cjatud2012
¯\_(ツ)_/¯
Silver Level
I know the STT community here is kinda small, but this topic can be applied to parts of tournaments as well, so it’s still worth learning about.
Basically, we’ve all heard about ICM and how the cEV of our decisions isn’t equal to the $EV, which is what we really care about, since of course we don’t want to win chips in the long run, we want to win money. The real question though is how can we use this to our advantage? Well, there are times in a STT, especially on the bubble, where we can be really aggressive with a big stack or even a medium/short stack and force our opponents to make -$EV plays. It is important to recognize these opportunities, which are based on stack sizes, the blind level, position, player reads, etc. We’ll assume from this point forward we’re playing the bubble of a 9-man STT with t1500 starting stacks, and the current stacks will all be listed before posting any blinds. Also, if anyone catches any errors with my math, please let me know. Let’s go ahead and look at a couple of different spots.
First, let’s look at a situation that’s probably pretty intuitive.
Blinds: t200/t400.
UTG: t800
BTN: t1000
SB (Hero): t8500
BB: t3200
Here, there are short stacks UTG and on the BTN, and the big blind is sitting semi-comfortably at 8bb’s. If UTG and BTN fold to us on the SB, we should be pushing any two cards. The reason is that it would be a disaster for the BB to get knocked out with a short stack about to be pot committed on the next hand. He would have to risk an almost guaranteed spot in the money, and is therefore going to call a very small percentage of the time. How often? Let’s look at the math:
The current equities are--
UTG: 0.128
BTN: 0.157
SB (Hero): 0.416
BB: 0.300
Should the BB call and win, the equities would be--
UTG: 0.122
BTN: 0.151
SB (Hero): 0.352
BB: 0.375
We can find the percentage of time the BB has to win with the following equation:
0 = x*(0.075) + (1-x)*(-0.300)
x = 0.8
So the BB needs an 80% chance to win for the call to be profitable. If we are pushing any two cards, only a range of QQ+ is going to be able to call profitably. Any time he calls wider than that, he is making a -$EV play.
So that’s an easy one. What do we do, though, when we don’t have the biggest stack at the table?
Blinds: 300/600
UTG: t5500
BTN: t1400
SB (Hero): t3300
BB: t3300
In this situation, the BTN is very short with less than 3bb’s. The BB has a little more than 5bb’s left before posting. Due to the imminent doom waiting for the small stack, the BB is making a mistake by calling too wide. Let’s try to look at the $EV of the decision again:
Current equities--
UTG: 0.338
BTN: 0.136
SB (Hero): 0.263
BB: 0.263
If BB calls and wins--
UTG: 0.366
BTN: 0.248
SB (Hero): 0.000
BB: 0.386
0 = x*(0.386-0.263) + (1-x)*(-0.263)
x = 0.681
This means the BB can only call profitably with the top 10% of hands or so, assuming we push 100% of our hands.
This situation would be very different if you put the player with the big stack in the BB:
Blinds: 300/600
UTG: t3300
BTN: t1400
SB (Hero): t3300
BB: t5500
Current equities--
UTG: 0.263
BTN: 0.136
SB (Hero): 0.263
BB: 0.338
If BB calls and wins--
UTG: 0.322
BTN: 0.254
SB (Hero): 0.000
BB: 0.424
If BB calls and loses--
UTG: 0.272
BTN: 0.147
SB (Hero): 0.368
BB: 0.213
0 = x*(0.424-0.338) + (1-x)*(0.213-0.338)
x = 0.592
Now, pushing any two cards in the SB is very exploitable, as villain can profitably call with 33+, Ax, Kx, Q3s+, Q6o+, J6s+, J8o+, T7s+, T9o, 98s.
It may also be a mistake to shove on the short stack.
Blinds: 300/600
UTG: t3300
BTN: t5500
SB (Hero): t3300
BB: t1400
Just looking at it from a cEV perspective, the villain has to call 800 to win 2000, getting 2.5:1 pot odds, so he’s getting the right price to call with any two cards. In terms of $EV:
Current equities--
UTG: 0.263
BTN: 0.338
SB (Hero): 0.263
BB: 0.136
If the BB calls and wins--
UTG: 0.258
BTN: 0.1335
SB (Hero): 0.173
BB: 0.233
0 = x*(0.233-0.136) + (1-x)*(-0.136)
x = 0.584
Once again, shoving wide isn’t the greatest play for us.
So what do you need to know? Basically, the presence of a short stack in relation to the blinds will allow us to make some aggressive plays. If we have a big stack, we can pretty much abuse the table no matter what. If we have don’t have a big stack, then we want to target players that are short but not desperate, probably between 5-10bb’s. These players will want to play tight, especially in the presence of a player who is about to be eliminated. Being able to recognize the opportunities will help us take control of the bubble and make good decisions. I'm not sure not all the math is perfect-- I feel like I ignored the blinds in most decisions, not to mention the equity associated with folding-- but the point of the post was to get players thinking about situations, based on stack sizes, where it is profitable to be very aggressive. Besides, it's late here, I'm tired, and I'm only halfway done with packing for my travels tomorrow, . So if anyone can catch mistakes, feel free to correct me, and I encourage everyone to discuss similar situations or other things we should consider here in this thread.
Basically, we’ve all heard about ICM and how the cEV of our decisions isn’t equal to the $EV, which is what we really care about, since of course we don’t want to win chips in the long run, we want to win money. The real question though is how can we use this to our advantage? Well, there are times in a STT, especially on the bubble, where we can be really aggressive with a big stack or even a medium/short stack and force our opponents to make -$EV plays. It is important to recognize these opportunities, which are based on stack sizes, the blind level, position, player reads, etc. We’ll assume from this point forward we’re playing the bubble of a 9-man STT with t1500 starting stacks, and the current stacks will all be listed before posting any blinds. Also, if anyone catches any errors with my math, please let me know. Let’s go ahead and look at a couple of different spots.
First, let’s look at a situation that’s probably pretty intuitive.
Blinds: t200/t400.
UTG: t800
BTN: t1000
SB (Hero): t8500
BB: t3200
Here, there are short stacks UTG and on the BTN, and the big blind is sitting semi-comfortably at 8bb’s. If UTG and BTN fold to us on the SB, we should be pushing any two cards. The reason is that it would be a disaster for the BB to get knocked out with a short stack about to be pot committed on the next hand. He would have to risk an almost guaranteed spot in the money, and is therefore going to call a very small percentage of the time. How often? Let’s look at the math:
The current equities are--
UTG: 0.128
BTN: 0.157
SB (Hero): 0.416
BB: 0.300
Should the BB call and win, the equities would be--
UTG: 0.122
BTN: 0.151
SB (Hero): 0.352
BB: 0.375
We can find the percentage of time the BB has to win with the following equation:
0 = x*(0.075) + (1-x)*(-0.300)
x = 0.8
So the BB needs an 80% chance to win for the call to be profitable. If we are pushing any two cards, only a range of QQ+ is going to be able to call profitably. Any time he calls wider than that, he is making a -$EV play.
So that’s an easy one. What do we do, though, when we don’t have the biggest stack at the table?
Blinds: 300/600
UTG: t5500
BTN: t1400
SB (Hero): t3300
BB: t3300
In this situation, the BTN is very short with less than 3bb’s. The BB has a little more than 5bb’s left before posting. Due to the imminent doom waiting for the small stack, the BB is making a mistake by calling too wide. Let’s try to look at the $EV of the decision again:
Current equities--
UTG: 0.338
BTN: 0.136
SB (Hero): 0.263
BB: 0.263
If BB calls and wins--
UTG: 0.366
BTN: 0.248
SB (Hero): 0.000
BB: 0.386
0 = x*(0.386-0.263) + (1-x)*(-0.263)
x = 0.681
This means the BB can only call profitably with the top 10% of hands or so, assuming we push 100% of our hands.
This situation would be very different if you put the player with the big stack in the BB:
Blinds: 300/600
UTG: t3300
BTN: t1400
SB (Hero): t3300
BB: t5500
Current equities--
UTG: 0.263
BTN: 0.136
SB (Hero): 0.263
BB: 0.338
If BB calls and wins--
UTG: 0.322
BTN: 0.254
SB (Hero): 0.000
BB: 0.424
If BB calls and loses--
UTG: 0.272
BTN: 0.147
SB (Hero): 0.368
BB: 0.213
0 = x*(0.424-0.338) + (1-x)*(0.213-0.338)
x = 0.592
Now, pushing any two cards in the SB is very exploitable, as villain can profitably call with 33+, Ax, Kx, Q3s+, Q6o+, J6s+, J8o+, T7s+, T9o, 98s.
It may also be a mistake to shove on the short stack.
Blinds: 300/600
UTG: t3300
BTN: t5500
SB (Hero): t3300
BB: t1400
Just looking at it from a cEV perspective, the villain has to call 800 to win 2000, getting 2.5:1 pot odds, so he’s getting the right price to call with any two cards. In terms of $EV:
Current equities--
UTG: 0.263
BTN: 0.338
SB (Hero): 0.263
BB: 0.136
If the BB calls and wins--
UTG: 0.258
BTN: 0.1335
SB (Hero): 0.173
BB: 0.233
0 = x*(0.233-0.136) + (1-x)*(-0.136)
x = 0.584
Once again, shoving wide isn’t the greatest play for us.
So what do you need to know? Basically, the presence of a short stack in relation to the blinds will allow us to make some aggressive plays. If we have a big stack, we can pretty much abuse the table no matter what. If we have don’t have a big stack, then we want to target players that are short but not desperate, probably between 5-10bb’s. These players will want to play tight, especially in the presence of a player who is about to be eliminated. Being able to recognize the opportunities will help us take control of the bubble and make good decisions. I'm not sure not all the math is perfect-- I feel like I ignored the blinds in most decisions, not to mention the equity associated with folding-- but the point of the post was to get players thinking about situations, based on stack sizes, where it is profitable to be very aggressive. Besides, it's late here, I'm tired, and I'm only halfway done with packing for my travels tomorrow, . So if anyone can catch mistakes, feel free to correct me, and I encourage everyone to discuss similar situations or other things we should consider here in this thread.
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