Quote:
Originally Posted by notR0ld4this
Note on flop P6 bets 55 into 180. He lays himself 3.27:1 on his bet...meaning if the bet wins the pot immediately 23.4% of the time or more he can bet two napkins profitably.
To keep P6 from betting napkins profitably the field must defend this flop bet at least 76.6% of the time between the 3 of us.
You should divide this unequally since P8 (me) has the strongest range, P1 next, and P2 has the weakest range....but lets keep it simple and say P8, P1 and P2 each need to defend at least 25.53% of the time to do their fair share.
Lets look at those ranges again, and keep P6 cbet frequency at 100%.
(keep in mind we've already shown that every player COULD call 100% of range on flop profitably)
P8: Starting range: 260 combos. Minimum continuing obligation 67 combos
Sets=6
Top pair=45
nut flush draw=9
other flush draws=7
AsQx=3
70 combos
Equity vs other players range right now: 50.75%
I'm going to NOT widen my range here to what it could be given pot odds, to account for players behind me/worst relative position.
P1: Starting range: 328 combos. Minimum continuing obligation 84 combos
Sets=6
Top pair=54
nut flush draw=10
other flush draws=16
86 combos
Equity vs other players range right now: 36.54% (P8 becomes 39.27%)
WAIT: P1 only needs 15.9% equity vs the field's current ranges to call profitably. So he can add some hands (again P8 could have too but didn't due to position)
Lets add all backdoor flush draws
All gutshots
All open ended straight draws
All paired hands: He now has 141 combos and 21.6% equity.
P2: Starting range: 450 combos. Minimum continuing obligation 115 combos
Sets=6
top pair=80
nut flush draw=10
other flush draw=17
AsQx=3
116 combos
Equity vs other players range right now=26.62%
But wait. P2 only needs 13.7% equity, so he can add some hands (and does)..
All his bd flush draws,
All gutshots,
All pairs 6+
All ATo+ with As,
He now has 181 combos and 21.76% equity
Equities after flop betting complete:
P6: 13.66%
P8: 40.48%
P1: 24.10%
P2: 21.76%
Turn=Q
tbc...
New Equities
P6: 14.80%
P8: 39.86%
P1: 23.53%
P2: 21.80%
Pot: 400
P2 checks. At this point he's overcalled pre flop given great odds then check/overcalled a very small bet on a semi wet flop oop, then checked again on a turn card that made the board even more wet. With the best relative position to the betting leader he can still be checking some fairly strong hands, but it's becoming a lot less likely he has a very strong hand (his range is still widest of all players except P6 so he is already the least likely player to hold a monster). Lets take away half of his sets and half of his KQ combos, and A
K
assuming he would have led this turn with those some of the times. He has:
160 combos (14.2% of hands) with 20.73% equity
P6 checks. At this point he's minraised pre, cbet weakly on a semi-wet flop, and when called in 3 positions has checked on an even more wet turn. Those are subjective observations. Objectively at this point his range is unquestionably the weakest of the 4 players (because he has his entire pre flop range still in mainly) and has poor position. I think it is safe to say he usually does not have the strongest hands in his range when he checks here (probably check-folding).
Let's take some of the hands he will almost always continue betting on the turn away (sets, nut flush draws, AK with flush draw, KQ, Pair+nut flush draws...I'm leaving in AA, AK with no flush draw, T
J
and T
J
, 7
6
, 7
8
7
8
, as his strongest potential check-calling hands...they are hands that are not great to be bet-calling but have too much equity to be check-folding to "normal" action):
After checking turn I have him on 209 combos, 18.5% of hands. 10.22% equity
P8: I have the strongest range (66 combos) of all 4 players with over 42% equity. Hands still in my range I'd always want to value bet:
Sets: 6 combos
2 pair (KQ) 9 combos
AK: 9 combos
total is 24 combos.
We should generally have an approximately 1:1 valuebet: bluff range on turn so we need about 24 bluff combos too:
All of our spade flush draws= 16 combos.
AQo=2 combos (this is sort of a merge, but it's part of our bet/folding range)
2/3 of our 9 KTo hands=6 combos (again a merge, part of our bet/folding range)
This is easy. Bet the combos that don't have T
, When you hold T
you've taken away some of your opponents flush draw combos, making their
range stronger
So we betting 48/66 combos still in our range. It's notable that our entire checking range consists of top pair, with 6 of those combos also having a
draw to go with it....we are NEVER check folding to one bet)
Equity of betting range: 46.62% (P1's equity is 24.25% when we bet)
Equity of checking range: 38.44% (P1's equity is 28.41% when we check)
We bet 351 into 400 laying 2.14:1 odds. Villain(s) need 31.2% equity to call (assuming he could magically be assured he's only caller)
Also I'm laying myself 1.14:1 to win immediately. If my opponents fail to defend between them more than 53.27% of the time I could bet any 2 napkins profitably for this amount.
At this point P1 has 2nd strongest range AND is only player in position on me AND we've already seen the other two players show weakness this betting round. We therefore will assign him a weighed responsibility (instead of 1/3) of this defense responsibility. Of the approx 54% equity the remaining 3 have vs me P1 has 24.25% of it, so he holds 45.5% of their collective equity. 45.5% x 53.27% defense requirement=MINIMUM 24.23% of his range he needs to defend with with.
P1: Started turn with 133 combos. Needs to continue AT LEAST 33 combos.
Needs 31.2% equity to call me.
I'm going to assume at this point in the hand P1 raises his sets almost every time. We will assume he would raise 5 of his 6 combos. Similarly he'd probably raise his KQ 2 pair hands most times, so lets say he raises every KQ combo that doesn't contain diamonds or spades (because holding diamonds or spades reduces number of flush draw combos in my range..thus strengthening it). So he raises 4 of his 9 KQ combos on turn. If he is playing well with about a 1:1 value: bluff ration on turn he will need at least 9 bluffs in his raising range as well...we will come back to that.
If he can somehow assume the other 2 players will fold he needs 31.2% to call. His remaining range has 33.64% so he can continue by calling with his ENTIRE range. (not to say this is optimal...especially since 31.2% requires other 2 players to fold. Since this player in reality ended up on the river with 23o, which shouldn't be in his range to start with, we will assume he will always keep his entire range when it can be supported by the math)
Note that if player raised all sets and all KQ combos he could still continue entire range with 31.79% equity. He'd now need to convert 15 of those combos to bluffs vs 9combos. We will proceed assuming he flats 6 of his monster combos.
He needs to bluff with 9 of those combos to balance is value bets. If he accurately gages our betting range he should do this with the hands which have worst equity vs AQ and KT and weak flush draws (the portions of our range that are most likely to be bet-folding). Obviously these hands should also be selected from among the bottom of his range
Let's start with 8
7
, 8
7
, 3
2
3
2
and add the 6 AJ and AT combos which have the A
taking away P8's NFD combos. That's 10 bluff combos.
So P1 is raising all but one of his sets, all KQ that do not have
, naked low gut shots, and Broadway gut shots with A
blocker.
He is calling everything else in his range (never folding)
His calling range is 114 combos and has 35.22% equity vs P8 (after P2 and P6 fold, which they do)
River is 2
Pot 1102
New equities
P8: 68.37%
P1: 31.63%
P8: Hands I definitely want to value bet every time:
sets: 6
KQ: 9
AK: 9
We should have approx 2:1 value:bluff ratio on river so we need about 12 bluffs
Incidentally we have exactly 12 naked
draws on river. If you do an equity heat map of our 48 combos it turns out that these 12 combos are conveniently the lowest equity combos vs our opponents remaining range...so there is no question they are the absolute best candidates for bluffs.
So P8 bets 36 combos and that betting range has 70.27% equity vs villains range
Bet is 701 into 1102 laying myself 1.57:1 to win pot immediately. If villain fails to defend 61% of the time or more I could bet any 2 napkins at this price and profit.
I lay villain 1803: 701 or 2.57:1 so he needs 28% equity to call.
P1: Must continue with at least 61% of his remaining 114 combos or 70 combos, and the portion he does so by calling needs 28% equity vs my betting range.
Hands he will want to raise every time:
KQ =5 (the 5 combos which he didn't raise on the turn)
sets =1 (the 1 combo which he didn't raise on the turn)
Villain should want a 2:1 value:bluff ratio on river so needs 3 bluffs to go with this. He can do one of two things here:
polarize: pick 3 combos that have hopeless equity vs my range (a lot of my bluffs are nut flush draws)
merge: pick 3 combos that do ok vs the bluff portion of my range that could maybe call.
Let's come back to that.
P1 is raising 9 combos so needs at least 61 more to fill out his 70. Those 61 need 28% equity.
Lets look at the strongest hands that he could call with:
AKo: 9combos
KJ: 12
KT: 12
K9: 3
K8: 3
K7: 3
AQ: 3
QJ: 1
QT: 1
Q9:1
6A:1
69: 3
68: 3
65: 3
65: 3
61 combos so far
4A: 1
45: 3
43: 3
2A: 2
23: 2
Total 1 pair hands villain could call with=72 hands.
Let's assume for a second villain merges. He would raise bottom 3 1 pair hands:
2
3
, 2
3
, and either A
2
or A
2
(ill assume diamonds because A
in his hand would severely strengthen my range by taking away 7 of my 12 flush draws in my river betting range)
His calling range is then at least 69 combos: at 37.08% (he can call wider until he gets down to 28% equity...but he didn't call so we can stop worrying about that
His raising range (the strongest i will face) is KQ (5 combos) 66 (one combo), 1 combo of A2 and 2 combos of 23.
So P1 bets 9 combos with 60.36% equity vs my range.
He bets 1402 into 1803 laying himself 1.28:1 to win the pot immediately. If I fail to defend at least 56.14% of the time he can do this with any 2 napkins and show a profit.
Further he lays me 3205:701, or 4.57:1 on the call. So I need 17.9% equity to call.
Back on P8: I need to continue with AT LEAST 21 combos and need at least 17.9% equity on the portion of those I call with.
Hands I will want to raise every time: KQo and all sets (remember he has 6 value combos and I am always beating/chopping at least 5 of them)
KQ: 9
sets: 6
We will need 7 bluffs to have a 2:1 value:bluff ratio Lets use our 7 weakest missed flush draws.
Our remaining combos are AKo, A
7
-A
J
This calling range has 23.04% equity vs his raising range.
If opponent had polarized instead, and taken 3 of the worst combos in his river range for his bluff raises, say 3 non-spade combos of his missed 57 straight draws, then our calling range has 38.21% equity vs his raising range.
Go one step further: A
7
, the weakest hand left in my range that could call on the river, has 33.34% equity if he's polarizing on the river.
So on the river, if he's merging we have zero equity. Call A7=-701
If he's polarizing we have 33.34% equity of 3906 pot=1302 for profit of +601
You have to be mighty confident (it'd have to be 46% likely he's merging or better) hes' merging to make usually calling A
7
"atrocious" here.
In my experience assuming a (non-superuser) player in a $22 MTT is merged 46% or more of the time in this spot would be giving way too much credit to the field. That should win the argument that calling his river minraise with A
7
is not only not "atrocious", but should actually be the default here.
That being said, the math also shows that arriving at the river with 2
3
or 2
3
is not unprofitable in P1s shoes (even if he did it by accident), and that IF he were to merge for the 3 bluff combos he needs to go with KQ and 66 in our scenario then those 2 combinations are part of the 3 most perfect ones he has to choose from.
Keep in mind this player did NOT arrive at river with one of those suited combos of 23, he got there with 23o. And he did so passively on every street until the river. This is NOT the mark of a player who would choose to merge the river (and choose the perfect combos to do it with).
If he's not a superuser he's terrible at poker. The average bad player will be polarized WAY more than they are merged on this river: Again A
7
is a good call.
Nothing I outlined here takes away from my belief that this player could possibly have been a superuser (if he had shown up with 23 of
or
in a vacuum of this one hand it would have made me consider I possibly got owned by a GTOish player....but even then it's the video and all of those hands that make me think he was likely a superuser. All this math was just to shut you up about the A
7
river call)