筹码 8 个大盲时已经没有「加注—弃牌」这条路:要么全下,要么弃。这张图给出 9 人桌每个位置的 Nash 全下范围——UTG 推 11%、CO 推 33%、按钮推 39%、小盲推 73%——并附上每一手牌的期望值(bb)。
| 位置 | 全下比例 | |
|---|---|---|
| UTG | 11.3% | 149 个组合 |
| MP | 19.5% | 258 个组合 |
| CO | 32.7% | 433 个组合 |
| BTN | 39.4% | 522 个组合 |
| SB | 73.2% | 970 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 +3.76 KK +2.93 QQ +2.55 JJ +2.24 AKs +2.13 AKo +2.01 TT +1.99 AQs +1.9
刚过零线(推弃几乎无差异): K9o +0.01 JTo +0.02 T7s +0.03 K5s +0.04 Q8s +0.05 65s +0.05
看着该推、其实亏钱: J7s -0.02 K3s -0.03 T9o -0.03 Q7s -0.05 Q6s -0.06 98o -0.06 85s -0.06 64s -0.06
8bb 已经深在全下区。开到 2.2bb 就投掉了四分之一以上的筹码,翻牌之后你又没有弃牌赢率——小加注只是把一个干净的全下搞成一团乱。直接推:对手弃了你白拿盲注,对手跟了你有两张活牌、后面也没有会打错的决策。
范围的形状几乎完全由「身后还剩几个人」决定。UTG 身后 8 个人,推 11%;小盲身后只剩 1 个人,推 73%——远比按钮宽——因为能跟的只有大盲一家,而大盲面对一个全下、池里只有一个死盲注时,必须弃掉很多牌。
真正值得研究的是 EV 那一列。EV 在 +0.00 到 +0.05bb 之间的牌其实什么都不决定:推或弃,长期差别是舍入误差。要背下来的是那些刚刚跌破零的牌——它们看着就该推,却在悄悄亏钱。
9 人桌几乎永远不该。开 2.2bb 之后你只剩约 5.8bb——任何你想继续的翻牌你都已经被绑住了,却还白送对手一个便宜的看牌机会,也给了自己一堆输不起的决策。全下能拿到同样的弃牌赢率,且没有这些坏处。
因为能跟的只有一个人。在按钮位,身后还有小盲和大盲两家可以醒过来;在小盲位,只有大盲能跟。池里有 1.5bb 死钱、对手又必须大量弃牌——于是约 73% 的牌全下都是盈利的。
10bb 推弃图(9人桌 Nash)12bb 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: 0.025 bb/hand.