aqqr
Rock Star
Silver Level
Once I saw the ranges of starting hands in a video for a HU SNG by Collin Moshman. It is showed how often a big blind had to do a 3-bet shove.
P.S It was on Russian and I could not be found on English. I remember that he used the "HoldemResources Calculator". I don't have this program and I decided to understand this ranges in more detail.
Although you have a strategy against of the opponent's game, you can't confidently assert that with an effective stack of less than 20bb, your opponent will play in the same style. It's happen when you used to play for a long time, but an opponent won or lost a big pot and an effective stack became less than 20bb. There is no guarantee that the "loose" opponent will continue to raise any air, and a "tight" opponent will raise only good hands. It's may be a complete opposite, and we'll have to spend some time studying your opponent's game. You can use a limp and watch how your opponent reacts to it and how he reacts to raising his limp. Until then, you won't have much information and you have to think about an "optimal" strategy, until we understand how best to exploit your opponent's mistakes.
My reasoning:
P. S The calculations were performed manually using "OpenOffice Calc" and "PokerStrategy.com Equilab". I'm not 100% sure that the calculations were made accurately. If you notice a mistake, please write me.
Variables:
Available variables based on the "PokerStrategy.com Equilab":
hr = 70.14%
hp = 49.62%
hc = 36.35%
Let's calculate BB's profit at a distance (in the big blinds):
pBB = wf + lf + wpf + lc + wc = [(1.5) * (1 - hr))] + [(-1) * 1.5 * hr * (1 - hp)] +
[(1.5) * hr * hp * (1 - hc)] + [(-1) * 20 * hr * hp * hc * (1 - pwc)] + [20 * hr * hp * hc * pwc] =
[(1.5) * 0.2986] + [1.5 * 0.7014 * 0.5038] + [(1.5) * 0.7014 * 0.4962 * (1 - 0.3635)] +
[20 * 0.7014 * 0.4962 * 0.3635 * (1 - 0.5336)] + [20 * 0.7014 * 0.4962 * 0.3635 * 0.5336] =
0.4479 - 0.5300 + 0.3323 -1.3301 + 1,1801 = 0,0801
wf = (1.5) * (1 - hr)) = (1.5) * 0.2986 = 0.4479 (BB's profit when SB makes an open fold)
lf = (-1) * 1.5 * hr * (1 - hp) = 1.5 * 0.7014 * 0.5038 = -0.5300 (BB's losing after folding to SB's mini-raise)
wpf = (1.5) * hr * hp * (1 - hc) = (1.5) * 0.7014 * 0.4962 * (1 - 0.3635) = 0.3323 (BB's profit after SB's fold to BB's 3-bet shove)
lc = (-1) * 20 * hr * hp * hc * (1 - pwc) = 20 * 0.7014 * 0.4962 * 0.3635 * (1 - 0.5336) = -1.3301 (BB's losing after folding to SB's mini-raise)
wc = 20 * hr * hp * hc * pwc = 20 * 0.7014 * 0.4962 * 0.3635 * 0.5336 = 1,1801 (BB's profit after loosing SB's when SB make a call BB's 3-bet shove)
Thus, we calculated the BB's profit, which makes 3-bet shove (+0.0801bb). SB is losing 0.0801bb. Next, we consider situations where one of the opponents deviates from this chart.
Situation # 1.1
SB raises 61.69% of hands instead of 70.14% (removed Q2o - Q6o, K2o - K6o). Therefore, BB wins 0.6516bb instead of 0.4499bb after the SB's open fold.
Result: BB: +0.2512bb, SB: -0.2512bb
Situation # 1.2
SB raises 85.52% of the hands instead of 70.14% (any not completely air). Therefore, SB wins 0.6643bb instead of 0.4499bb after folding BB to raise SB.
Result: BB: -0.2312bb, SB: +0.2312bb
Situation # 2.1
SB calls a BB's 3-bet shove with 27.6% of hands instead of 36.35%. Therefore, if SB make fold on BB's 3-bet shove, BB wins 0.378bb instead of 0.3323bb.
Result: BB: + 0,0714bb, SB: -0,0714bb
Situation # 2.2
SB calls a BB's 3-bet shove with 45.1% of hands instead of 36.35%. Therefore, if BB winning after calling a BB's 3-bet shove, BB wins 1.6376bb instead of 1.1801bb.
Result: BB: + 0,244bb, SB: -0,244bb
Situation # 3.1
BB makes a 3-bet shove with 33.33% of hands instead of 49.62%. Therefore, if BB make a fold to SB's raise, SB wins 0.7014bb instead of 0.53bb.
Result: BB: -0.0161bb, SB: +0.0161bb
Situation # 3.2
BB makes a 3-bet shove with 58.37% of hands instead of 49.62%. Therefore, if SB make a fold on BB's a 3-bet shove, BB will win 0.3909bb instead of 0.3323bb.
Result: BB: + 0.102bb, SB: -0.102bb
Subtotals:
P.S It was on Russian and I could not be found on English. I remember that he used the "HoldemResources Calculator". I don't have this program and I decided to understand this ranges in more detail.
Although you have a strategy against of the opponent's game, you can't confidently assert that with an effective stack of less than 20bb, your opponent will play in the same style. It's happen when you used to play for a long time, but an opponent won or lost a big pot and an effective stack became less than 20bb. There is no guarantee that the "loose" opponent will continue to raise any air, and a "tight" opponent will raise only good hands. It's may be a complete opposite, and we'll have to spend some time studying your opponent's game. You can use a limp and watch how your opponent reacts to it and how he reacts to raising his limp. Until then, you won't have much information and you have to think about an "optimal" strategy, until we understand how best to exploit your opponent's mistakes.
My reasoning:
- If a BB folds more than 50% hands, a SB will get automatically profit by mini-raises with any cards. [(SB raise 1.5bb) / (1.5bb in the pot + 1.5bb raise SB) = 1/2 = 50%]
- SB shouldn't mini-raises with air, as in a call our raise we'll play with a bad hand or will make a fold to 3-bet shove. About 3/4 it's ok.
- SB must defend a raise after BB's 3-bet shove, making a call on a wide range. Otherwise, BB will do 3-bet shove each time and get automatic profit. Hand for a call to BB's 3-bet shove must be better than a BB's range (around 50% hands).
P. S The calculations were performed manually using "OpenOffice Calc" and "PokerStrategy.com Equilab". I'm not 100% sure that the calculations were made accurately. If you notice a mistake, please write me.
Variables:
- hr (Percentage of hands SB's a mini-raise)
- hp (Percentage of hands BB's 3-bet shove)
- hc (The percentage of hands SB's for call BB's 3-bet shove)
- pwc (BB's probability of winning after SB's a call 3-bet shove)
- wf (BB's profit when SB make an open fold)
- lf (BB's losing after folding to SB's mini-raise)
- wpf (BB's profit after SB's folding to BB's 3-bet shove)
- lc (BB's loss after winning SB's when SB make a call BB's 3-bet shove)
- wc (BB's profit after loosing SB's when SB make a call BB's 3-bet shove)
- pBB (BB's total profit)
Available variables based on the "PokerStrategy.com Equilab":
hr = 70.14%
hp = 49.62%
hc = 36.35%
Let's calculate BB's profit at a distance (in the big blinds):
pBB = wf + lf + wpf + lc + wc = [(1.5) * (1 - hr))] + [(-1) * 1.5 * hr * (1 - hp)] +
[(1.5) * hr * hp * (1 - hc)] + [(-1) * 20 * hr * hp * hc * (1 - pwc)] + [20 * hr * hp * hc * pwc] =
[(1.5) * 0.2986] + [1.5 * 0.7014 * 0.5038] + [(1.5) * 0.7014 * 0.4962 * (1 - 0.3635)] +
[20 * 0.7014 * 0.4962 * 0.3635 * (1 - 0.5336)] + [20 * 0.7014 * 0.4962 * 0.3635 * 0.5336] =
0.4479 - 0.5300 + 0.3323 -1.3301 + 1,1801 = 0,0801
wf = (1.5) * (1 - hr)) = (1.5) * 0.2986 = 0.4479 (BB's profit when SB makes an open fold)
lf = (-1) * 1.5 * hr * (1 - hp) = 1.5 * 0.7014 * 0.5038 = -0.5300 (BB's losing after folding to SB's mini-raise)
wpf = (1.5) * hr * hp * (1 - hc) = (1.5) * 0.7014 * 0.4962 * (1 - 0.3635) = 0.3323 (BB's profit after SB's fold to BB's 3-bet shove)
lc = (-1) * 20 * hr * hp * hc * (1 - pwc) = 20 * 0.7014 * 0.4962 * 0.3635 * (1 - 0.5336) = -1.3301 (BB's losing after folding to SB's mini-raise)
wc = 20 * hr * hp * hc * pwc = 20 * 0.7014 * 0.4962 * 0.3635 * 0.5336 = 1,1801 (BB's profit after loosing SB's when SB make a call BB's 3-bet shove)
Thus, we calculated the BB's profit, which makes 3-bet shove (+0.0801bb). SB is losing 0.0801bb. Next, we consider situations where one of the opponents deviates from this chart.
Situation # 1.1
SB raises 61.69% of hands instead of 70.14% (removed Q2o - Q6o, K2o - K6o). Therefore, BB wins 0.6516bb instead of 0.4499bb after the SB's open fold.
Result: BB: +0.2512bb, SB: -0.2512bb
Situation # 1.2
SB raises 85.52% of the hands instead of 70.14% (any not completely air). Therefore, SB wins 0.6643bb instead of 0.4499bb after folding BB to raise SB.
Result: BB: -0.2312bb, SB: +0.2312bb
Situation # 2.1
SB calls a BB's 3-bet shove with 27.6% of hands instead of 36.35%. Therefore, if SB make fold on BB's 3-bet shove, BB wins 0.378bb instead of 0.3323bb.
Result: BB: + 0,0714bb, SB: -0,0714bb
Situation # 2.2
SB calls a BB's 3-bet shove with 45.1% of hands instead of 36.35%. Therefore, if BB winning after calling a BB's 3-bet shove, BB wins 1.6376bb instead of 1.1801bb.
Result: BB: + 0,244bb, SB: -0,244bb
Situation # 3.1
BB makes a 3-bet shove with 33.33% of hands instead of 49.62%. Therefore, if BB make a fold to SB's raise, SB wins 0.7014bb instead of 0.53bb.
Result: BB: -0.0161bb, SB: +0.0161bb
Situation # 3.2
BB makes a 3-bet shove with 58.37% of hands instead of 49.62%. Therefore, if SB make a fold on BB's a 3-bet shove, BB will win 0.3909bb instead of 0.3323bb.
Result: BB: + 0.102bb, SB: -0.102bb
Subtotals:
- SB gotta make a raise around 3/4 of hands, and BB gotta raise 1/2 hands (This actions is more or less optimal for both opponents);
- If SB will raise more tight (around 2/3 of hands), then he''ll lose potential profit.
- When expanding SB's raise range in more than 4/5 hands, he gets a bigger potential profit. Provided that BB rarely does a 3-bet shove.
- If SB calls BB's a 3-bet shove on a wide range, then BB gets a bigger potential profit.
- If BB raises less than 1/2 hands, he loses his expectation, since SB gets an automatic profit by raising on a wide range.
- If BB does a 3-bet shove with more than 1/2 hands, he does not give SB automatic profit with his wide raise range, however, if SB make a call a 3-bet shove, BB risks loose the whole stack for 3bb.
