o | 88 | 87s | 86s | 85s | 84s | 83s | 82s |
| A7o | K7o | Q7o | J7o | T7o | 97o | 87o | 77 | 76s | 75s | 74s | 73s | 72s |
| A6o | K6o | Q6o | J6o | T6o | 96o | 86o | 76o | 66 | 65s | 64s | 63s | 62s |
| A5o | K5o | Q5o | J5o | T5o | 95o | 85o | 75o | 65o | 55 | 54s | 53s | 52s |
| A4o | K4o | Q4o | J4o | T4o | 94o | 84o | 74o | 64o | 54o | 44 | 43s | 42s |
| A3o | K3o | Q3o | J3o | T3o | 93o | 83o | 73o | 63o | 53o | 43o | 33 | 32s |
| A2o | K2o | Q2o | J2o | T2o | 92o | 82o | 72o | 62o | 52o | 42o | 32o | 22 |
| AA | AKs | AQs | AJs | ATs | A9s | A8s | A7s | A6s | A5s | A4s | A3s | A2s |
| AKo | KK | KQs | KJs | KTs | K9s | K8s | K7s | K6s | K5s | K4s | K3s | K2s |
| AQo | KQo | QJs | QTs | Q9s | Q8s | Q7s | Q6s | Q5s | Q4s | Q3s | Q2s | |
| AJo | KJo | QJo | JJ | JTs | J9s | J8s | J7s | J6s | J5s | J4s | J3s | J2s |
| ATo | KTo | QTo | JTo | TT | T9s | T8s | T7s | T6s | T5s | T4s | T3s | T2s |
| A9o | K9o | Q9o | J9o | T9o | 99 | 98s | 97s | 96s | 95s | 94s | 93s | 92s |
| A8o | K8o | Q8o | J8o | T8o | 98o | 88 | 87s | 86s | 85s | 84s | 83s | 82s |
| A7o | K7o | Q7o | J7o | T7o | 97o | 87o | 77 | 76s | 75s | 74s | 73s | 72s |
| A6o | K6o | Q6o | J6o | T6o | 96o | 86o | 76o | 66 | 65s | 64s | 63s | 62s |
| A5o | K5o | Q5o | J5o | T5o | 95o | 85o | 75o | 65o | 55 | 54s | 53s | 52s |
| A4o | K4o | Q4o | J4o | T4o | 94o | 84o | 74o | 64o | 54o | 44 | 43s | 42s |
| A3o | K3o | Q3o | J3o | T3o | 93o | 83o | 73o | 63o | 53o | 43o | 33 | 32s |
| A2o | K2o | Q2o | J2o | T2o | 92o | 82o | 72o | 62o | 52o | 42o | 32o | 22 |
全下部分频率全下弃牌
最赚的牌: AA +3.97 KK +3.07 QQ +2.61 JJ +2.27 AKs +2.12 TT +1.99 AKo +1.98 AQs +1.78
刚过零线(推弃几乎无差异): K7s +0.01 KTo +0.01 QTo +0.01 A6o +0.01 Q8s +0.02 JTo +0.02 T7s +0.03 86s +0.04
看着该推、其实亏钱: 96s -0.01 A4o -0.01 75s -0.02 54s -0.02 K5s -0.03 T9o -0.03 J7s -0.04 Q6s -0.06
12bb 正好在边界上:还深到可以最小加注、面对全下再弃;又浅到大多数价值牌宁可直接全下。诚实的用法是把这张图当作下限——图上显示为盈利全下的牌,你随时可以闭眼推,不管你还打算拿它做什么。
各个位置收紧得并不均匀。对比 10bb 和 12bb:UTG 几乎没动(9% → 7%),小盲却从 69% 掉到 63%。前位的推弃范围本来就紧到不能再紧,多两个盲注的深度几乎不改变什么;被砍掉的是那些宽的、靠偷盲支撑的范围——因为它们本来就只靠弃牌赢率盈利。
EV 数字在这里比 8bb 时更要紧,因为筹码已经大到「被跟真的疼」。一个 +0.02bb 的全下不是策略,是噪声。用那些明确为正的牌搭建你的范围,把接近零的那一带留给你有 read 的局面。
基本还算。12bb 最小加注是可行的,但纯推弃只损失极少 EV,同时消灭了全部翻后错误。如果你对自己的「加注—弃牌」没把握,照这张图推——实战 EV 反而更高,哪怕理论上略差一点。
因为它已经接近下限了(9% → 7%)。UTG 只推那些「面对 8 个随时可能醒过来的人也盈利」的牌——对子和大 A——而这些牌在几乎任何短码下都盈利。随深度缩水的是那些靠弃牌赢率吃饭的宽范围(BTN、SB)。
8bb 推弃图(9人桌 Nash)10bb 推弃图(9人桌 Nash)15bb 推弃图(9人桌 Nash)20bb 推弃图(9人桌 Nash)UTG 枪口位开局范围(6人桌)大盲防守按钮开局(6人桌)
推弃表是自算的 chip-EV Nash 均衡(蒙特卡洛手牌类赢率,25000 样本,seed 1234)。已知局限,如实说明:不考虑 ICM;模型在算被跟概率时不做去牌——所以杂色 A(它其实阻断了对手的 AA/AK/AQ/AJ)被略微低估。本档可利用度: 0.048 bb/hand.