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Bet Sizing w/ different stacks
Your opponent is known to call often and see most rivers. You have seen him PF min-raise monsters and junk all day and can’t distinguish between the two. ¿Unlucky that he isn’t a Russian cookie eater tell-box right?
He makes it 2 bb and you call in the big blind with 96hh. The flop is 669. The pot is 4.5 bb and heads-up.
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My argument with this post is that our hero should carefully select how much they bet on the flop, turn, and river with the goal of:
— getting all in by the river
— making a pot-size bet on the river
For example,
With 10 bb, can we bet 1/2 pot on the flop, turn, and river and still be all-in by the river?
— PF = pot is 4.5
— F = hero bets 2.25, calls 2.25, pot is 9
— T = hero bets 4.5, calls 4.5, pot is 18
— R = we want to bet 18 bb but our hero has only 3.25 bb left.
**Betting the river would be too small and not a pot-sized river bet.
With 20 bb, betting 1/2 pot on each street would leave you with 13.25 bb on the river. This bet is not a pot-sized river bet. It is reasonable to bet 13.25 bb into 18.00 bb and you probably get called by this opponent.
With 30 bb, betting 1/2 pot on each street leaves you with 23.25 bb on the river. This is an over-bet on the river that might not get called by this type of opponent. Then again, maybe it does 🙂
This means that the ideal stack size for this (bet 50% strategy) is somewhere between 20 bb and 30 bb. With the goal of having 18 bb left to make a pot-sized bet on the river, you would need to start the hand with ~26.75 bb to make this play ideal.
20 bb Strategy
Consider how you might adjust the bet sizing with a 20 bb stack to instead make a larger bet on the river by betting less than 1/2 pot on the flop and turn.
What if you tried to bet 1/4 pot, 1/2 pot, then full pot?
PF = 4.5 bb
F = bet 1.125 bb, pot is (4.5 + 2.25 = 6.75)
T = bet 3.375 bb, pot is (4.5 + 2.25 + 6.75 = 13.50
R = we want to bet 13.50 bb
The ideal stack for this betting strategy is 13.50 bb + 6.5 bb = 20 bb.
What if you try the Jamie Gold play of (bet 1/2, check, bet full pot)?
PF = 4.5 bb
F = bet 2.25 bb, pot is (4.5 + 4.5 = 9)
T = check, check
R = we want to bet 9 bb
With this strategy,
How many chips should the villains have to make this ideal?
Jamie invested 2 bb pre-flop, 2.25 bb on flop, and 9 bb on river. Although this only adds up to 13.25 bb, I would argue that a player w/ 20 bb to start the hand could open and have Jamie defend to see this scenario. When he bets 9 bb on the river, that scare most opponents and apply pressure and many stack sizes. With only 20 bb, that is close to 50% of the stack and frankly they need to have “it” to make that call on the river in the late stages of a tournament. With 25 bb, 9 bb on the river is still almost 1/3 of my stack. In essence, only the deepest stacked players could make the loosest calls. Everyone besides (Allen Cunningham) had a medium to small stack lost to Jamie because he applied pressure and they folded to this strategy. He tried it against Allen Cunningham but Allen’s larger stack forced Jamie to hit the brakes before the river and Jamie actually adjusted his plan. Watch the footage, you will see the bet check big bet line over and over.
Lastly,
We can try 1/3 pot, 2/3 pot, and full pot to see what happens.
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
The ideal stack for this betting strategy is 17.50 bb + 8.5 bb = 26 bb.
By clicking the standard “1/2 pot” button on each street, each individual investment you make is not being adjusted for the available “supply”.
#sustainability 🙂
Instead, adjust your bet sizing to the situation.
You can hit the nuts at any time, are you ready to get it in?
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3 Replies
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Adam, I am way behind on the forums but this is very interesting. Is there a formula to determine bet sizing needed for each street to get it in by the river based on number of blinds in the pot and the effective size remaining. That would be an interesting tidbit… and if the sizing is too small, then calculate the sizing needed to get it in on two streets (any 2 will do to keep opponent on the hook). Or even choosing between the two… if you think the opponent will jump at weakness but fold if 3 streets of aggression, what is the pattern needed for 3 or 2 streets??
For example, what if there are 6 bb in the middle and effective stack is 20 bb or 30 or 40 or 50. How do we get it in on 2 or 3 streets? Seems like we should be able to do something with the P1 (pot after pre-flop action), E1 (effective stack remaining after preflop action) and S (number of streets) to calculate the consistent %P needed so that E3 (effective stack after the turn action) = P3 (Pot after the turn action)
I will let the geniuses generalize, but for example:
P1=6 E1=40 and S=3
if %P = 50%, then P3 = 6+6+12 = 24 and E3=40-3-6=31
We want E3=%p*P3 right?
E3 = E1 – (%P x P1) – (%P x (P1 + (2 x %P x P1)
P3 = P1 + (2 x %P x P1) + (2 x %P x (P1 + (2 x %P x P1)))
Therefore, since we want E3 = P3,
E1 – (%P x P1) – (%P x (P1 + (2 x %P x P1) = P1 + (2 x %P x P1) + (2 x %P x (P1 + (2 x %P x P1)))
E1 – (%PxP1) – (%PxP1) + (2x%P) + (%P^2) + (%PxP1) = P1 + (2x%PxP1) + (2x%PxP1) + (2x%Px2%PxP1)
E1 – %PxP1 + 2x%P + %P^2 = P1 + 4x%Px%P1 + 4x%PxP1
I think my algebra is messing up but you get my point; can we solve for %P given these assumptions..?
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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.
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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 🙂
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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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