Saturday, June 6, 2015

Semibluff To Made Hand Ratio

We discussed shoving in on the turn but realized the drawback was opponents may simply choose to trap you and if you are semibluffing too often, you can lose more than you win. In fact, you'd have to successfully pick up the pot nearly 80% of the time to make money if you ONLY were able to semibluffed all in on the turn and never were able to move in with a made hand.

If my opponent is able to exploit me by ONLY calling the flop when he has any pair and ALSO call the all in on the turn if I miss, but folding if I hit draw on the turn, I'm going to be losing money from this strategy since he will be able to call me probably close to 50% of the time, if he also tightens up preflop.

Fortunately, I WILL make a big hand such as two pair occasionally even when I play suited connectors. I will also make a straight, trips, and I will also play premium hands like AA and KK from time to time and my lower and mid pairs may also flop a set or hit one on the turn.

So all is not lost. Additionally the ability to "slow down" is what provides the "slow gear" that Doyle talked about so that opponent cannot just exploit your style. The question though is if my opponents ARE able to capitalize off my style, what is the most frequently I could semibluff vs having a made hand and still profit?

To know this, we first have to determine how much we can lose if opponent flat calls us on the flop half the time and with the intention of calling the turn when we miss?

50% of the time we win 8.25
of the remaining 50%, we HIT the turn 15% of the time and our opponent folds after calling the flop.
We add 16.5 to our stack from the flop 7.5% of the time.

Opponent calls flop, we don't improve and opponent calls turn and we don't improve to the river. We lose 97 of our big blinds that remained on the flop from a stack of 100 big blinds before the flop. This happens 85% of the remaining 42.5% of the time or 36.125%.
The remaining 6.375% f the time, we miss the turn but get it all in and hit the river. We add 101.5 big blinds to our stack minus the 3 we already put in preflop or 98.5.
We would lose 23.4 big blinds if we only did this with 7 outers and never improved our outs on the turn and never had an actual hand.   However, what we can look at is what happens when our opponent mistakes us for a draw, instead gets money in with us having a 80% to win effectively.
Opponent still folds when they THINK we make a draw. Although with a scare card they may fold slightly more often than if we actually have that draw because if we have a flush draw there are two more scare cards in the deck since we don't have it it is close enough.
So we still win 4.125 on the flop, 1.2375 on the turn. Opponent then calls drawing very slim. Since he calls with any pair he MAY have outs to runner runner, and he may occasionally have better than a pair. So we will say we win 80% of the time he calls.

When we take this line WITH a made hand, we are winning 30.6075. When we take this hand with a semibluff we are losing 23.40. This gives us two ratios or percentages of made hands to semibluffs. We can add those two numbers together and divide by their opposite to determine the percentage of the time we need to have that to break even.

23.3994/54.0069 is 43.326686%. So 43.33% of the time we need to have a made hand vs the perfect opponent to neutralize him. (assuming this strategy preflop can also neutralize the cost of the blinds which may not be true and assuming with every hand in between we can break even which may not be true.) 30.6075/54.0069 or 56.67% of the time we can have a semibluff.

If this trapping opponent DIDN'T know we specifically adjusted for them and thus was playing to trap to his own fault, we'd want a much larger percentage of made hands to semibluffs. If our opponent wasn't trying to trap us and wasn't playing us correctly we'd probably want MORE semibluff hands.

With this in mind we can look at the percentage composition of a given preflop hand vs the odds it hits. We then will have a total percentage of time we hit a bluffing opportunity vs a double up opportunit. We can then try to adjust the hand range to find a good ratio. The goal will be to then find a looser preflop range with the same ratio across each individual position to try to optimize it so the strongest hands are played in position. That way we at least have an idea where to take our strategy if our opponent is really tough. We can then loosen up or tigthen up based upon how we think our opponents will be playing us. This provides some good flexibility on our made hands to semibluff ratio.

In real life we shouldn't automatically have a predetermined play robotically, but we certainly could alternate between two robotic styles like this with a far more in depth, intangible one for every non draw and non twopair or better hand. However, it probably would be more optimal to exploit opponents by playing some draws slow and some top pair and overpair hands fast, and against other opponents playing even the more longshot draws fast like middle and bottom pair and gutshots and backdoor draws.

However, EITHER plaing a fundamentally strong baseline where we cannot be exploited OR alternating from one extreme to another where our opponents can lose a lot IF they try to exploit us but don't realize we adjusted is still a perfectly okay way to play.
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To determine the made hand to semibluff ratio we need to know the probability of pairs hitting a set and suited connectors hitting two pair vs various draws as well as a hand like ace king hitting two pair and if we want to also play Ace king when it hits top pair top kicker fast as well as an overpair fast than we can incorporate that as well. That will of course be vulnerable to the player who only calls the all in with a set or two pair or better, where playing more semibluffs fast is better against him. However, it will play really well against the player who calls with any pair in attempt to exploit our semibluffs.

Probability of being dealt two suited cards like 67s 4/1326 or 0.30%
Given 67s
probability of flopping an 8+out draw 21.390%
probability of gutshot draw 14.370%
probability of flopping 2 pair or better 5.582%
[probability of pairing hand on flop 26.940%]


Ratio of draws to made hands is 86.5% draws, 13.5% made hands. Note we are looking at pairs as seperate event and missing the flop or backdoor as seperate event since we will not play those fast.
A pair flops a set or better 11.755% of the time. It might flop an open ended draw with outs to a set or straight as well but that's complicated since there always will be a potential straight out there so the outs may not actually win. As such, the equity against the players who will call our all in may be less than 10 outs.

Probability of being dealt a pair like 55 6/1326.
Probability of flopping a set 11.755%

If we had chose one pair and one suited connector and always raised either hand, a raise would represent a pair 60% of the time. We want this ratio to be closer to a pair 65% of the time.  The ratio of 13 pairs to 10 suited connectors would work pretty closely.
The ratio of 7 pairs to 5 or 6 suited connectors would be close enough as would 5 pairs to 4 suited connectors.

But there are only 7 suited connectors that really "count". This is because 23s can only make two different straights if the A45 or 456 flops. AKs can only make one. 98 can make 4. QJT, JT7, T76,765. Like I said before, you could get away with playing overpairs like a set most of the time against the opponents who will call you with a pair. So you may be able to increase the number of suited connectors or decrease the odds of flopping two pair or a set as a result. So with this in mind you may be able to add in suited 1 gappers which are less likely to flop straight draws that are open ended as they have to hit the card between the two.

Also, if we choose not to play gutshot draws fast, the ratio can be closer to holding a pair 48% of the time. or 21 suited connectors for 13 pairs or 7 pairs to 11 suited connectors or 5 pairs to 8 suited connectors.

If we AREN'T pushing with gutshot draws, this probably makes our semibluffs more profitable and as a result we can even adjust the ratio to be more denominated by suited connectors than pairs than we already would.  However, because the straight possibilities and draw possibilities decrease as we add one gap connectors or connectors above JTs or below 45s,  the calculation may not be exactly right to the other side so it may balance out....

Regardless, this is just an estimation and you probably won't be playing exactly like this anyways since you can adapt for your table.

Nevertheless we can construct a tight strategy of playing for early position, a medium or middle position and a loose for late position.
Early position:
5 pairs to 4 suited connectors TT+,45s,56s,67s,78s. I like to represent both low card flops and high card flops so I prefer the low connectors. They also are less likely to run into higher straights by opponents playing AK or KQ or QJ or  JT than the higher ones.
Add AJ+ to make up 7.05% of hands
Alternative for those who don't play gutshots fast.
5 pairs to 8 suited connectors: TT+ 45s,56s,67s,78s,89s,T9s,JTs,QJs plus AQ+
Although QJ is not a suited connector we can also add AK and AQ which occasionally will be suited so overall it's close enough.  This will be 7.05% of hands.
Middle Position:
7 to 6: 88+,45s,56s,67s,78s,89s,T9s. We should also add in AT+, KQ,QJ,JT to make up 13.35% of hands
Alternate 7 to 11
88+,45s,56s,67s,78s,89s,T9s,36s,57s,68s,79s,8Ts. plus AJ+,KQ,QJ,JT for 13.65% of hands.

Late position
13 to 10
22+,45s,56s,67s,78s,89s,T9s,36s,57s,68s,79s,. Plus basically any halfway decent hand. You should play close to 50% of hands in lat position in my opinion but at least 20%. 

Alternate 13 to 21
This is basically any pair and any suited connector or suited gapper including those around the edges.

Note: It's important to note which hands you designate as in your suited connector range so you don't get caught playing suited 2 gappers fast for example or your AK and QJ hands that aren't designated in the range if you want to maintain proportion to your sets. Technically you will hit more twopair+ as well but you should play those slow as well but realistically as long as you attempt to counterbalance your draws with overpairs and two pairs and occasionally slow down on your draws you can keep it pretty close to balanced so opponents can't exploit you...

Overall, you shouldn't need to play so precise before the flop and after the flop, but since there may be your opponents who you are worried about, just be aware of how to adjust.

This is mostly here so you know  where the baseline is and how to deviate from it.

If opponents try to trap you a lot with one pair hands play more pairs and fewer suited connectors, and start playing fast with your AK and AQ and KQ and AA and KK type hands when they hit top pair or overpairs or better as well. If opponents start playing better draws, add in suited aces 2 through king so that you have the superior draw to a flush and the suited broadway connectors and unsuited connectors so you are drawing to the best straight.


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