Forum Replies Created
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13 hands of data is not significant — yet, not useless.
With a 3bet of 29%, this means that this villain has 3bet 3-4 of the last 13 hands.
His mindset is more likely “gamble gamble” and not “patient assassin”.
Action
— utg opens 2 bb
— button 3bets to 5.22 bb
— villain calls
Ranges
The villain min-raised from early position and then called the small 3-bet oop to get heads-up. Since, he didn’t 4-bet, I think we can assume he doesn’t have a top tier hand. Thus, I would start with this generic range
— pocket pairs = 22, 33, 44, 55, 66, 77, 88
— aces = A2, A3, A4, A5, A6, A7, A8, A9, AT
— others = KQ, KJ, KT, K9, QJ, QT, Q9, JT, J9, T9, 98, 87, 76, 65
The hero 3-bet mis-clicked and then forgot his cards (happens to the best of us). This range might be a bit loose for some and bit tight for others. It’s just a guess.
— pocket pairs = 99, TT, JJ, QQ, KK, AA
— aces = AJ, AQ, AK
— others = KQ
Intentions
Given the action, I assume that the villain will check most flops to the hero. I also assume that the hero will c-bet the majority of flops. With a pot size of (5.22 bb + 5.22 bb + 1 bb + 0.5 bb ~~~ 12 bb). The hero could c-bet a few different sizes: 3 bb, 6 bb, or 9 bb. All of these bet sizes have pros and cons.
On the flop 3h5s7s,
The villains pf calling range could have hit this board.
— sets = 33, 55, 77 — (3 combos each)
— two pair = 75, 73, 53 — (9 combos each)
— straight = 64 — (16 combos)
— one pair = 88, 66, 44, 22 — (6 combos each)
— gut-shots = 98, 76, 65 — (16, 12, 12 combos)
— flush draws = these are possible for both ranges
The hero should c-bet this board.There is a small chance that villain hit a set, two pair, or a straight on this flop.
If you have AA, you can more safely check the turn because there are favorable turn cards and very few bad outs that can get you in more trouble. Checking is more dangerous for a hand like AK because you’re allowing a lot of combos to hit a free card. My play is to c-bet 6 bb on this flop with the majority of my hands.
Turn Play
The board 3h5s7s2s and the villain leads full pot into you. The 2s makes the board draw heavy. Any As, Ks, Qs will want to see the river. Also, A4 has a wheel. The full pot bet size offers 2:1 odds which means you break-even with a 33% win rate. With implied odds and the right hand, you could consider playing this one by either calling or raising.
If you have AA with As, you have an over-pair and nut flush draw. Would you jam over the 12 bb bet with this hand?
If you have AK with As, you have two overs and the nut flush draw. Should you call with this hand?
If you have AKss, you have hit the nut flush. Should you raise or call with this hand?
You actually re-raise to ~52 bb and villain calls.
What the heck 😡
At this point, I’m going to assume that the villain is a fish. Given this, I would bet big on the river with my strongest range and check the river (expecting to get called when I bet river) with my weakest range.
River Play
The pot is ~116 bb and the board reads 3h5s7s2s8h
The villain checks.
The hero should bet with flushes, sets, and any As hands as a bluff.
I can’t find any weak hands in the hero’s range that hero should check on the river. I would probably bet 99 on the river. If called, I assume the villain has a weird two pair more often than a set or straight. They might also have a weird one pair + draw type hand like (54 or 76).
Spoiler
I followed your rules and didn’t read ahead.
The opponents line is pretty strong.
— flop — check, check
— turn — they donk bet pot, you 3-bet, they call
— river — they check, you bet big, they put you all in
Ace high is never good on this board but there is merit to bluff with it. The pot is huge. He checked river because he knows that you won’t check behind with nothing. When you bet, the villain should know that you’re bluffing some of the time because you have no showdown value. Assuming you bluffed with AK or AQ with As….bluffing should get some hands to fold, especially at this stack depth. Just not sure it’s wise against the gamble gamble type. My preference is to pull this move on the patient assassin.
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In the villains spot with 22 – 66, I think he might 3-bet with hopes of getting heads-up and finding out where he/she is at. By calling the 2.5 bb with a small pocket pair, you’re looking to flop a set or usually fold and you’re giving others a chance to raise you out. At a final table, my move is to 3-bet these small pocket pairs or fold them. I think a lot of players call with their small pairs here, I would do otherwise in this spot.
If you assume:
AQ vs. (AA-99; AQo, ATs, KQs)
combos
big pocket pairs — AA, KK, QQ = 12 combos
small pocket pairs — JJ, TT, 99 = 18 combos
better aces (AK) — 12 combos
chop aces (AQ) — 6 combos
suited aces (AJs, ATs) — 12 combos * 2
suited king (KQs) — 3 combos — (since you have AQo, you block one)
You’re losing to 42 / 75 = 56% of the combos
You’re beating 27 / 75 = 36% of the combos
You will chop 6 / 75 = 8% of the combos
hand equity and EV
foldEV = (1 – %c)(6.5 bb)
— AQ vs. AA = 12% — callEV = (%c)[(12%)(18 bb) – (88%)(14 bb)] = (-10.16c)
— AQ vs. KK = 32% — callEV = (%c)[(32%)(18 bb) – (68%)(14 bb)] = (-3.76c)
— AQ vs. QQ = 33% — callEV = (%c)[(33%)(18 bb) – (67%)(14 bb)] = (-3.44c)
— AQ vs. JJ = 46% — callEV = (%c)[(46%)(18 bb) – (54%)(14 bb)] = (-0.72c)
— AQ vs. TT = 46% — callEV = (%c)[(46%)(18 bb) – (54%)(14 bb)] = (-0.72c)
— AQ vs. AK = 27% — callEV = (%c)[(27%)(18 bb) – (73%)(14 bb)] = (-5.36c)
— AQ vs. AJ = 68% — callEV = (%c)[(68%)(18 bb) – (32%)(14 bb)] = (+7.76c)
— AQ vs. AT = 68% — callEV = (%c)[(68%)(18 bb) – (32%)(14 bb)] = (+7.76c)
— AQ vs. KQ = 68% — callEV = (%c)[(68%)(18 bb) – (32%)(14 bb)] = (+7.76c)
-0.88c
Your AQ has an overall -0.88 weight on your Call EV against this range.
Thus,
When they always call (c=1)
foldEV = (0%)(6.5 bb) = 0
callEV = (100%)(-0.88) =
When they call 75% of the time
foldEV = (25%)(6.5 bb) = 1.625 bb
callEV = (75%)(-0.88) = -0.66 bb
When they call 50% of the time
foldEV = (50%)(6.5 bb) = 3.25 bb
callEV = (50%)(-0.88) = -0.44 bb
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This seems like a shove to me but it’s also very close.
1) By shoving, you will win (0.5+1.0+2.5+2.5) = 6.5 bb if both opponents fold. A stack increase of close to 50%.
2) You would be offering direct pot odds of (20.5 / 11.5) = (1.8 to 1) because your opponent needs to call (14 bb – 2.5 bb) = 11.5 bb to win (6.5 bb + 14 bb) = 20.5 bb. To break-even, the opponent would need to win about 35.7% = (1 / 2.8).
3) Find the %call and %fold when you shove.
Assume that the utg opener folds if you shove.
Assume the accidental limper wanted to 3-bet with:
——– has a monster (AA, KK, QQ) — (3 + 6 + 3 = 12 combos)
——– has a smaller pair (JJ – 22) — (6 * 10 = 60 combos)
——– has a stronger ace (AK) — (12 combos)
——– has a weaker ace (AJ, AT) — (12 * 2 = 24 combos)
——– has speculative hands (KJ, JT, T9) — (16 * 3 = 48 combos)
Identify which of these hands will call a shove.
My best guess is something like:
——– AA, KK, QQ, JJ, TT, 99, AK, AJ, KJ
——– (3 + 6 + 3 + 6 + 6 + 6 + 12 + 12 + 16) = 70 combos
This means that the opponent will 3 bet with (12 + 60 + 12 + 24 + 48) = 154 combos and will only call with 70 combos.
The %call is 45% (70 / 154) and the %fold is 55% when you shove.
Calculate the hand equity
— AQ vs. AA = 12%
— AQ vs. KK = 32%
— AQ vs. QQ = 33%
— AQ vs. JJ = 46%
— AQ vs. 22 = 49%
— AQ vs. AK = 27%
— AQ vs. AJ = 68%
— AQ vs. KJ = 60%
— AQ vs. JT = 61%
4) Find the Expected Value
foldEV = (%fold)(amount win by shoving)
foldEV = (54%)(0.5 + 1.0 + 2.5 + 2.5) = (0.54)(6.5 bb) = 3.51
callEV = (%call)[(%win)(amount win) – (%lose)(amount lose)]
callEV vs AA = (45%)[(12%)(6.5 bb + 11.5 bb) – (88%)(14 bb)] = -4.57
callEV vs KK = (45%)[(32%)(18 bb) – (68%)(14 bb)] = -1.69
callEV vs QQ = (45%)[(33%)(18 bb) – (67%)(14 bb)] = -1.55
callEV vs JJ = (45%)[(46%)(18 bb) – (54%)(14 bb)] = 0.324
callEV vs TT = (45%)[(46%)(18 bb) – (54%)(14 bb)] = 0.324
callEV vs 99 = (45%)[(46%)(18 bb) – (54%)(14 bb)] = 0.324
callEV vs AK = (45%)[(27%)(18 bb) – (73%)(14 bb)] = -2.41
callEV vs AJ = (45%)[(68%)(18 bb) – (32%)(14 bb)] = 3.49
callEV vs KJ = (45%)[(60%)(18 bb) – (40%)(14 bb)] = 2.34
foldEV = 3.51
positiveEV = 2.34 + 3.49 + 0.324 * 3 = 6.802
negativeEV = -4.57 – 1.69 – 1.55 – 2.41 = -10.22
totalEV = (3.51 + 6.80 – 10.22) = 0.092 bb
Based on my assumptions and calculations, this seems like a marginal shove.
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I wrote a python script to get some quick results.
Here my pushing EV against the opener with two variables:
— size of the opener range (chance)
— hero’s equity vs that range (win)
Each calculation assumes a 2.5bb open and a 3-bet to 10bb.
For those of you stomping your feet about my 3-bet size, I’ll include data for a 7bb and 8bb….so take a chill pill. I was trying to keep things simple 🙂
In general, I found that the best EV spots for the hero occur:
— as %win increases (more EV when the hero expects to win more often)
— as %chance increases (more EV when the opener has a wider range)
_________
open 2.5bb, 3-bet to 10bb
vs. opener Win = 10 Chance = 20 EV = 43.0
vs. opener Win = 20 Chance = 20 EV = 86.0
vs. opener Win = 30 Chance = 20 EV = 129.0
vs. opener Win = 40 Chance = 20 EV = 172.0
vs. opener Win = 10 Chance = 40 EV = 86.0
vs. opener Win = 20 Chance = 40 EV = 172.0
vs. opener Win = 30 Chance = 40 EV = 258.0
vs. opener Win = 40 Chance = 40 EV = 344.0
vs. opener Win = 10 Chance = 60 EV = 129.0
vs. opener Win = 20 Chance = 60 EV = 258.0
vs. opener Win = 30 Chance = 60 EV = 387.0
vs. opener Win = 40 Chance = 60 EV = 516.0
vs. opener Win = 10 Chance = 80 EV = 172.0
vs. opener Win = 20 Chance = 80 EV = 344.0
vs. opener Win = 30 Chance = 80 EV = 516.0
vs. opener Win = 40 Chance = 80 EV = 688.0
How do you use this?
Take your opponents range and structure it as strong and weak. If you look at combos, you can make better estimates of %chance but here, I’ll say 80% of their range is strong and 20% is weak.
After you build these two ranges, calculate your equity.
Imagine having pocket 55 — @FiveByFive
You are deciding whether to push or fold over the top of an open.
— 80% of the time, they have an over-pair and you have a 20% chance to win
— 20% of the time, they have two overs and you have a 40% chance to win
vs. opener Win = 20 Chance = 80 EV = 344.0
vs. opener Win = 40 Chance = 20 EV = 172.0
The EV of this spot is 344 + 172 = 516
I hope you’re looking at my answer and wondering “what the heck”, that should be losing proposition. You would be correct!!!
This answer needs to be compared to the original stack size (before acting) to make sense out of it. In these calculations, I assumed that the 1 bb=100, open size was 2.5 bb = 250, and the 3-bet size was 10 bb = 1000.
This means that pushing pocket 5’s in this scenario is a negative EV play because you’re investing 1000 and returning only 516. This is a net loss of 484.
As promised
_________
open 2.5bb, 3-bet to 7bb
vs. opener Win = 10 Chance = 20 EV = 31.0
vs. opener Win = 20 Chance = 20 EV = 62.0
vs. opener Win = 30 Chance = 20 EV = 93.0
vs. opener Win = 40 Chance = 20 EV = 124.0
vs. opener Win = 10 Chance = 40 EV = 62.0
vs. opener Win = 20 Chance = 40 EV = 124.0
vs. opener Win = 30 Chance = 40 EV = 186.0
vs. opener Win = 40 Chance = 40 EV = 248.0
vs. opener Win = 10 Chance = 60 EV = 93.0
vs. opener Win = 20 Chance = 60 EV = 186.0
vs. opener Win = 30 Chance = 60 EV = 279.0
vs. opener Win = 40 Chance = 60 EV = 372.0
vs. opener Win = 10 Chance = 80 EV = 124.0
vs. opener Win = 20 Chance = 80 EV = 248.0
vs. opener Win = 30 Chance = 80 EV = 372.0
vs. opener Win = 40 Chance = 80 EV = 496.0
_________
open 2.5bb, 3-bet to 7bb
vs. opener Win = 10 Chance = 20 EV = 35.0
vs. opener Win = 20 Chance = 20 EV = 70.0
vs. opener Win = 30 Chance = 20 EV = 105.0
vs. opener Win = 40 Chance = 20 EV = 140.0
vs. opener Win = 10 Chance = 40 EV = 70.0
vs. opener Win = 20 Chance = 40 EV = 140.0
vs. opener Win = 30 Chance = 40 EV = 210.0
vs. opener Win = 40 Chance = 40 EV = 280.0
vs. opener Win = 10 Chance = 60 EV = 105.0
vs. opener Win = 20 Chance = 60 EV = 210.0
vs. opener Win = 30 Chance = 60 EV = 315.0
vs. opener Win = 40 Chance = 60 EV = 420.0
vs. opener Win = 10 Chance = 80 EV = 140.0
vs. opener Win = 20 Chance = 80 EV = 280.0
vs. opener Win = 30 Chance = 80 EV = 420.0
vs. opener Win = 40 Chance = 80 EV = 560.0
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https://bracket.rec.poker/?bracket=2022&id=630545061
Bracket ID = 630545061Round 1 Winners:
GopherBoyTJM (Taylor Maas)
BLUFFSTORINI (Jim Reid)
kekgeek65 (Jacob Kieke)
MonkieSystem (Keith Brandt)
Obner (Jack Burke)
Combinkley (Eric Gin)
dealer412 (Andrew Feist)
PokerGeekMN (John Somsky)Round 2 Winners:
GopherBoyTJM (Taylor Maas)
kekgeek65 (Jacob Kieke)
Obner (Jack Burke)
PokerGeekMN (John Somsky)Round 3 Winners:
GopherBoyTJM (Taylor Maas)
Obner (Jack Burke)Round 4 Winners:
Obner (Jack Burke)Tournament Champion:
Obner (Jack Burke) -
Call > Raise > Fold
This is an excellent thread.
+1 to misclick for doing the research
+1 to taylor for posting a great spot
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Takeaways
— actively take notes on interesting spots (i.e. donk bet dangerous turn cards)
— review hands and think about how you would play them differently in that spot
— leave yourself reminders (unanswered questions, current strategy)
— working in groups offers differing viewpoints and outside of “your” box thinking
— set learning goals for yourself
Cool Article @MonkieSystem
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Questions
1) Will hitting 2 pair win at showdown?
2) Will hitting 3 of a kind win at showdown?
Assumptions:
The pot is 100 chips.
There are 2 cards to come (turn + river)
The opponent is betting B chips.
You would be calling B to win (100 + B).
Calling EV = (%call)[(%win)(amount win) – (%lose)(amount lose)]
To profit from calling, your CallEV >= 0
To do the math, I’m going to do it from the villains perspective to find out the minimum bet size to have callEV > 0. This should be equivalent to what you want.
Case 1 — only gutshot outs
4 outs
CallEV = 0 = C * (W * (P + B) – L * (B))
%call
You’re assuming that you will call the bet every time, thus C = 1 or 100%.
%win
To win, you need to hit 4 outs of 47 cards and then assume that you don’t improve by hitting 43 non-outs on the 46 remaining river cards. This looks like, (4/47)*(43/46) = 8%….to hit 4 outs on turn or river.
0 = (8%)(100+B) – (92%)(B)
0 = B(8% – 92%) + (8%)(100)
B(84%) = (8%)(100)
B = 10 chips.
If the opponent bets less than 10 chips, it’s a profitable call with your gut-shot.
Case 2 — gutshot + 2 pair + trip outs
9 outs
CallEV = 0 = C * (W * (P + B) – L * (B))
%win
To win, you need to hit 9 outs of 47 cards and then assume that you don’t improve by hitting 38 non-outs on the 46 remaining river cards. This looks like, (9/47)*(38/46) = 16%.
0 = (16%)(100+B) – (84%)(B)
0 = B(16% – 84%) + (16%)(100)
B(68%) = (16%)(100)
B = 24 chips.
If the opponent bets less than 24 chips, it’s a profitable call with your gut-shot.
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Hand 1
sets or quads — 33, 55, 99, TT, QQ — 13 combos
straights — KJ, J8 — 32 combos
two pair — 95, 93, 9Q, 53, 5Q, 3Q, T9, T5, T3, QT — 78 combos
pocket pairs — AA, KK, JJ, 88, 77, 66, 44, 22 — 6 combos each — 48 combos
top pair — AQ, KQ, QJ, Q8, Q7, Q6, Q4, Q2 — 12 combos each — 144 combos
worse kicker — KT, JT, T8, T7, T6, T4, T2 — 8 combos each — 56 combos
missed draws — AK, AJ, A8, K8, J7, 87, 76, 86, 64, 42 — 16 combos each — 160 combos
Some of these hands should be removed or weighted because of our opponents action. Our opponent limped from SB, called a raise PF, checked 953 flop, bet T turn, and bet Q river.
— I would argue that they rarely call PF out of position with Q3 or Q5, bet turn, and then get lucky on the river. This logic applies to other hands.
— I would argue that smaller pairs like 88 or 77 would never bet the turn with 3 over-cards on the board, out of position, and into the PF aggressor.
Before removing any of those hands, here is an estimate of where I’m at.
I can beat 246 combos
— 160 missed draws
— 56 worse kickers
— 30 smaller pocket pairs
I lose to 285 combos
— 13 sets or quads
— 32 straights
— 78 two pairs
— 18 larger pocket pairs (JJ, KK, AA)
— 144 top pair
I estimate to win 246 / 531 or 46.3%
___________________________________________
If I revise the list and remove specific holdings, we can make a better guess.
sets or quads — 33, 55 — 6 combos
(small sets are more likely than large sets, remove QQ, TT, and 99)
straights — KJ, J8 — 32 combos
(both of these hands are possible, the turn is favorable for both)
two pair — 95, 93, 9Q, 53, T9, T5, T3, QT — 60 combos
(flopped two-pairs are more likely than rivered two-pairs, remove Q3, Q5)
pocket pairs — — 0 combos
(the smallest pocket pairs 22, 44, 66, 77, 88 wouldn’t bet turn and river)
(I doubt my opponent will slow play a large pocket pair, remove AA, KK, JJ)
top pair — QJ, Q8 — 24 combos
(betting the turn with a Q implies a draw, remove Q2, Q4, Q6, Q7)
(strong Q’s are less likely to limp PF, remove AQ, KQ)
worse kicker — KT, JT, T8 — 50% of 24 combos = 12 combos
(remove T7, T6, T4, T2 because calling with them PF out of position is silly)
(I’m not convinced that KT, JT, or T8 will fire again on river, maybe remove 50%)
missed draws — AK, AJ, A8, K8, J7, 87, 76, 86, 64, 42 — 48 combos
(some players will fold the 42, 64, 76, and 86 pre-flop, some will call, maybe 25%)
(most players will raise AK, AJ and A8 pre-flop from the small blind, maybe 67%)
(K8 and J7 are possible for betting turn and bluffing river)
After the revision,
I can beat
— 48 missed draws and 12 worse kickers = 60 combos
I lose to:
— 24 top pair, 60 two pair, 32 straights, and 6 sets or quads = 122 combos
Thus, I win 60 / 182 or 33% of the time.
Amazing what revision and filtering can do 🙂
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Flopping a flush w/ AKss
— there are 13 cards of each suit (c, d, h, s). When you have a suited starting hand, there are 11 left and 3 of them need to hit the flop and avoiding the 39 non flush cards. Thus, (11/50)(10/49)(9/48) = 990 / 117600 = 0.00841 or 0.84%.
Flopping a flush draw w/ AKss
— on this flop, you have 11 spades and 2 of them have to be on the flop along w/ 1 of the 39 non flush cards. Thus (11/50)(10/49)(39/48) = 0.0364 or 3.64%. However, you need to think of all the different ways of sorting a unique 2-tone flop. The ways are (abc, acb, bac, bca, cab, cba) which is 6 however you need to make another adjustment. Assume that (a = b) because they are the same suit and c is the non-flush card. If you look at it this way, (aac, aca, aac, aca, caa, caa), you can see that we have replicates making only 3 unique ways of repping the 2-tone flop.
Thus, 3.64% * 3 = 10.9%
Hitting the backdoor flush w/ AKss
— this implies the flop is a rainbow and we will see all five cards
— the flop should have 1 of the 11 spades, and 2 of the 39 non-flush cards (c,d,h).
— the turn should be 1 of the remaining 10 spades
— the river should be 1 of the remaining 9 spades
— thus, the calculation is (11/50)(39/49)(38/48)(10/47)(9/46) = 0.00577 however lets think of how many ways to express the board with a rainbow flop and the backdoor hitting. Think of it as (abcaa, acbaa, bacaa, bcaaa, cabaa, cbaaa) which is 6 ways, thus (0.00577 * 6) = 0.0346 or 3.46%.
Doing similar math post-flop
— if you look at the math post-flop with the turn and river to be dealt, then (10/47)(9/46) = 4.16% is the chance that the turn and river will be the same suit.
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@SteveFredlund
In my examples above,
my goal was to bet full pot on the river or as close to it as possible.
In my example, bet 1/3, 2/3, full pot.
PF = 4.5 bb
F = bet 1.5 bb, pot is (4.5 + 3 = 7.5 bb)
T = bet 5 bb, pot is (4.5 + 3 + 10 = 17.5 bb)
R = we want to bet 17.5 bb
For you, the effective stack is 40 bb and you want to get it in.
My instinct was to try 2/3rd pot with a big stack.
PF = 6 bb
F = bet 2/3rd or 4 bb (6 + 4 + 4 = 14 bb)
T = bet 2/3rd or 9 bb (14 + 9 + 9 = 32 bb)
R = we want to bet 32 bb or full pot. We have invested 4 + 9 = 13 bb. We have 27 bb on the river. The goal was to bet 32 bb. 27 bb is 5 bb short of 32 bb but I still think betting 27 bb into 32 bb (%p = 85%) on the river looks good.
If you bet 1/2
PF = 6 bb
F = bet 1/2 or 3 bb (6 + 3 + 3 = 12 bb)
T = bet 1/2 or 6 bb (12 + 6 + 6 = 24 bb)
R = we want to bet 24 bb on the river. We have invested 9 bb. We have 31 bb remaining on the river. Betting all in on the river would be an over-bet of 7 bb.
For this case I think betting larger on the turn makes it easier to bet all-in without over-betting river. If you bet 2/3 on turn, then you would bet 8 bb with 29 remaining and making the pot size (12 + 8 + 8 = 28 bb). Betting 2/3rd on turn makes this a better river shove by (+1 bb).
Thus I think bet 1/2, 2/3, full pot with 40 bb is a great line to remember for 3 streets.
____________________________________________________________________________________
For your question
We want E3=%p*P3 right?
— in english, I think this means
E3 = river stack size
%p = size of the bet on flop and turn (assuming this is constant like 50% bet)
P3 = size of the pot on the river.
I would say that
PF = 6 bb
F = %p * 2 * PF + PF
T = %p * 2 * PF + F
R = we want our stack on the river (P3) to be equal to (PF + F + T).
R = 2 * (%p * 2 * PF) + PF
R = 4 * (%p) * PF + PF
In your case, you would would need (4) * (1/2) * (6 bb) + 6 bb = 18 bb on the river.
In your terminology: P3 = R and E3 = 18 bb on the river.
You would need to start the hand with:
18 + PF + 1/2PF + 1/2(1/2PF + PF) = 18 + 2.25PF = 18 + 13.5 = 21.5 bb.
You can check if E3 = 18 bb when %p = 1/2:
18 bb = 4 * (%p) * 6 bb + 6 bb
12 bb = 24 * %p
%p = 12 / 24 = 1/2 — which makes sense 🙂
____________________________________
This function is linear if p is constant on both streets.
If you were to change it up and bet 1/2 flop, 2/3 turn, then the function shifts.
I would assume it shifts somewhere closer to the average of the two bets
PF + F + T = PF + 1/2PF + PF + 2/3*(5/2PF) = 2.67PF on the river.
As shown, 2.67 * 6 = 16 bb.
If you try 1/2, full, full,
= PF + F + T
= PF + (1/2 * PF + PF) + (1 * 2.5 * PF)
= 4PF or 24 bb w/ investment of (3 + 12 = 15 bb) — you need (24 + 15 = 39 bb)
If you try full, 1/2, full,
= PF + F + T
= PF + (1 * PF + PF) + (0.5 * 2.5 * PF)
= 4.125PF or 24.75 bb w/ investment of (6 + 12 = 18 bb) <b style=”font-family: inherit; font-size: inherit;”>– you need (24.75 + 18 = 42.75 bb).
The order of how you bet matters. By betting large early, you need a larger effective stack and I would say you risked unnecessary (~4 bb) with this two similar permutations.
I don’t know Steve, I tried.
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or play against PokerSnowie
An online training site based on artificial intelligence.
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As a teacher, my approach would depend on the student.
“playing the player, not the cards”
— will your friend be interested in learning the statistical and mathematics of poker or would they prefer learning about common scenarios and strategies?
— do they want to read books, watch videos, or learn by doing?
If they prefer to learn by doing, the RecPoker Nightly is a great starting point for any player trying to learn the basics. It’s free. It’s fun. It’s about community. Lastly, it has cool people like @Jim @SteveFredlund and many others.
My approach when I started playing (18 — poker boom) was to read books. There are some very good cash game books. I think Dan Harrington is one of the best at explaining difficult topics in an easy way. Another great author Ed Miller. His book on small stakes is next to my toilet. Lastly, I’m a numbers guy but The Psychology of Poker helped me think differently.
– Harrington on Cash Games (Dan Harrington)
– Small Stakes No Limit Hold’em (Ed Miller)
– The Psychology of Poker (Alan Schoonmaker)
For tournaments, there are some excellent packages that can teach strategy on several stages. Some really good poker players to watch are Jon Van Fleet (Apestyles) & Ryan Laplante (Protential). They think at a high level but explain things in an easy way.
If he is willing to study on his own, start with
— hand equity
— statistics & probability
— bet sizing
— stack depth
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Fold EV = (%F)(Pot) = (1-%C)(Pot)
Call EV = (%C)[(%W)(Pot + Bet) – (1-%W)(Bet)]
Total EV = Fold EV + Call EV
Scenario 1
— When you have no chance to win and you estimate the opponent should fold 50% of the time when you bet.
According to the graph,
— The x-intercept for this graph is 100 when W=0% and C=50%. This represents the maximum amount that I should bet to make it a +EV spot. If I bet larger, I’m risking too much. When I bet smaller, my call EV is being minimized, thus I’m risking less to possibly get my opponent to fold.
Fold EV = (fold50% * 100) = 50
Call EV = (call50% * (-B)) = -B/2
Total EV = 50 – B/2
— The slope of the Total EV plot is (-1/2) and the y-intercept is 50. The y-intercept represents the “best we can do” in-terms of total EV when we win less than 50% of the time. In this case, the y-intercept is equal to our fold EV since we have negative call EV with 0% chance to win.
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With 18 bb starting,
When you jam all-in,
foldEV = (% opponent when you jam) * (amount win when fold)
foldEV = (maybe 80%) * (your 1 bb + opponent raised to 3.1 bb)
foldEV = (80%)(4.1 bb)
foldEV = 3.28 bb
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callEV = (% opponent calls jam) * [(% hero wins) * (amount win when call) – % hero loses)*(amount hero is risking)]
callEV = (%OppCall)*[(%HeroWin)(amount win) – (%HeroLose)(amount lose)
callEV = (20%) * [(maybe 50% to win)(18 bb * 2) – (50% to lose)(18 bb – 3.1 bb)
callEV = (20%) * [(50%)(36bb ) – (50%)(15 bb)]
callEV = (20%)*[18 – 7.5]
callEV = (20%) * 11.5
callEV = 2.3 bb
Obv, change the variables if you wish,
Jamming is worth 3.28 + 2.30 = 5.58 bb when:
— opponent calls 20%
— hero wins 50%
Compare this to when you call the opponents raise,
= (%win)(amount win) – (%lose)(amount lose)
= (50%)(3.1 bb * 2) – (50%)*(3.1 bb – 1 bb)
= (50%)(6.2 bb) – (50%)(2.1 bb)
= 3.1 bb – 1.05 bb
= 2.9 bb
Jamming is better than calling.
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Hand 1
— agree that raising to 3.5 PF is good
— for the c-bet, I do that a large % of the time when I’ve raised PF. Plan A was to take it down pre-flop. To be honest, my decision to check the flop was mostly PLAYER dependent and STACK dependent. This particular player scared me, why? He acted like a wildcard. He was comfortable, feeling good, and showed confidence. I watched him win big pots and both times, he was aggressive post-flop. In my mind, c-betting the flop with Ace high isn’t good against this type of player. If I c-bet, my range is pocket pairs and big cards, most of which missed this flop. Rob mentions that my opponent might be stabbing turn because he thinks I have AK based on my action. Totally Agree.
— @TaylorMaas mentions that Canterbury players are full of shit when you check the flop and attack weakness. Oh boy is that True!
— Yes, AT is likely ahead of the range my opponent has but I honestly expect my opponent to check-raise if he caught a piece, then I have to fold.
— I like @petvet about raising gets weaker T’s to call me.
— By calling the turn bet, I indeed was trapping and thought I had the best hand. With my stack size (~22 bb) after calling, I decided to give him rope and see how he plays river. If I were to raise, I would be risking some portion of my 22 bb by raising over a 4 bb bet. I could raise to 10 bb, 12 bb, or more but I would be committed in all cases. Weird stack size. As Chris mentions, there are some bad rivers (J, Q, K) for 12 bad outs…one of them actually hits. When it hit, I had to think of some Qx hands that would make sense to call PF and bet turn. On the 953TQ board, I couldn’t think of many besides QJ, QT, Q9, and Q8.
— @Jim the villain bet 8 bb on the river.
I called, the villain showed a weaker T4.
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This is a revision.
https://www.geogebra.org/classic/rnvq9ctf
It shows the Fold EV, Call EV, Total EV and the numbers being calculated.
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With 16 bb,
I’m trying to avoid the players who:
— are unpredictable
— apply post-flop pressure
— defend the blinds a lot
— float the flop a lot
— are not afraid to get involved
It’s easier to hunt the injured antelope than a healthy one.
I would say that your line looks pretty strong.
When he faces your shove, you could probably have these hands:
— top of range –> (AA, KK, QQ, JJ, AT, KT, QT, JT)
— drawing hands –> (AKdd, 98dd, A3dd)
The opponents JT plays very poorly against this range of hand combos that you’re representing. I’m not surprised that he thought about it. In his mind, you should be folding to his 40k bet on the turn A LOT of the time. Instead, you shoved and surprised him. The board looks pretty dry so I think most players sigh call w/ top pair hands like JT or T9 but I bet that he thought he was behind when calling off ~10% of his stack.