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  • Stack Size Analysis

    Posted by arw on September 6, 2020 at 7:44 am

    Here is the scenario,

    You have 100 bb and are looking for opportunities to apply pressure and use leverage. How can you exploit different stack sizes?

    To make it easy, let’s say that we are playing big blind ante which means the blinds and antes add up to 2.5 bb before action begins. The villain opens kind of large to 3.75 bb and you defend from the big blind. The pot size is 10 bb. I like easy math.

    Now, on the flop, our opponent c-bets 5 bb into 10 bb to try and take it down. As the big stack, we have 3 options (fold, call, or raise). This brings me to the topic of the day — “STACK SIZES”. Our optimal decision depends on our opponents stack size.

    15 bb — If our opponent has 15 bb and they bet 5 bb of it, they would be calling their remaining 10 bb all-in. The pot size of 10 bb is 67% of their stack size. This is a spot where our opponent has invested 33% of their stack and they have 1.0 pot sized bets remaining. <i style=”font-family: inherit; font-size: inherit;”> If we raise all-in, we would be offering reverse pot odds of = (15 bb + 10 bb) to (15 bb – 5 bb) = (25 bb) to (10 bb) or 2.5 to 1 odds. As Yoda would say,<i style=”font-family: inherit; font-size: inherit;”> “fold equity have we don’t”.

    20 bb — If our opponent has 20 bb and they bet 5 bb of it, they would be calling their remaining 15 bb all-in. The pot size of 10 bb is 50% of their stack size. They have invested 25% of their stack and they have 1.5 pot sized bets remaining. If we raise all-in, we would be offering reverse pot odds of = (20 bb + 10 bb) to (20 bb – 5 bb) = (30 bb) to (15 bb) or 2.0 to 1 odds.

    25 bb — If our opponent has 25 bb and they bet 5 bb of it, they would be calling their remaining 20 bb all-in. The pot size of 10 bb is 40% of their stack size. They have invested 20% of their stack and they have 2.0 pot sized bets remaining. If we raise all-in, we would be offering reverse pot odds of = (25 bb + 10 bb) to (25 bb – 5 bb) = (35 bb) to (20 bb) or 1.75 to 1 odds.

    30 bb — If our opponent has 30 bb and they bet 5 bb of it, they would be calling their remaining 25 bb all-in. The pot size of 10 bb is 33% of their stack size. They have invested 16.7% of their stack and they have 2.5 pot sized bets remaining. If we raise all-in, we would be offering reverse pot odds of = (30 bb + 10 bb) to (30 bb – 5 bb) = (40 bb) to (25 bb) or 1.6 to 1 odds.

    To conclude, I’ve added an excel sheet where you can identify the:

    —- % pot size = size of the pot in relation to the size of the effective stack

    —- % bet size = size of the bet in relation to the size of the effective stack

    To find the reverse pot odds of you decide to re-raise them all-in.

    arw replied 3 years, 7 months ago 1 Member · 2 Replies
  • 2 Replies
  • arw

    Member
    September 6, 2020 at 8:44 am

    Example 1

    We are middle stages of a tournament. In this hand, we expect our opponent to open a range of 13 * 6 = 78 combos of pocket pairs (AA – 22) and 20 * 16 = 320 combos of any broadway (AK – JT). This range represents 78 + 320 = 398 of the 1326 starting hand combos or an opening range of about 30%.

    50/100 – 10 handed

    (pot = 50 + 100 + 10 ante = 250)

    We have 2800 chips and our opponent has us covered. Pre-flop, our opponent opens to 300 on the button and we defend in the big blind. The pot size is 750. On the flop of ________, our opponent c-bets 375 or 50% of the pot.

    Stack Size = 2500

    Pot Size = 750

    Bet Size = 375

    = (2500 + 750) / (2500 – 375) = 3250 / 2125 = 1.53 to 1

    If the opponent folds, you earn 750 + 375 = 1125 chips without showing your hand.

    If the opponent calls, the opponent needs to win ~39% of the time to break-even.

    If the flop is 432 rainbow, our opponent should have an over-pair or a set (78 / 398 ~ 20%) of the time and two overs (320 / 398 ~ 80%) of the time.

    Let’s say that you have 98 suited and this was not your flop!!! But maybe it’s a spot to re-raise all-in and hope for a fold. The opponent is expected to call with any over-pair or any set and fold all the broadway over-cards that also missed the flop. They call 20% and fold 80% of their c-betting range.

    Should you re-raise?

  • arw

    Member
    September 6, 2020 at 10:53 am

    Is this a spot to re-raise?

    On 432 rainbow, you have 98 suited.

    — if called by AK-JT, you lose about 75% —— lets say they always fold to a raise

    — if called by AA-TT, you lose about 95% —— let’s say they always call to a raise

    — if called by set, you lose 100% —— let’s say they always call

    Overall, you’re called 20% of the time with about 5% hand equity or your getting a fold 80% of the time with some just-in-case equity of 25%.

    FOLD EV

    = (% fold)(amount win)

    = (80%)(750 + 375)

    = (80%)(1125)

    = 900

    CALL EV

    = (% call)[(%win)(amount win) – (% lose)(amount lose)]

    = (20%)[(5%)(2500+2500+750) – (95%)(2500)]

    = (20%)[(5%)(5750) – (95%)(2500)]

    = (20%)[(287.5 – 2499.05)]

    = (20%)(2211.55)

    = -442.31

    TOTAL EV = Fold EV + Call EV

    = (900) – (442.31) = 457.69

    _______________________________________________________________


    If you add some additional calling hands like an extra 10% of hands, then you should recalculate your EV.

    FOLD EV

    = (% fold)(amount win)

    = (70%)(750 + 375)

    = (70%)(1125)

    = 787.5

    CALL EV

    = (% call)[(%win)(amount win) – (% lose)(amount lose)]

    = (30%)[(5%)(5750) + (25%)(5750) – (95%)(2500) – (75%)(2500)]

    = (30%)[287.5 + 1437.5 – 2375 – 1875]

    = (30%)(1725 – 4250)

    = (30%)(-2525)

    = -757.5

    TOTAL EV = Fold EV + Call EV

    = (787.5) – (757.5) = 30

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