N1H111SM's Miniverse

2019/06/05 Share

# Introduction

Second, we should note that the best way to approach a problem may often seem backwards or cause us to pause for a while and come back later when we have more information. For instance, suppose on the flop we want to figure out what our bluffing to value raising ratio should be. To accomplish this, we must first know how often we’re going to bet the river with a balanced range, what bet sizing should be used on the turn and river, and how position effects our range.

# Preflop (3,4,5)-betting Frequencies

• 3-bet bluff通常需要在67-70%的情况下奏效才能盈利。
• 4-bet bluff通常需要在54-60%的情况下奏效才能盈利。
• 5-bet bluff通常需要在40-50%的情况下奏效才能盈利。

• 如果一个玩家从来不flat call对手的3-bet，那么他需要在15-20%的频率下对自己的open raise进行防守。这个频率还可以适当降低因为还有其他的玩家会帮助防守。
• 3-bet的玩家如果也不flat call对手的4-bet，那么他需要在40-46%的频率下对自己的3-bet进行防守。
• 4-bet的玩家需要在50-60%的频率下call对手的5-bet all-in。

# Preflop Raise, First in Ranges

• 这手牌的EV如果不是恰好等于0，那么它必须接近于0。一手牌只以一定频率被用来open raise的时候它可能就会达到0EV；而它如果总是被拿来open raise，则它的EV会更倾向于变成负。例如UTG拿着56s以75%的频率做open raise是一个接近于0EV的行动，但是如果100%频率则非常容易被剥削从而变成-EV的策略。

• 这手牌在面对对手的3-bet是需要经常fold的。因为拿最弱的牌去call对手的3-bet不是一件很好的事。

• 这手牌在面对对手的call时的EV会大于-3.5BB，这是因为即便是一手非常弱的手牌也有可能在后面几条街上实现它的equity。
• 这手牌在看见flop时的EV不会大于+1.5BB。因为德扑是一个0和游戏，如果在open raise range中最差的手牌也能够有大于盲注大小的EV，这就说明cold caller没有使用optimal的策略，他的冷跟策略是-EV的。

open raiser利用自己range中最弱的牌将自己的3.5BB投入风险以赢得底池中的1.5BB，结合上文中提到的最弱的牌在遭遇cold call和reraise时都是-EV的，那么它需要在至少70%的情况下能够吓走对手才能够获得收益。这样就意味着如果其余的玩家如果构成了超过30%的3-bet频率，那么对于open raiser来说，他再使用这种在遭遇3-bet时fold的牌进行open raise就不再是一件有利可图的事了。

# Maximum 3-bet Range

Opening Range Maximum 3-Betting Percentage Value 3-Betting Percentage Value Component of 3-Betting Range
UTG 6.9 2.76 AA-QQ, AK
MP 8.5 3.4 AA-JJ, AK, AQs
CO 11.2 4.6 JJ+, AJs+, AQo
BTN 16.3 6.52 TT+, ATs+, KQs+, AJo+

• It is weaker than the average hand in a preflop cold calling range. 它比冷跟preflop raise的范围的平均牌力要弱。
• On the flop, the preflop raiser will often be out of position unless he opened on the button or is just called by a blind. 在flop上，preflop raiser通常都处于不利位置，除非他在BTN位open并且仅有盲注跟注。
• If one of the blinds does call (thus letting the preflop raiser see a flop in position), the pot will be smaller since there is less extra dead money from the blinds. 如果大小盲中的一个玩家确实跟注了，虽然这会让open raiser在后面几条街上处于有利位置，但这也导致底池比其他玩家跟注的情况要小一些，因为底池中失去了原来盲注位的死钱。

It’s important to design ranges where all of our theory and beliefs make sense and must not allow ourselves to have a contradicting thought process. We now are equipped with a great set of restrictions, or parameters, which will tell us what we can and cannot do when designing opening ranges and defending ranges from all the positions.

In order to quickly illustrate this concept, let’s imagine we are playing at an aggressive table and open the worst hand in our theoretically correct UTG opening range for 3.5 big blinds. We are 3-bet 30 percent of the time total and are cold called another 25 percent of the time. Furthermore, let’s be generous and assume our expected value when our open is called is on average 0 EV. We can now plug in these variables to figure out that the expected value of opening the worst hand in an UTG opening range at this table is -0.375 big blinds.

That is the UTG player expects to on average lose -0.375 big blinds when he opens the worst hand in his theoretically correct UTG opening range.

Notice we are not breaking even at this table by opening the worst hand in our theoretically correct raise first in range. Our opponents are playing too aggressively and our weak hand does poorly against opponents who 3-bet 30 percent total. The fact that theoretically correct raises can have a negative expected value against certain opponents shouldn’t surprise anyone. For instance, a theoretically correct bluff on the flop will lose money against opponents who refuse to fold.

While we would break even if our opponents always 3-bet or folded and they 3-bet 30 percent total, we must not forget to take into account our open will sometimes be called. This is something which can easily be forgotten when performing calculations. It’s easy to think “since I break even when my opponent calls, it doesn’t change anything,” but this is not true. When our opponents fold we win 1.5 big blinds, yet when one of them calls, we win 0 big blinds.

This showcases the fact that as long as our opponents have any sort of reasonable cold calling ranges, they must be 3-betting significantly less than 30 percent of the time combined. If instead they always reraise with all these hands, we have no incentive to open with the weak hands in our theoretically correct opening range.

call raise fold
90% 0 10%