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Harrington (small pair 55)
Problem 24
Harrington’s Workbook
6 Left, All Top Pros
12k/24k + 300 —> (pot = 54,000)
Ivey opens to 70k from cutoff with 520,000 starting
You’re David Williams with pocket 55 in the small blind and 2,200,000 starting
— fold
— call 58k
— raise to 200k
— raise all in to 520k
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DH starts by looking at combinations and building an opening range for Ivey.
— any pair — AA KK QQ JJ TT 99 88 77 66 55 44 33 22 — (78 combos)
— any ace — AK, AQ, AJ, AT, A9, A8, A7, A6, A5, A4, A3, A2 — (208 combos)
— any broadway — KQ KJ KT QJ QT JT — (96 combos)
Total Combos = 78 + 208 + 96 = 382 combos
DH next tries to identify which hands Ivey will call a shove with and which he will fold…assuming David Williams goes all in.
If we assume that Ivey calls with:
— AA, KK, QQ, JJ, TT, 99 — (6 combos * 6 ways = 36 combos)
— AK, AQ, AJ — (16 combos * 3 ways = 48 combos)
Ivey will call 22% with (36 + 48 = 84 combos) and will fold 78% with (382 – 84 = 298 combos).
Expected Value Outcomes:
(I) – 78% of the time, Ivey folds and we win $124,000
(II) – 22% of the time, Ivey calls and we win $124,000 + $450,000 = $574,000
(III) – 22% of the time, Ivey calls and we lose $58,000 + $450,000 = $508,000
What are we up against and how often do we win?
— 36 of the 84 combos being over-pairs (99 – AA) — (36 / 84 = 42.8%)
— 48 of the 84 combos being big aces (AK, AQ, AJ) — (48 / 84 = 57.2%)
Thus,
vs. over-pairs — 22% call * 42.8% chance * 20% win = 0.018
vs. over-cards — 22% call * 57.2% chance * 54% win = 0.067
This means that we will win (1.8% + 6.7% = 8.5%) and lose (22% – 8.5% = 13.5%)
DH doesn’t calculate it, but David Williams has Fold EV when he pushes here.
You can find the %fold = (298 / 382) = 78% and %call = (84 / 382) = 22%.
Fold EV = (%fold)(amount win)
Fold EV = (78%)($54,000 + $70,000)
Fold EV = (0.78)($124,000)
Fold EV = $96,732
Call EV = (%call)[(%win * amount win) – (%lose * amount lose)]
Call EV = (22%)[(8.5%)($574,000) – (13.5%)($508,000)]
Call EV = (22%)[($48,790) – ($68,580)]
Call EV = (22%)[-$19,790]
Call EV = -$4,354
Total EV = Fold EV + Call EV
Total EV = $96,732 – $4,354
Because of the high %fold, this has a positive expectation.
In this instance, pushing with 55 was the right play.
Don’t get any ideas @FiveByFive 😛
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2 Replies
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I have to agree with @FiveByFive . Your analysis is spot on.
Fold equity is HUGE, especially on final tables with ICM in play. The fact that Williams has such a huge chip lead over Ivey makes for a big ICM factor. We don’t know the other chip stacks, so we can’t calculate exactly how much ICM is in play here. But we know enough to know that Ivey can’t call off here with anything less than a premium hand.
The moral of this story is, when our chip stack gets down into the 20’s or below, don’t waste 2 or more bb with a hand that has to fold to a rejam. You’re risking a rejam if there are stacks in the teens left to act, or a huge stack. ICM pressure makes this principle even more important.
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