Saturday, June 23, 2018
How Often Opponents Need To Defend (or more) to Deny Bluffs profit
Wednesday, June 20, 2018
Bluffing
When you choose to bluff you want to have a hand not strong enough to call because you have value to continue by just calling. However, you can still bluff with the bottom end of your hand range that has value in calling and you especially can do so with hands with bad reverse implied odds and only marginal value to call. Hands like low pocket pairs has value vs one bet but not vs multiple if opponents narrow their range with streets and that prefer not to see multiple streets where play becomes more difficult you can consider raising as a bluff.
Assume opponent has 55+,AQo+,AJs+,KQs and he raises 2.2 in the ante stages in a tournament.
You can technically call if you are 32.26% to win.
That means you can call the raise with:
44+,A9o+,KTo+,QTo+,J9o+,T9o,A2s+,K6s+,Q8s+,J7s+,T7s+,97s+,87s
If our opponent will call a 3bet with tighter than TT+,AKo,AQs+ we can raise with any two profitably assuming we bet pot
If our opponent plays exactly this range we'd probably only want value over the calling range which may only be TT,JJ,AQs and sometimes AK, sometimes, AKs and sometimes QQ.
bluff equity vs opponents assumed calling range for reference:
33 35.898%
22 35.318%
Q7s 32.359%
Q6s 32.609%
Q5s 32.504%
Q4s 32.224%
Q3s 31.851%
Q2s 31.474%
K5s 31.452%
54s 31.429%
65s 31.382%
K4s 31.157%
76s 31.087%
J6s 30.983%
75s 30.174%
K3s 30.763%
K2s 30.366%
64s 30.033%
53s 29.973%
86s 29.903%
43s 29.689%
Q9o 29.890%
J8o 29.002%
85s 28.911%
74s 28.746%
96s 28.558%
T6s 28.231%
32s 27.844%
A8o 27.079%
K9o 27.776%
T8o 26.098%98o 25.545%
If our opponents make more mistakes after the flop we can bluff raise with a wider range.
On the flop:
On the flop bluff raising is a little bit different, but let's take a J72 board with 2 spades and one heart and let's look at an opponent who bets something like:
66+,22,A9s+,A5s,A2s,AJo+, J9 or a better jack J7s+,K7s,T9s,T7s,97s+,87s,57s,67s
All flushdraws we can mostly call and sometimes raise as a semibluff.
all 22 89.19% most often raise, occasionally call
all JJ 93.23% most often raise, occasionally call
all 77 90.75% most often raise, occasionally call
all QQ 68.26% usually raise, sometimes call
all KK 72.54% usually raise, sometimes call
all AA 76.59% usually raise, sometimes call
all AJ 66.71% call mostly, sometimes raise
all A2 33.70% almost always call
all 88 35.10% almost always call
all 99 38.59% almost always call
all TT 42.11% call
all AA 76.59%
all a7 40% call
backdoor spades (highcard) AK 31.42% mostly call, rarely raise
backdoor spades (lowcard) AK 30.75% mostly call, rarely raise
backdoor spades (suited hearts) AK 30.56% mostly call, rarely raise
backdoor spades (highcard) t9 28.52% mostly call, rarely raise
backdoor spades (lowcard) t9 28.52% mostly call, rarely raise
backdoor spades (suited hearts) t9 28.52% mostly call, rarely raise
backdoor spades (suited hearts) t8 27.22% mostly call, rarely raise
backdoor spades (highcard) t8 27.09% mostly call, rarely raise
backdoor spades (suited hearts) 98 27.06% mostly call, rarely raise
no draw AK 27.04% mostly call, rarely raise
backdoor spades (highcard) 98 26.92% mostly call, rarely raise
backdoor spades (lowcard) t8 26.84% mostly call, rarely raise
backdoor spades (lowcard) 98 26.64% mostly call, rarely raise
backdoor spades (highcard) AQ 25.91% mostly call, sometimes raise
backdoor spades (suited hearts) AQ 25.44% mostly call, sometimes raise
no draw t9 25.38% mostly call, sometimes raise
backdoor spades (lowcard) AQ 25.18% mostly call, sometimes raise
all 66 24.56% usually bluff raise
all 55 24.18% usually bluff raise
no draw t8 24.02% float or bluff raise mixture
all 33 23.89% usually bluff raise
no draw 98 23.84% float or bluff raise mixture
all 44 23.46% usually bluff raise
backdoor spades (highcard) AT 22.63% float or bluff raise mixture
backdoor spades (highcard) kt 22.17% float or bluff raise mixture
backdoor spades (suited hearts) kt 22.05% float or bluff raise mixture
backdoor spades (suited hearts) AT 21.95% float or bluff raise mixture
backdoor spades (suited hearts) qt 21.87% float or bluff raise mixture
backdoor spades (highcard) qt 21.75% float or bluff raise mixture
backdoor spades (lowcard) kt 21.62% float or bluff raise mixture
no draw AQ 21.58% float or bluff raise mixture
backdoor spades (lowcard) AT 21.56% usually bluff raise, sometimes fold
backdoor spades (lowcard) qt 21.46% float or bluff raise mixture
backdoor spades (highcard) A9 21.09% usually bluff raise, sometimes fold
backdoor spades (highcard) A8 20.88% usually bluff raise, sometimes fold
backdoor spades (suited hearts) A9 20.55% usually float, sometimes bluff raise, sometimes fold
backdoor spades (highcard) k9 20.40% usually float, sometimes bluff raise, sometimes fold
backdoor spades (suited hearts) k9 20.33% usually float, sometimes bluff raise, sometimes fold
backdoor spades (suited hearts) A8 20.30% usually float, sometimes bluff raise, sometimes fold
backdoor spades (suited hearts) q9 20.17% usually bluff raise, sometimes float, sometimes fold
backdoor spades (highcard) q9 20.01% usually bluff raise, sometimes float, sometimes fold
backdoor spades (lowcard) A9 20% usually bluff raise, sometimes float, sometimes fold
backdoor spades (lowcard) k9 19.87% bluff raise or fold
backdoor spades (lowcard) q9 19.74% bluff raise or fold
backdoor spades (lowcard) A8 19.42% bluff raise or fold
backdoor spades (highcard) A5 19.05% usually float, sometimes bluff raise, sometimes fold
backdoor spades (highcard) A4 18.70% usually float, sometimes bluff raise, sometimes fold
backdoor spades (highcard) A3 18.70% usually float, sometimes bluff raise, sometimes fold
backdoor spades (suited hearts) A5 18.47% usually float, sometimes bluff raise, sometimes fold
no draw kt 18.31% sometimes bluff raise, sometimes fold
no draw AT 18.15% sometimes bluff raise, sometimes fold
no draw qt 18.14% sometimes bluff raise, sometimes fold
backdoor spades (suited hearts) A4 18.10% usually fold, sometimes mixed bluff raise or fold
backdoor spades (suited hearts) A3 18.10% usually fold, sometimes mixed bluff raise or fold
backdoor spades (highcard) A6 17.88% usually fold, sometimes mixed bluff raise or fold
backdoor spades (suited hearts) A6 17.30% usually fold, sometimes mixed bluff raise or fold
backdoor spades (lowcard) A5 17.25% usually fold, sometimes mixed bluff raise or fold
backdoor spades (lowcard) A4 16.90% usually fold, sometimes mixed bluff raise or fold
backdoor spades (lowcard) A3 16.90% usually fold, sometimes mixed bluff raise or fold
no draw A9 16.64% usually fold, sometimes mixed bluff raise or fold
no draw k9 16.47% usually fold, sometimes mixed bluff raise or fold
no draw A8 16.43% usually fold, sometimes mixed bluff raise or fold
no draw q9 16.33% usually fold, sometimes mixed bluff raise or fold
backdoor spades (lowcard) A6 16.10% usually fold, sometimes mixed bluff raise or fold
backdoor spades (suited hearts) 86 15.42% mostly fold very rarely float
backdoor spades (highcard) 86 14.86% mostly fold very rarely bluff raise
backdoor spades (lowcard) 86 14.68% mostly fold very rarely bluff raise
no draw A5 14.64% no draw
backdoor spades (suited hearts) 45 14.44% mostly fold very rarely float
backdoor spades (suited hearts) 65 14.38% mostly fold very rarely float
no draw A4 14.30% mostly fold very rarely bluff raise
no draw A3 14.30% mostly fold very rarely bluff raise
backdoor spades (suited hearts) 96 14.13% mostly fold very rarely float
backdoor spades (suited hearts) 95 13.98% mostly fold very rarely float
backdoor spades (highcard) 96 13.77% mostly fold very rarely bluff raise
backdoor spades (highcard) 45 13.76% mostly fold very rarely bluff raise
backdoor spades (lowcard) 45 13.75% mostly fold very rarely bluff raise
backdoor spades (highcard) 65 13.72% mostly fold very rarely bluff raise
backdoor spades (lowcard) 65 13.70% mostly fold very rarely bluff raise
backdoor spades (highcard) 95 13.65% mostly fold very rarely bluff raise
no draw A6 13.38% fold. only rare opponent specific decisions
backdoor spades (lowcard) 96 13.30% fold. only rare opponent specific decisions
backdoor spades (suited hearts) 34 13.25% mostly fold very rarely float
backdoor spades (lowcard) 95 13.12% fold. only rare opponent specific decisions
backdoor spades (highcard) 34 12.48% fold. only rare opponent specific decisions
backdoor spades (lowcard) 34 12.48% fold. only rare opponent specific decisions
no draw 86 11.78% fold. only rare opponent specific decisions
no draw 45 10.85% fold. only rare opponent specific decisions
no draw 65 10.80% fold. only rare opponent specific decisions
no draw 96 10.60% fold. only rare opponent specific decisions
no draw 95 10.20% fold. only rare opponent specific decisions
no draw 34 9.57% fold. only rare opponent specific decisions
Some opponents fold often enough on the flop or on prior streets for you to profitably be able to bet any 2 cards but even so, you don't want to give opponent reason to adjust so unless you specifically know this opponent isn't capable of adjusting or only very occasionally mix in these bluffs when you haven't bluffed in awhile, you haven't played a pot with this opponent in awhile, your opponent maybe hasn't been tilted and doesn't have a reason to change his play and you haven't had a spot where you can bluff anyone in awhile especially this opponent. In that case the cards really don't matter but even so, I see no reason why you can't at least have some standards just in case your assumptions are wrong.... At least on the flop. By the river hands will approach zero equity or 100% and have much fewer hands between. On the turn there will still be some longshot draws with one card to improve and hands like KQ that could hit the top pair and still not be good but have at least some chance (like under 10%) of winning when called.
on say a J728 board with 2 suits you might bluff hands like:
KQ with flush draw
A2-A6 with flush draw.
A9
AT
KQ no flush draw
A7
A2
Value hands after 2 streets of betting go down.
On the river it's more about which river cards you bluff and how often then what hand since bluffs will have pretty close to zero chance of winning when called. Bluffs should be much less frequent on the river than on the flop and even than on the turn.
Theoretical bluff to value ratio looks something like this. For a half the pot bet you are giving your opponents 3 to 1 and therefore they only need to be right 1/4 times. You should bluff such you are indifferent to whether or not they call because if you bluff more often they can always call and if you bluff less often they can always fold bluff catchers.
So on the river you should bluff 25% of the time to make them right on 1/4 calls.
On the turn you get to leverage the possibility of multiple bets and hands that are value on the turn may lose value when facing a n additional bet so you can bluff more as some bluff hands will improve and become value hands and some value hands will decline. The purpose of bluffing more is so that the river frequency matches the ratio needed and to have balance for multiple possible rivers to represent.
So you should actually bluff if you intend on 2 half the pot bets 1-(.75*.75)=43.75% and on the flop
1-(.75*.75*.75) =57.8125% on the flop.
With larger bets your opponents get worse pot odds and therefore have to call less often so you can bluff more often and still force opponent to break even. However, keep in mind this % is not of total hands that you have, but total hands that you bluff. So given your opponent can fold more often, fewer hands have value when called and therefore, fewer bets for value and so the total % of hands you bluff might not be any larger and may even be smaller if you bet bigger.
Minimum defend frequency=bluff catching.
Your opponent has to defend some percentage of the time to prevent you from bluffing profitably with any two cards so on the river they need to call you based upon the price you get when you bet. You are risking 1 half bet to get 2 halfbets on a half pot bet so opponents must defend you 50% of the time by calling or raising.
I don't know how it works on the river, but let's just assume it procedes similarly to how we can bluff more. I believe if we bluff more our opponent can continue more (and rebluff more). So I believe if we bet half pot bet our opponent should defend 87.5% on the flop, 75% on the turn and 50% on the river to deny us the ability to parlay multiple bets and bluff successfully with any two.
That may be a little high, but certainly if our opponent defends a pot size bet less than 50% on any street we can profitably bluff with any two and many of the bluffing hands will have some equity on earlier streets so we can bluff pretty widely and should defend at least some percentage more than 50% when our opponent bets half the pot. We not only have to protect our hands but also protect multiple streets of multiple hands and force our opponent to consider a wide range of hands that we can have.
I think to confirm this we can run a simulation but I will do that later perhaps..
You never should bluff more than 50% on the river unless you know opponent folds too often and won't adjust.
Assume opponent has 55+,AQo+,AJs+,KQs and he raises 2.2 in the ante stages in a tournament.
You can technically call if you are 32.26% to win.
That means you can call the raise with:
44+,A9o+,KTo+,QTo+,J9o+,T9o,A2s+,K6s+,Q8s+,J7s+,T7s+,97s+,87s
If our opponent will call a 3bet with tighter than TT+,AKo,AQs+ we can raise with any two profitably assuming we bet pot
If our opponent plays exactly this range we'd probably only want value over the calling range which may only be TT,JJ,AQs and sometimes AK, sometimes, AKs and sometimes QQ.
bluff equity vs opponents assumed calling range for reference:
33 35.898%
22 35.318%
Q7s 32.359%
Q6s 32.609%
Q5s 32.504%
Q4s 32.224%
Q3s 31.851%
Q2s 31.474%
K5s 31.452%
54s 31.429%
65s 31.382%
K4s 31.157%
76s 31.087%
J6s 30.983%
75s 30.174%
K3s 30.763%
K2s 30.366%
64s 30.033%
53s 29.973%
86s 29.903%
43s 29.689%
Q9o 29.890%
J8o 29.002%
85s 28.911%
74s 28.746%
96s 28.558%
T6s 28.231%
32s 27.844%
A8o 27.079%
K9o 27.776%
T8o 26.098%98o 25.545%
If our opponents make more mistakes after the flop we can bluff raise with a wider range.
On the flop:
On the flop bluff raising is a little bit different, but let's take a J72 board with 2 spades and one heart and let's look at an opponent who bets something like:
66+,22,A9s+,A5s,A2s,AJo+, J9 or a better jack J7s+,K7s,T9s,T7s,97s+,87s,57s,67s
All flushdraws we can mostly call and sometimes raise as a semibluff.
all 22 89.19% most often raise, occasionally call
all JJ 93.23% most often raise, occasionally call
all 77 90.75% most often raise, occasionally call
all QQ 68.26% usually raise, sometimes call
all KK 72.54% usually raise, sometimes call
all AA 76.59% usually raise, sometimes call
all AJ 66.71% call mostly, sometimes raise
all A2 33.70% almost always call
all 88 35.10% almost always call
all 99 38.59% almost always call
all TT 42.11% call
all AA 76.59%
all a7 40% call
backdoor spades (highcard) AK 31.42% mostly call, rarely raise
backdoor spades (lowcard) AK 30.75% mostly call, rarely raise
backdoor spades (suited hearts) AK 30.56% mostly call, rarely raise
backdoor spades (highcard) t9 28.52% mostly call, rarely raise
backdoor spades (lowcard) t9 28.52% mostly call, rarely raise
backdoor spades (suited hearts) t9 28.52% mostly call, rarely raise
backdoor spades (suited hearts) t8 27.22% mostly call, rarely raise
backdoor spades (highcard) t8 27.09% mostly call, rarely raise
backdoor spades (suited hearts) 98 27.06% mostly call, rarely raise
no draw AK 27.04% mostly call, rarely raise
backdoor spades (highcard) 98 26.92% mostly call, rarely raise
backdoor spades (lowcard) t8 26.84% mostly call, rarely raise
backdoor spades (lowcard) 98 26.64% mostly call, rarely raise
backdoor spades (highcard) AQ 25.91% mostly call, sometimes raise
backdoor spades (suited hearts) AQ 25.44% mostly call, sometimes raise
no draw t9 25.38% mostly call, sometimes raise
backdoor spades (lowcard) AQ 25.18% mostly call, sometimes raise
all 66 24.56% usually bluff raise
all 55 24.18% usually bluff raise
no draw t8 24.02% float or bluff raise mixture
all 33 23.89% usually bluff raise
no draw 98 23.84% float or bluff raise mixture
all 44 23.46% usually bluff raise
backdoor spades (highcard) AT 22.63% float or bluff raise mixture
backdoor spades (highcard) kt 22.17% float or bluff raise mixture
backdoor spades (suited hearts) kt 22.05% float or bluff raise mixture
backdoor spades (suited hearts) AT 21.95% float or bluff raise mixture
backdoor spades (suited hearts) qt 21.87% float or bluff raise mixture
backdoor spades (highcard) qt 21.75% float or bluff raise mixture
backdoor spades (lowcard) kt 21.62% float or bluff raise mixture
no draw AQ 21.58% float or bluff raise mixture
backdoor spades (lowcard) AT 21.56% usually bluff raise, sometimes fold
backdoor spades (lowcard) qt 21.46% float or bluff raise mixture
backdoor spades (highcard) A9 21.09% usually bluff raise, sometimes fold
backdoor spades (highcard) A8 20.88% usually bluff raise, sometimes fold
backdoor spades (suited hearts) A9 20.55% usually float, sometimes bluff raise, sometimes fold
backdoor spades (highcard) k9 20.40% usually float, sometimes bluff raise, sometimes fold
backdoor spades (suited hearts) k9 20.33% usually float, sometimes bluff raise, sometimes fold
backdoor spades (suited hearts) A8 20.30% usually float, sometimes bluff raise, sometimes fold
backdoor spades (suited hearts) q9 20.17% usually bluff raise, sometimes float, sometimes fold
backdoor spades (highcard) q9 20.01% usually bluff raise, sometimes float, sometimes fold
backdoor spades (lowcard) A9 20% usually bluff raise, sometimes float, sometimes fold
backdoor spades (lowcard) k9 19.87% bluff raise or fold
backdoor spades (lowcard) q9 19.74% bluff raise or fold
backdoor spades (lowcard) A8 19.42% bluff raise or fold
backdoor spades (highcard) A5 19.05% usually float, sometimes bluff raise, sometimes fold
backdoor spades (highcard) A4 18.70% usually float, sometimes bluff raise, sometimes fold
backdoor spades (highcard) A3 18.70% usually float, sometimes bluff raise, sometimes fold
backdoor spades (suited hearts) A5 18.47% usually float, sometimes bluff raise, sometimes fold
no draw kt 18.31% sometimes bluff raise, sometimes fold
no draw AT 18.15% sometimes bluff raise, sometimes fold
no draw qt 18.14% sometimes bluff raise, sometimes fold
backdoor spades (suited hearts) A4 18.10% usually fold, sometimes mixed bluff raise or fold
backdoor spades (suited hearts) A3 18.10% usually fold, sometimes mixed bluff raise or fold
backdoor spades (highcard) A6 17.88% usually fold, sometimes mixed bluff raise or fold
backdoor spades (suited hearts) A6 17.30% usually fold, sometimes mixed bluff raise or fold
backdoor spades (lowcard) A5 17.25% usually fold, sometimes mixed bluff raise or fold
backdoor spades (lowcard) A4 16.90% usually fold, sometimes mixed bluff raise or fold
backdoor spades (lowcard) A3 16.90% usually fold, sometimes mixed bluff raise or fold
no draw A9 16.64% usually fold, sometimes mixed bluff raise or fold
no draw k9 16.47% usually fold, sometimes mixed bluff raise or fold
no draw A8 16.43% usually fold, sometimes mixed bluff raise or fold
no draw q9 16.33% usually fold, sometimes mixed bluff raise or fold
backdoor spades (lowcard) A6 16.10% usually fold, sometimes mixed bluff raise or fold
backdoor spades (suited hearts) 86 15.42% mostly fold very rarely float
backdoor spades (highcard) 86 14.86% mostly fold very rarely bluff raise
backdoor spades (lowcard) 86 14.68% mostly fold very rarely bluff raise
no draw A5 14.64% no draw
backdoor spades (suited hearts) 45 14.44% mostly fold very rarely float
backdoor spades (suited hearts) 65 14.38% mostly fold very rarely float
no draw A4 14.30% mostly fold very rarely bluff raise
no draw A3 14.30% mostly fold very rarely bluff raise
backdoor spades (suited hearts) 96 14.13% mostly fold very rarely float
backdoor spades (suited hearts) 95 13.98% mostly fold very rarely float
backdoor spades (highcard) 96 13.77% mostly fold very rarely bluff raise
backdoor spades (highcard) 45 13.76% mostly fold very rarely bluff raise
backdoor spades (lowcard) 45 13.75% mostly fold very rarely bluff raise
backdoor spades (highcard) 65 13.72% mostly fold very rarely bluff raise
backdoor spades (lowcard) 65 13.70% mostly fold very rarely bluff raise
backdoor spades (highcard) 95 13.65% mostly fold very rarely bluff raise
no draw A6 13.38% fold. only rare opponent specific decisions
backdoor spades (lowcard) 96 13.30% fold. only rare opponent specific decisions
backdoor spades (suited hearts) 34 13.25% mostly fold very rarely float
backdoor spades (lowcard) 95 13.12% fold. only rare opponent specific decisions
backdoor spades (highcard) 34 12.48% fold. only rare opponent specific decisions
backdoor spades (lowcard) 34 12.48% fold. only rare opponent specific decisions
no draw 86 11.78% fold. only rare opponent specific decisions
no draw 45 10.85% fold. only rare opponent specific decisions
no draw 65 10.80% fold. only rare opponent specific decisions
no draw 96 10.60% fold. only rare opponent specific decisions
no draw 95 10.20% fold. only rare opponent specific decisions
no draw 34 9.57% fold. only rare opponent specific decisions
Some opponents fold often enough on the flop or on prior streets for you to profitably be able to bet any 2 cards but even so, you don't want to give opponent reason to adjust so unless you specifically know this opponent isn't capable of adjusting or only very occasionally mix in these bluffs when you haven't bluffed in awhile, you haven't played a pot with this opponent in awhile, your opponent maybe hasn't been tilted and doesn't have a reason to change his play and you haven't had a spot where you can bluff anyone in awhile especially this opponent. In that case the cards really don't matter but even so, I see no reason why you can't at least have some standards just in case your assumptions are wrong.... At least on the flop. By the river hands will approach zero equity or 100% and have much fewer hands between. On the turn there will still be some longshot draws with one card to improve and hands like KQ that could hit the top pair and still not be good but have at least some chance (like under 10%) of winning when called.
on say a J728 board with 2 suits you might bluff hands like:
KQ with flush draw
A2-A6 with flush draw.
A9
AT
KQ no flush draw
A7
A2
Value hands after 2 streets of betting go down.
On the river it's more about which river cards you bluff and how often then what hand since bluffs will have pretty close to zero chance of winning when called. Bluffs should be much less frequent on the river than on the flop and even than on the turn.
Theoretical bluff to value ratio looks something like this. For a half the pot bet you are giving your opponents 3 to 1 and therefore they only need to be right 1/4 times. You should bluff such you are indifferent to whether or not they call because if you bluff more often they can always call and if you bluff less often they can always fold bluff catchers.
So on the river you should bluff 25% of the time to make them right on 1/4 calls.
On the turn you get to leverage the possibility of multiple bets and hands that are value on the turn may lose value when facing a n additional bet so you can bluff more as some bluff hands will improve and become value hands and some value hands will decline. The purpose of bluffing more is so that the river frequency matches the ratio needed and to have balance for multiple possible rivers to represent.
So you should actually bluff if you intend on 2 half the pot bets 1-(.75*.75)=43.75% and on the flop
1-(.75*.75*.75) =57.8125% on the flop.
With larger bets your opponents get worse pot odds and therefore have to call less often so you can bluff more often and still force opponent to break even. However, keep in mind this % is not of total hands that you have, but total hands that you bluff. So given your opponent can fold more often, fewer hands have value when called and therefore, fewer bets for value and so the total % of hands you bluff might not be any larger and may even be smaller if you bet bigger.
Minimum defend frequency=bluff catching.
Your opponent has to defend some percentage of the time to prevent you from bluffing profitably with any two cards so on the river they need to call you based upon the price you get when you bet. You are risking 1 half bet to get 2 halfbets on a half pot bet so opponents must defend you 50% of the time by calling or raising.
I don't know how it works on the river, but let's just assume it procedes similarly to how we can bluff more. I believe if we bluff more our opponent can continue more (and rebluff more). So I believe if we bet half pot bet our opponent should defend 87.5% on the flop, 75% on the turn and 50% on the river to deny us the ability to parlay multiple bets and bluff successfully with any two.
That may be a little high, but certainly if our opponent defends a pot size bet less than 50% on any street we can profitably bluff with any two and many of the bluffing hands will have some equity on earlier streets so we can bluff pretty widely and should defend at least some percentage more than 50% when our opponent bets half the pot. We not only have to protect our hands but also protect multiple streets of multiple hands and force our opponent to consider a wide range of hands that we can have.
I think to confirm this we can run a simulation but I will do that later perhaps..
You never should bluff more than 50% on the river unless you know opponent folds too often and won't adjust.
Saturday, June 9, 2018
General poker principals:
General poker principals:
There are certain frequencies that opponents need to call with in order to prevent you from bluffing with any two. With multiple opponents they should at a minimum act in aggregate to call enough to force you to break even on bluff attempts. So if you are betting preflop for 2 times the pot or 3 big blinds into a 1.5 big blind pot when opponents fold they should each call at least this often given you raised with this many opponents. That will cause them to effectively fold about 2/3rds of the time. They should call slightly more than this, but this is a good baseline that you can apply on any street where you bet 2 times the pot.
1)33.33%
2)18.15%
3)12.50%
4)9.53%
5)7.7%
6)6.46%
7)5.56%
8)4.89%
When the antes kick in you are betting pot preflop (and sometimes minraise is less than pot) and your opponents must call you at least this often.
Defend range for a 1x pot bet:
1) 50%
2) 29.29%
3) 20.63%
4) 15.91%
5) 12.95%
6) 10.91%
7) 9.43%
8) 7.41%
For post flop considerations given the number of opponents you face let's also look at half pot and 1/3rd pot bets
Defend range for half pot bet:
1) 66.66%
2) 42.27%
3) 30.66%
4) 24.02%
5) 19.73%
6) 16.73%
7) 14.53%
8) 12.83%
For 1/3rd pot bet they need to collectively defend 75% of the time.
Some caveats to this.
The more streets left over, the more opponents can/should call, and the higher frequency you can/should bluff.
A toy game example by Matthew Janda showed 2/3rds pot betting where you bet 33% value and bluff 66% on the flop, then 49% bluff, 51% value on the turn, and then 30% bluff and 70% value on the river. I assume that also applies preflop. Also with an increased price such as in the big blind you can call more often to defend and you don't have to continue as often on the flop because of the pot odds you got on the prior round of betting. Also to be considered, in real poker hands that can draw to very strong hands or be used in bluffs when they miss are more valuable while hands with weak kickers, low cards that can be outkicked and out drawn and marginal hands that can only be used to bluff catch lose value.... particularly those that are not always strong enough to beat bluffs when we bluff catch.
If you actually work out hands, you need to use equity calculators to determine which specific hands these are on specific flops, and how opponents can shed these hands on each street with a round of betting.
Given this defend range, you want to only raise with hands that have value. If opponents call too often you don't really want to add in bluffs but if opponents call more than this the value hands go up and the hands that were considered bluffs now have value.
You only need about 33% equity to call a preflop raise of 2.2 big blinds when the blinds and antes are involved which means you can flat call very widely. While technically we have your opponent defending much less often, that is the minimum threshold to where bluffing with zero equity assuming the betting ends after the hand is profitable.
Nevertheless, we can consider anything that has equity when you call a bet to also be of value to bet. technically we may prefer a smaller pot with hands with 33% to 50% equity but raising gives us a chance at the blinds so in my mind this is close enough. Technically we'd probably have a mixed strategy and sometimes want to just call with the mediums strength hands plus occasionally stronger hands to protect it.
So what hands have equity?
Given we raise with number of opponents left and opponents defend often enough to force our bluffs to break even.
Pre-Ante stage:
1: 22+, A2+, K3+, Q8+, J9+, Q4s+, J7s+, T7s+, 98s, 87s
2: 22+, A4+, KT+,QJ,A2s+, K8s+,Q9s+,J9s+,T8s+,98s
3: 44+,A9o+,KQo,A7s+,KTs+,QTs+,JTs
4: 55+, AT+,KQ, A8s+, KTs+,QTs+,JTs
5: 77+, AQ+, ATs+, KQs
6: 88+, AK, AQs+
7: 99+, AK, AQs+
8: TT+, AK, AQs+
I would personally want to shed hands with kicker troubles and insert hands with more drawing potential. I would be very comfortable flat calling with this range as well if an opponent bet from a given spot with a number of opponents left before he raised.
Nevertheless, we can also bluff. We may wish to bluff with those hands not quite strong enough to flat call, or use those hands just on the bottom end of the range, particularly those without great drawing potential but that might make a lot of stronger kicker hands to fold like A2 or K3 or KJ or A9 or suited connectors or suited jacks, queens and kings (as opposed to suited aces which can draw to the best possible flush).
I would totally be comfortable playing an equal amount of value bet to bluff ranges. If we double our hand range total we roughly end up with the following hands:
value plus bluffs:
1: Any 2 (minus some bad hands)(85%)
2:22+,A2s+,K2s+,Q2s+,J2s+,T6s+,96s+,85s+,74s+,63s+,52s+,42s+,32s,A7o+,K9o+,Q9o+,J9o+,T7o+,97o+,86o+,75o+,64o+,54o,43o,32o (52%)
3:22+,A2s+,K9s+,Q9s+,J9s+,T8s+,97s+,86s+,75s+,64s+,53s+,42s+,32s,A9o+,KTo+,QTo+,J9o+,T9o,98o
(29.4%)
4:22+,A2s+,K9s+,Q9s+,J9s+,T8s+,97s+,86s+,75s+,64s+,53s+,42s+,32s,AJo+,KJo+,QJo,JTo (23.2%)
5: 44+,A9s+,K9s+,Q9s+,J8s+,T8s+,97s+,86s+,75s+,64s+,53s+,43s,32s,AQo+,KQo (16.4%)
6: 55+,A2s+,KJs+,QTs+,J9s+,T8s+,97s+,86s+,76s,65s,54s,43s,AKo (13.9%) - sometimes fold the weaker hands
7: 66+,ATs+,KQs,QJs,JTs,T8s+,98s,87s,76s,65s,54s,43s,32s,AKo (9.8%) - sometimes fold weaker hands
8: 77+,AQs+,A5s,KQs,QJs,JTs,T9s,98s,87s,76s,65s,54s,AKo (8.1%) (sometimes fold weaker hands)
But remember, we can probably bluff a little more than this, but if our opponents call too often we don't need to bluff (we could if our opponents also make post flop errors) and if they fold too often we can always bluff with as many as possible. Given the possible postflop errors if our opponents fold too often we can actually play any two. If our opponents call too often we have to have sufficient pot odds and implied odds to make up for the hands that are behind to call which means we can't really play any two without being really deep and to do so profitably will require more variance than is helpful in the early stages of tournaments. But we can play a wider range against worse opponents in general but it's also profitable to play a tighter range against loose opponents as we will get more value.
Ante stages: In the ante stages the eqution changes.
This is our value range vs what should be looser opponents:
equity to have value: 33%
1:22+,A2o+,k2o+,q2+,j2o+,T3o+,95o+,85o+,75o+,64o+,53o+ (85.5%)
2:22+,A2o+,K2o+,
3:22+,A2o+,K2o+,Q8o+,J8o+,T9o+,98o,87o,76o,A2s+,K2s+,Q2s+,J4s+,T6s+,95s+,84s+,74s+,63s+,52s+,43s (55.4%)
4:22+,A2o+,K8o+,QTo+,A2s+,K2s+,Q4s+,J8s+,T7s+96s+,85s+,74s+,63s+,53s+,43s (38.8%)
5:22+,A2o+,KTo+,QTo+,A2s+,K2s+,Q8s+,J8s+,T7s+,96s+,85s+,75s+,64s+,53s+,43s (35.1%)
6:22+,A2o+,KTo+,QJo,A2s+,K2s+,Q8s+,J8s+,T8s+,97s+,86s,76s,65s,54s (32.1%)
7:22+,A2o+,Kto+,A2s+,K4s+,Qts+,J9s+,T8s+,97s+,87s,76s,65s,54s (29.4%)
8:22+,ATo+,KTo+,A2s+,K5s+,QTs+,JTs,T9s,98s
We could probably play any two cards most of the time if we wanted to and we wouldn't have to have that wide of a preflop bluff range to do so.
value+bluffs when bluffs equal value
1:100%
2:100%
3:100%
4:77.6%
5:70.2%
6:64.2%
7:58.8%
8:39.6%
However, this doesn't quite consider how we might counter light 3betting and as a result it becomes more intricate to analyze and so we're better off probably playing a little bit tighter.
When our opponents bet we can 3bet as well. In general, if our opponents fold often enough we can 3bet any two, if they fold or call we want to have the bottom end of our calling range (or just slightly worse) in adddition to our strongest hands. If they tend to call widely we could 3bet for thin value with suited broadway strong aces and mid pair or better.
With one opponent, when we get to the river after 3 streets of large betting we need to have trips, two pair, straights and flushes if we fold such that we force our opponent to break even on bluffs on each street. But we should be calling with most pairs and most draws and even backdoor draws on certain flops, then we need to improve to a strong pair or a pair with a draw or top pair or better and then we need to have the big hands by the river. We can probably be a little bit looser than this because our opponent should bluff more on the flop and turn than on the river. With smaller betting overpair and top pair is probably good enough to call.
The above is all solid poker fundamentals. There are two more things to consider, bluff catching vs bluff frequency.
If we arrive on the river and we have the nuts or a total bluff, we want to bluff with a frequency that will cause our opponent to break even on bluff catches. If we were to bluff any more than this, our opponent should always call and profit off doing so. If we were to bluff less than this, our opponent would never call.
Conversely, our opponent should call such that he forces our bluff to break even. If he were to call more than this we should never bluff and if he folds more than this we should always bluff.
So if we bet the pot our opponent is getting 2 to 1 on his calls. If he bluff catches he can call twice and lose and be right on the 3rd and break even. So we should make him right exactly 1/3 and we should bet with a bluff 33% of the time and with value 66% of the time.
If we bet half the pot our opponent is getting 3 to 1, we should make him right exactly 1/4 times or bluff 25% of the time, value 75% of the time.
If we bet 10 times the pot our opponent, we should bluff 10/2.
We should never bluff more than half the time unless we know our opponent folds more than he should.
Our opponent should call a pot sized bet 50% of the time, a 1/2 pot sized bet 2/3rds of the time, a 2x pot bet 1/3rd of the time a 10x pot bet 1/11th of the time, a 1/10th pot sized bet 10/11 of the time. If our opponents call less often we can profitably bluff with any two and should find ways to enter this situation more often if possible. If our opponents call more often, we should try to eliminate hands that will end up only being bluffs and we should avoid bluffing.
This is how great poker is played, by working out the perfect strategy, determining how strategy changes as frequencies are higher or lower, and knowing what it looks like so when we see an opponent call down with only a pair we know he calls one or more streets too often and we can bluff less against him and value bet more. Our profit comes from mistakes by opponents.
Tournament poker is a little bit different. Accumulating 100% of the chips does not yield 100% of the prize pool but more like 20% of the prize pool. According to some poker theorists this means that the chips we stand to win are not worth the chips we risk losing. I think the opposite is true to the degree by which you sufficiently manage to reduce your chip varience to where you aren't at risk of ruin or elimination.
This is how a positive expected value risk effects return as risk increases. This is what it looks like:
https://forexboat.com/wp-content/uploads/2015/03/Slide2-1024x576.png
We can get a better return to volatility with lower risk. Since a 10% decline requires an 11% gain to get back to even, a 20% loss requires a 25% gain to get back to even and a 90% loss requires a 1000% gain to get back to even and a 95% loss requires a 2000% gain to get back to even we want to reduce volatility if we can do so, especially since there is a minimum bet that actually increases. We can't afford the chip volatility, at least while we still have a choice. Eventually there should be some tradeoff.
We should take on as much risk as we can without reducing our edge or unnecessarily increasing our volatility. Eventually, we run out of options without taking risk and accumulating chips with no risk of ruin becomes impossible. Knowing this, there is some logic in seeking excess risk even with a negative return with the idea being that when we survive we will gain the ability to accumulate more chips for longer that will hopefully pay for the cost of the unnecessary risk when we don't survive. The chips we are able to accumulate following a double up are worth more than the chips we risk, meaning that with 60 big blinds we can accumulate chips safely at a faster rate with less risk than the alternative of not taking that risk so that it probably is worth more. A skilled player in the right structure can parlay a well timed double up into never having to be all in for the rest of the tournament! Conversely, early on in the tournament, a skilled player can parlay an increased chance of survival into significantly more chips without ever being all in and continue to grow until the blinds become say 20% of the starting stack or more. Survival is clearly super valuable early on, but when we get too short stacked the remainder of the tournament we will resort to more of a luckfest if we don't double up and if we do we can then make small constant, continuous pressure to accumulate chips. Therefore, making a just slightly a little bit too reckless bluffs and shoves and all in calls to stay above certain levels knowing that if we get caught we still have a decent chance of doubling up and once we do we will be hard to deny a final table may actually be the best strategy. It's hard to know for sure as under a certain amount of big blinds I actually think being tighter than 99% of tournament pros not named Phil Hellmuth suggest is actually correct. The chances of tripling up go up and although a top skilled player's EV increases from 40 big blinds to 80 big blinds and higher there's a certain spot as a short stack where you have no leverage and so going from 8 big blinds to 16 doesn't do you much good, but going from 6 big blinds to 4 actually does because you now have a larger side pot and leverage of opponents stack to push other players out with a chance to more than triple up with a big favorite to win if you are patient enough.Sit a pro in with 20 big blinds and he might be able to have a decent win rate. Stick one in with 10 big blinds and antes and way more hands become way more profitable. To some players this means they can't pass up any opportunity to profit but I say they should pass up more because they will get even more profitable opportunity if they don't risk elimination on only a slightly profitable shove like 98s or K6 or something.
Let's look at the kelly criterion (risk management) based strategy for accumulating chips as our stack declines and we have to creatively come up with new ways to maintain an edge without variance.
Antes:
80-150BBs 3bet 6BBs+2 streets of value half pot.
50-80BBs minraise+3 streets of value 55% pot down to 40%
~50BBs 3bet 2.75, Cbet steal attempt
25-50BBs minraise+2 streets of value 70% pot down to 40%
25BBs-50BBs minraise+ overbet one street 2.5x pot down to 1x pot. or check back and minraise 1 street 1.25pot down to .50 pot.
15-25BBs minraise+2 streets 40% pot down to 20% pot
12.5BBs-15BBs minraise min bet 3 streets
10BBs-12.5BBs minraise min bet 2 streets
7-10BBs minraise min bet 1 street
7-15BBs minraise steal muck if wrong
MOVES given # of blinds:
75-50 3 bet bluff and continuation bet
35-50 bluff raise flop (no ante) after a 3BB call
35-50 3bet bluff with greater discretion and more selective 3betting
30-50 bluff raise flop (ante) after a 2BB call.
25-45 minraise flop & Cbet bluffs (ante)
25-40 check behind your backdoor draws and gutshot on the flops and bluff raise turn with low pair and some kind of draw by the turn as a semibluff. You will also be checking for pot control most of the time with good hands anyways.
20-30 Float flop wide to bluff after a minraise preflop
15-25 check back flop and float turn wider rather than bluff raise and bluff some rivers when checked to
12-25 minraise+really selective cbet bluffs. You won't be Cbetting often and when you do Cbet you will often check back the turn instead, but you can occasionally Cbet bluff if you are really selective about it.
7-30BB minraise steal attempt with no plans to continue
-----------------------------
[Ideally you never have to enter the wildly volatile strategy that risks your entire chips or even close to it but realistically you will. As such, at some stage that is way before it becomes a shovefest I believe it's acceptable to accept a wildly voltile strategy willing to risk it all once and go back to more profitable, lower risk chip accumulation. It's better to risk it all once while you have a lot of chips and can gain a lot of chips for a lot more levels of increasing blinds than have to get it all in 3 times with the best hand. A 60% favorite only has a 21.6% chance of advancing after 3 all ins]. If during volatile play you get knee capped or you decide you're better off waiting it out until conditions change you have a little bit of wiggle room left and looking to triple up rather than double up and you are more looking to protect survival with only the best cards you can wait for. Knowing the best situation you can wait for given your edge and the blind structure, I would be willing to risk it all with a hand that was As strong as I could expect 50% of the time to see at least once given the hands left. I would ideally want to adjust this for flops turns and rivers as well as preflop but you can only do what you can do.
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Let's discuss the moves.
In order to bluff you have to identify someone that can fold. When that's the case you want hands just at the bottom or just below the hands that have value to call so that you either aren't giving up that much, or you aren't giving up anything at all in exchange for using them to bluff... Preflop that's probably going to be any ace, King6-King 9, Queen4-Queen 8, JT,JT suited 2 and 3 gap connectors, low suited connectors, suited K2-K5 and Q2-Q5 and J5-J8 and unsuited connectors and unsuited mid and high gappers (J9,T8,97,86) plus maybe weak broadway hands. That does NOT mean by any means to ALWAYS use these hands to bluff. But when you have these hands it's better to use them to bluff than others and you probably don't have to worry about missed opportunity as there will be plenty of opportunity to come.
So you want to look for a loose preflop raiser capable of folding to aggression and either passive or straight forward after the flop in case you get caught so you at least have some ways to win if/when you decide to.
After the flop if you are going to bluff raise you want to remove all the hands that are capable of calling except maybe the bottom end of them. That is, bottom pair, lowe pocket pair, gutshot draws. And then you are going to look for the high end of hands that you have decided to fold. Backdoor straight & flush draws, ace high with a backdoor gutshot, backdoor 3 to straight draws backdoor straight flush draws with 1 gap (45 with a 7 and the suit to a flush) and other nuances.
This is your "trickery" range. Your "trickery range" is what you are willing to use to float or bluff with IF the conditions are right but you may prefer to fold some or most of the time. Your trickery range is where you either bluff raise or call to represent something and bluff raise some percentage of turns given some specific action and specific cards. You are going to take a free card on most good draws while bluffing most longshot draws and improved to one pair and you are going to give up some cards and you are going to bluff on some scare cards as well.
You might sometimes float more widely if the opponent always Cbets and folds too often on the turn or if he never check raises the turn and has some combination of checking a lot, check/folding a high % of the time he checks, betting the flop too widely or having too many weak hands preflop that he has to get rid of somewhere after the flop.
Everything else is knowing your situation, knowing the flop, knowing your opponent, knowing what to look for and then just taking advantage of it. You should know what percentages opponents should call you and then whether they call more or less and as a result what that might look like on the flop or turn, and what your action might be on each street as a result. You should know your percentages as well
You should know the structure and identify soft spots where the ante is larger relative to the small blind such as 1/3rd the small blind and also where large increases in the amount to steal is and you should be aware of where the final table is. If the final table occurs with an average stack of 15 big blinds, you simply take the number of chips in play divided by 9 for the average chips at the final table and then divide it by 15 to get the big blind you expect. You can figure out how many you have left by paying the blinds and antes plus or minus a low varience skill edge and see where that gets you and at what point you may have to take on more risk if you fall below a certain amount of chips. You may have to work a little harder and take a little more risk at risk of volatility/survival in order to maintain enough chips if the structure is fast enough. but figure this stuff out.
You also want to know aside from calling and bluffing frequencies that you should raise with the top and bottom parts of your range and check your medium strength hand but you should occasionally vary your play. Maybe 75% of the time you bet with the value range plus some percentage of bluffs and 25% you check/call those hands (or check/fold the bluffs), you may need to check raise bluff and check raise value bet some too which complicates things a little but as long as you have a general idea of when and why to do this, that's okay. If your opponent calls too widely you don't want to bluff but you instead increase your value range.
There's probably a lot of other details to know such as adjusting to tournament structure, adjusting to the bubble, 4betting vs 3betting range, 4bet bluffing, etc and in the money considerations but I'm a little unconventional about that stuff. I like to flat call more and manage the risk even with big hands so I end up trapping but I'm really not trying to as much as I'm trying to control pot size. If you constantly do this and opponents don't see you show down a big hand and you 3bet or 4bet for the first time in forever, they're going to assume you have a good hand if they're a thinking player capable of folding and so you probably can get away with a bluff, but at what cost? I could see an argument for playing this way just before the antes or just after or in a really big tournament where you know there's a lot of poker to be played and a fairly fast structure. Maybe some percentage of the time you get knocked out but when you don't you get a lot of chips and if you show a willingness to risk it all your opponents might not 3bet you anymore unless they want action or are willing to take risk themselves. Either way, that is an informational advantage and you gain fear equity that allows you to increase your rate of stealing. So I have seen players fold 30 hands in a row that then start raising every hand and then when they get 3bet they 4bet shove with 26off and they may even do it again. Sure, it's probably an unprofitable play but if you induce enough weak/tight play and a little bit wider range willing to risk it all (you'll get paid off when you have the absolute nuts) it's worth the cost of one hand, particularly if you can get such a big stack that risk no longer is a concern and you can play a pretty much max EV strategy until your stack reduces in size or others catch up.
There are certain frequencies that opponents need to call with in order to prevent you from bluffing with any two. With multiple opponents they should at a minimum act in aggregate to call enough to force you to break even on bluff attempts. So if you are betting preflop for 2 times the pot or 3 big blinds into a 1.5 big blind pot when opponents fold they should each call at least this often given you raised with this many opponents. That will cause them to effectively fold about 2/3rds of the time. They should call slightly more than this, but this is a good baseline that you can apply on any street where you bet 2 times the pot.
1)33.33%
2)18.15%
3)12.50%
4)9.53%
5)7.7%
6)6.46%
7)5.56%
8)4.89%
When the antes kick in you are betting pot preflop (and sometimes minraise is less than pot) and your opponents must call you at least this often.
Defend range for a 1x pot bet:
1) 50%
2) 29.29%
3) 20.63%
4) 15.91%
5) 12.95%
6) 10.91%
7) 9.43%
8) 7.41%
For post flop considerations given the number of opponents you face let's also look at half pot and 1/3rd pot bets
Defend range for half pot bet:
1) 66.66%
2) 42.27%
3) 30.66%
4) 24.02%
5) 19.73%
6) 16.73%
7) 14.53%
8) 12.83%
For 1/3rd pot bet they need to collectively defend 75% of the time.
Some caveats to this.
The more streets left over, the more opponents can/should call, and the higher frequency you can/should bluff.
A toy game example by Matthew Janda showed 2/3rds pot betting where you bet 33% value and bluff 66% on the flop, then 49% bluff, 51% value on the turn, and then 30% bluff and 70% value on the river. I assume that also applies preflop. Also with an increased price such as in the big blind you can call more often to defend and you don't have to continue as often on the flop because of the pot odds you got on the prior round of betting. Also to be considered, in real poker hands that can draw to very strong hands or be used in bluffs when they miss are more valuable while hands with weak kickers, low cards that can be outkicked and out drawn and marginal hands that can only be used to bluff catch lose value.... particularly those that are not always strong enough to beat bluffs when we bluff catch.
If you actually work out hands, you need to use equity calculators to determine which specific hands these are on specific flops, and how opponents can shed these hands on each street with a round of betting.
Given this defend range, you want to only raise with hands that have value. If opponents call too often you don't really want to add in bluffs but if opponents call more than this the value hands go up and the hands that were considered bluffs now have value.
You only need about 33% equity to call a preflop raise of 2.2 big blinds when the blinds and antes are involved which means you can flat call very widely. While technically we have your opponent defending much less often, that is the minimum threshold to where bluffing with zero equity assuming the betting ends after the hand is profitable.
Nevertheless, we can consider anything that has equity when you call a bet to also be of value to bet. technically we may prefer a smaller pot with hands with 33% to 50% equity but raising gives us a chance at the blinds so in my mind this is close enough. Technically we'd probably have a mixed strategy and sometimes want to just call with the mediums strength hands plus occasionally stronger hands to protect it.
So what hands have equity?
Given we raise with number of opponents left and opponents defend often enough to force our bluffs to break even.
Pre-Ante stage:
1: 22+, A2+, K3+, Q8+, J9+, Q4s+, J7s+, T7s+, 98s, 87s
2: 22+, A4+, KT+,QJ,A2s+, K8s+,Q9s+,J9s+,T8s+,98s
3: 44+,A9o+,KQo,A7s+,KTs+,QTs+,JTs
4: 55+, AT+,KQ, A8s+, KTs+,QTs+,JTs
5: 77+, AQ+, ATs+, KQs
6: 88+, AK, AQs+
7: 99+, AK, AQs+
8: TT+, AK, AQs+
I would personally want to shed hands with kicker troubles and insert hands with more drawing potential. I would be very comfortable flat calling with this range as well if an opponent bet from a given spot with a number of opponents left before he raised.
Nevertheless, we can also bluff. We may wish to bluff with those hands not quite strong enough to flat call, or use those hands just on the bottom end of the range, particularly those without great drawing potential but that might make a lot of stronger kicker hands to fold like A2 or K3 or KJ or A9 or suited connectors or suited jacks, queens and kings (as opposed to suited aces which can draw to the best possible flush).
I would totally be comfortable playing an equal amount of value bet to bluff ranges. If we double our hand range total we roughly end up with the following hands:
value plus bluffs:
1: Any 2 (minus some bad hands)(85%)
2:22+,A2s+,K2s+,Q2s+,J2s+,T6s+,96s+,85s+,74s+,63s+,52s+,42s+,32s,A7o+,K9o+,Q9o+,J9o+,T7o+,97o+,86o+,75o+,64o+,54o,43o,32o (52%)
3:22+,A2s+,K9s+,Q9s+,J9s+,T8s+,97s+,86s+,75s+,64s+,53s+,42s+,32s,A9o+,KTo+,QTo+,J9o+,T9o,98o
(29.4%)
4:22+,A2s+,K9s+,Q9s+,J9s+,T8s+,97s+,86s+,75s+,64s+,53s+,42s+,32s,AJo+,KJo+,QJo,JTo (23.2%)
5: 44+,A9s+,K9s+,Q9s+,J8s+,T8s+,97s+,86s+,75s+,64s+,53s+,43s,32s,AQo+,KQo (16.4%)
6: 55+,A2s+,KJs+,QTs+,J9s+,T8s+,97s+,86s+,76s,65s,54s,43s,AKo (13.9%) - sometimes fold the weaker hands
7: 66+,ATs+,KQs,QJs,JTs,T8s+,98s,87s,76s,65s,54s,43s,32s,AKo (9.8%) - sometimes fold weaker hands
8: 77+,AQs+,A5s,KQs,QJs,JTs,T9s,98s,87s,76s,65s,54s,AKo (8.1%) (sometimes fold weaker hands)
But remember, we can probably bluff a little more than this, but if our opponents call too often we don't need to bluff (we could if our opponents also make post flop errors) and if they fold too often we can always bluff with as many as possible. Given the possible postflop errors if our opponents fold too often we can actually play any two. If our opponents call too often we have to have sufficient pot odds and implied odds to make up for the hands that are behind to call which means we can't really play any two without being really deep and to do so profitably will require more variance than is helpful in the early stages of tournaments. But we can play a wider range against worse opponents in general but it's also profitable to play a tighter range against loose opponents as we will get more value.
Ante stages: In the ante stages the eqution changes.
This is our value range vs what should be looser opponents:
equity to have value: 33%
1:22+,A2o+,k2o+,q2+,j2o+,T3o+,95o+,85o+,75o+,64o+,53o+ (85.5%)
2:22+,A2o+,K2o+,
3:22+,A2o+,K2o+,Q8o+,J8o+,T9o+,98o,87o,76o,A2s+,K2s+,Q2s+,J4s+,T6s+,95s+,84s+,74s+,63s+,52s+,43s (55.4%)
4:22+,A2o+,K8o+,QTo+,A2s+,K2s+,Q4s+,J8s+,T7s+96s+,85s+,74s+,63s+,53s+,43s (38.8%)
5:22+,A2o+,KTo+,QTo+,A2s+,K2s+,Q8s+,J8s+,T7s+,96s+,85s+,75s+,64s+,53s+,43s (35.1%)
6:22+,A2o+,KTo+,QJo,A2s+,K2s+,Q8s+,J8s+,T8s+,97s+,86s,76s,65s,54s (32.1%)
7:22+,A2o+,Kto+,A2s+,K4s+,Qts+,J9s+,T8s+,97s+,87s,76s,65s,54s (29.4%)
8:22+,ATo+,KTo+,A2s+,K5s+,QTs+,JTs,T9s,98s
We could probably play any two cards most of the time if we wanted to and we wouldn't have to have that wide of a preflop bluff range to do so.
value+bluffs when bluffs equal value
1:100%
2:100%
3:100%
4:77.6%
5:70.2%
6:64.2%
7:58.8%
8:39.6%
However, this doesn't quite consider how we might counter light 3betting and as a result it becomes more intricate to analyze and so we're better off probably playing a little bit tighter.
When our opponents bet we can 3bet as well. In general, if our opponents fold often enough we can 3bet any two, if they fold or call we want to have the bottom end of our calling range (or just slightly worse) in adddition to our strongest hands. If they tend to call widely we could 3bet for thin value with suited broadway strong aces and mid pair or better.
With one opponent, when we get to the river after 3 streets of large betting we need to have trips, two pair, straights and flushes if we fold such that we force our opponent to break even on bluffs on each street. But we should be calling with most pairs and most draws and even backdoor draws on certain flops, then we need to improve to a strong pair or a pair with a draw or top pair or better and then we need to have the big hands by the river. We can probably be a little bit looser than this because our opponent should bluff more on the flop and turn than on the river. With smaller betting overpair and top pair is probably good enough to call.
The above is all solid poker fundamentals. There are two more things to consider, bluff catching vs bluff frequency.
If we arrive on the river and we have the nuts or a total bluff, we want to bluff with a frequency that will cause our opponent to break even on bluff catches. If we were to bluff any more than this, our opponent should always call and profit off doing so. If we were to bluff less than this, our opponent would never call.
Conversely, our opponent should call such that he forces our bluff to break even. If he were to call more than this we should never bluff and if he folds more than this we should always bluff.
So if we bet the pot our opponent is getting 2 to 1 on his calls. If he bluff catches he can call twice and lose and be right on the 3rd and break even. So we should make him right exactly 1/3 and we should bet with a bluff 33% of the time and with value 66% of the time.
If we bet half the pot our opponent is getting 3 to 1, we should make him right exactly 1/4 times or bluff 25% of the time, value 75% of the time.
If we bet 10 times the pot our opponent, we should bluff 10/2.
We should never bluff more than half the time unless we know our opponent folds more than he should.
Our opponent should call a pot sized bet 50% of the time, a 1/2 pot sized bet 2/3rds of the time, a 2x pot bet 1/3rd of the time a 10x pot bet 1/11th of the time, a 1/10th pot sized bet 10/11 of the time. If our opponents call less often we can profitably bluff with any two and should find ways to enter this situation more often if possible. If our opponents call more often, we should try to eliminate hands that will end up only being bluffs and we should avoid bluffing.
This is how great poker is played, by working out the perfect strategy, determining how strategy changes as frequencies are higher or lower, and knowing what it looks like so when we see an opponent call down with only a pair we know he calls one or more streets too often and we can bluff less against him and value bet more. Our profit comes from mistakes by opponents.
TOURNAMENT POKER
Tournament poker is a little bit different. Accumulating 100% of the chips does not yield 100% of the prize pool but more like 20% of the prize pool. According to some poker theorists this means that the chips we stand to win are not worth the chips we risk losing. I think the opposite is true to the degree by which you sufficiently manage to reduce your chip varience to where you aren't at risk of ruin or elimination.
https://forexboat.com/wp-content/uploads/2015/03/Slide2-1024x576.png
We should take on as much risk as we can without reducing our edge or unnecessarily increasing our volatility. Eventually, we run out of options without taking risk and accumulating chips with no risk of ruin becomes impossible. Knowing this, there is some logic in seeking excess risk even with a negative return with the idea being that when we survive we will gain the ability to accumulate more chips for longer that will hopefully pay for the cost of the unnecessary risk when we don't survive. The chips we are able to accumulate following a double up are worth more than the chips we risk, meaning that with 60 big blinds we can accumulate chips safely at a faster rate with less risk than the alternative of not taking that risk so that it probably is worth more. A skilled player in the right structure can parlay a well timed double up into never having to be all in for the rest of the tournament! Conversely, early on in the tournament, a skilled player can parlay an increased chance of survival into significantly more chips without ever being all in and continue to grow until the blinds become say 20% of the starting stack or more. Survival is clearly super valuable early on, but when we get too short stacked the remainder of the tournament we will resort to more of a luckfest if we don't double up and if we do we can then make small constant, continuous pressure to accumulate chips. Therefore, making a just slightly a little bit too reckless bluffs and shoves and all in calls to stay above certain levels knowing that if we get caught we still have a decent chance of doubling up and once we do we will be hard to deny a final table may actually be the best strategy. It's hard to know for sure as under a certain amount of big blinds I actually think being tighter than 99% of tournament pros not named Phil Hellmuth suggest is actually correct. The chances of tripling up go up and although a top skilled player's EV increases from 40 big blinds to 80 big blinds and higher there's a certain spot as a short stack where you have no leverage and so going from 8 big blinds to 16 doesn't do you much good, but going from 6 big blinds to 4 actually does because you now have a larger side pot and leverage of opponents stack to push other players out with a chance to more than triple up with a big favorite to win if you are patient enough.Sit a pro in with 20 big blinds and he might be able to have a decent win rate. Stick one in with 10 big blinds and antes and way more hands become way more profitable. To some players this means they can't pass up any opportunity to profit but I say they should pass up more because they will get even more profitable opportunity if they don't risk elimination on only a slightly profitable shove like 98s or K6 or something.
Let's look at the kelly criterion (risk management) based strategy for accumulating chips as our stack declines and we have to creatively come up with new ways to maintain an edge without variance.
No Ante:
Above 150 Bbs you can
raise 3BBs and 2/3rds pot bet 3 streets of value
100-150Bbs raise 3BBs
and pot bet 2 streets of value or 3.5BBs 50% pot 3 streets of value
60-100BBs raise 3BBs
and 2/3rds pot bet 2 streets of value OR 2BB 50% pot 3 streets of
value
40-60BBs raise 2BBs and
2/3rds pot bet 2 streets of value Or 40% pot 3 streets
30-40BBs raise 2BBs and
½ pot bet 2 streets of value. OR 30% pot 3 streets of value
20-30BBs raise 2BBs and
40% pot bet 2 streets of value. Or 20% pot 3 streets
Antes:
80-150BBs 3bet 6BBs+2 streets of value half pot.
50-80BBs minraise+3 streets of value 55% pot down to 40%
~50BBs 3bet 2.75, Cbet steal attempt
25-50BBs minraise+2 streets of value 70% pot down to 40%
25BBs-50BBs minraise+ overbet one street 2.5x pot down to 1x pot. or check back and minraise 1 street 1.25pot down to .50 pot.
15-25BBs minraise+2 streets 40% pot down to 20% pot
12.5BBs-15BBs minraise min bet 3 streets
10BBs-12.5BBs minraise min bet 2 streets
7-10BBs minraise min bet 1 street
7-15BBs minraise steal muck if wrong
MOVES given # of blinds:
75-50 3 bet bluff and continuation bet
35-50 bluff raise flop (no ante) after a 3BB call
35-50 3bet bluff with greater discretion and more selective 3betting
30-50 bluff raise flop (ante) after a 2BB call.
25-45 minraise flop & Cbet bluffs (ante)
25-40 check behind your backdoor draws and gutshot on the flops and bluff raise turn with low pair and some kind of draw by the turn as a semibluff. You will also be checking for pot control most of the time with good hands anyways.
20-30 Float flop wide to bluff after a minraise preflop
15-25 check back flop and float turn wider rather than bluff raise and bluff some rivers when checked to
12-25 minraise+really selective cbet bluffs. You won't be Cbetting often and when you do Cbet you will often check back the turn instead, but you can occasionally Cbet bluff if you are really selective about it.
7-30BB minraise steal attempt with no plans to continue
-----------------------------
[Ideally you never have to enter the wildly volatile strategy that risks your entire chips or even close to it but realistically you will. As such, at some stage that is way before it becomes a shovefest I believe it's acceptable to accept a wildly voltile strategy willing to risk it all once and go back to more profitable, lower risk chip accumulation. It's better to risk it all once while you have a lot of chips and can gain a lot of chips for a lot more levels of increasing blinds than have to get it all in 3 times with the best hand. A 60% favorite only has a 21.6% chance of advancing after 3 all ins]. If during volatile play you get knee capped or you decide you're better off waiting it out until conditions change you have a little bit of wiggle room left and looking to triple up rather than double up and you are more looking to protect survival with only the best cards you can wait for. Knowing the best situation you can wait for given your edge and the blind structure, I would be willing to risk it all with a hand that was As strong as I could expect 50% of the time to see at least once given the hands left. I would ideally want to adjust this for flops turns and rivers as well as preflop but you can only do what you can do.
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Let's discuss the moves.
In order to bluff you have to identify someone that can fold. When that's the case you want hands just at the bottom or just below the hands that have value to call so that you either aren't giving up that much, or you aren't giving up anything at all in exchange for using them to bluff... Preflop that's probably going to be any ace, King6-King 9, Queen4-Queen 8, JT,JT suited 2 and 3 gap connectors, low suited connectors, suited K2-K5 and Q2-Q5 and J5-J8 and unsuited connectors and unsuited mid and high gappers (J9,T8,97,86) plus maybe weak broadway hands. That does NOT mean by any means to ALWAYS use these hands to bluff. But when you have these hands it's better to use them to bluff than others and you probably don't have to worry about missed opportunity as there will be plenty of opportunity to come.
So you want to look for a loose preflop raiser capable of folding to aggression and either passive or straight forward after the flop in case you get caught so you at least have some ways to win if/when you decide to.
After the flop if you are going to bluff raise you want to remove all the hands that are capable of calling except maybe the bottom end of them. That is, bottom pair, lowe pocket pair, gutshot draws. And then you are going to look for the high end of hands that you have decided to fold. Backdoor straight & flush draws, ace high with a backdoor gutshot, backdoor 3 to straight draws backdoor straight flush draws with 1 gap (45 with a 7 and the suit to a flush) and other nuances.
This is your "trickery" range. Your "trickery range" is what you are willing to use to float or bluff with IF the conditions are right but you may prefer to fold some or most of the time. Your trickery range is where you either bluff raise or call to represent something and bluff raise some percentage of turns given some specific action and specific cards. You are going to take a free card on most good draws while bluffing most longshot draws and improved to one pair and you are going to give up some cards and you are going to bluff on some scare cards as well.
You might sometimes float more widely if the opponent always Cbets and folds too often on the turn or if he never check raises the turn and has some combination of checking a lot, check/folding a high % of the time he checks, betting the flop too widely or having too many weak hands preflop that he has to get rid of somewhere after the flop.
Everything else is knowing your situation, knowing the flop, knowing your opponent, knowing what to look for and then just taking advantage of it. You should know what percentages opponents should call you and then whether they call more or less and as a result what that might look like on the flop or turn, and what your action might be on each street as a result. You should know your percentages as well
You should know the structure and identify soft spots where the ante is larger relative to the small blind such as 1/3rd the small blind and also where large increases in the amount to steal is and you should be aware of where the final table is. If the final table occurs with an average stack of 15 big blinds, you simply take the number of chips in play divided by 9 for the average chips at the final table and then divide it by 15 to get the big blind you expect. You can figure out how many you have left by paying the blinds and antes plus or minus a low varience skill edge and see where that gets you and at what point you may have to take on more risk if you fall below a certain amount of chips. You may have to work a little harder and take a little more risk at risk of volatility/survival in order to maintain enough chips if the structure is fast enough. but figure this stuff out.
You also want to know aside from calling and bluffing frequencies that you should raise with the top and bottom parts of your range and check your medium strength hand but you should occasionally vary your play. Maybe 75% of the time you bet with the value range plus some percentage of bluffs and 25% you check/call those hands (or check/fold the bluffs), you may need to check raise bluff and check raise value bet some too which complicates things a little but as long as you have a general idea of when and why to do this, that's okay. If your opponent calls too widely you don't want to bluff but you instead increase your value range.
There's probably a lot of other details to know such as adjusting to tournament structure, adjusting to the bubble, 4betting vs 3betting range, 4bet bluffing, etc and in the money considerations but I'm a little unconventional about that stuff. I like to flat call more and manage the risk even with big hands so I end up trapping but I'm really not trying to as much as I'm trying to control pot size. If you constantly do this and opponents don't see you show down a big hand and you 3bet or 4bet for the first time in forever, they're going to assume you have a good hand if they're a thinking player capable of folding and so you probably can get away with a bluff, but at what cost? I could see an argument for playing this way just before the antes or just after or in a really big tournament where you know there's a lot of poker to be played and a fairly fast structure. Maybe some percentage of the time you get knocked out but when you don't you get a lot of chips and if you show a willingness to risk it all your opponents might not 3bet you anymore unless they want action or are willing to take risk themselves. Either way, that is an informational advantage and you gain fear equity that allows you to increase your rate of stealing. So I have seen players fold 30 hands in a row that then start raising every hand and then when they get 3bet they 4bet shove with 26off and they may even do it again. Sure, it's probably an unprofitable play but if you induce enough weak/tight play and a little bit wider range willing to risk it all (you'll get paid off when you have the absolute nuts) it's worth the cost of one hand, particularly if you can get such a big stack that risk no longer is a concern and you can play a pretty much max EV strategy until your stack reduces in size or others catch up.
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