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Saturday, December 26, 2009

COTW #1: Equity Exploration

Video By *Split*

Example of 3-betting:
BTN opens to $4, SB folds, we 3-bet to $12 from the BB. We are risking $12 to win $4.50 so BTN has to fold: 12/(12+4.50) = 72.7% for us to BE and any more would show an immediate profit. To further this example, assume we know that the BTN opens about 30% to steal and will only continue with the top of his range which we can estimate from our reads, but lets say that he will continue with AQ+, TT+ which is 4.7% of hands. The math for how often he continues given a 30% OTB open range is: 4.7/30 = ~16%. Conversely, this means he will be folding 84% of the time to our 3-bet. From the math we did earlier, he only needs to fold 72.7% of the time for us to make a profit and in this scenario, he is folding 84% which means we are making a lot of money! We can play around with the ranges and adjust accordingly versus different opponents, loose or tight and get an idea of how profitable or -EV our plays are this way. Before we get any further though, we should keep in mind what is called
variable effect. Continuing with the example above, lets assume that the BTN will sometimes add a couple of random hands to play back at you with, let's say 4 more hands. The extra 4 hands changes the range he will continue with from 4.7% to 8.3% so 8.3/30 = ~28% of the times he is continuing and 72% of the times he will fold. So even if he adds in some random hands, our 3-bet is actually BE.

BTN 3-bet 30% of hands = 100% of his range
4.7% of hands (not including variable effect) = 100% of his continuation range
4.7/30 = 16% of the times he will continue and conversely 100-16 = 84% he will fold

8.3% of hands (including
variable effect) = 100% of his continuation range
8.3/30 = 28% of the times he will continue and conversely 100-28 = 72% he will fold

Quick Example on 4-betting:
Full stacks of $100 at 100nl. We are OTB and make it $4, BB makes it $12, we decide to 4-bet and make it $30 and the BB shoves. We will have to call $70 to win $130.50 meaning we would need ~35% equity to call here versus the BB's shoving range here. If we made it $39 and he shoves, the equity required for a call changes dramatically: $61 to win $139.50 or ~30% equity. Using an example: If we have 65s an decided to 3-bet and believe that the BB's shoving range is QQ+, AK then our equity versus that range is ~ 31% meaning in the first scenario we would have to fold, but the second we would call.

Weighted ranges to calculate for variable effect is more accurate than just throwing random hands into pokerstove.
Ex. We are getting it in pre-flop with QQ vs a villain's range if we feel we have enough equity. Lets assume that the villain is very active/aggressive and will get it in light 70% of the time with 99+, AQ+ (5.1%) and 30% of the time (
variable effect), he will get it in much tighter with JJ+, AK (3.0%). We can calculate the equity of our QQ vs the two ranges and then weight it accordingly. So versus 99+, AQ+ we have ~58% equity. Versus JJ+, AK, we have ~47% equity. 70% of the time we have 58% equity and if we multiply the two we get a weighted equity of .406 or 40.6%. 30% of the time we have 47% equity and if we multiply the two we get a weighted equity of .141 or 14%. By adding the two weighted equities, we will get our total equity which comes out to be .406+.141 = .547 or 54.7%. In this case we are calling since anything over 50% equity is good. Using a weighted range requires that you have a decent amount of history and or read.

Stoxpoker Combo
Example using Stox Combo: We raise 5x with AQss against a very loose weak/passive half stacker at 200nl. We PSB CB flop of 6s2s9x and get called. The pot is now $66 and we have $68 in the effective stack, the turn is 2x, should we shove?

Using Stox Combo, we can give villain a range and then select a range we believe he will continue with on the turn. We can evaluate his
continuation range and the program will spit out how many combos he will have that will continue and break it down by groups such as TP, trips/sets, etc. So for example: villain will continue on the 6s2s9x2x flop with any pair, TP, 2pair, trips/sets, FD, OESD and FH given a range of 22+, 43s+, J9s+, Q9s+, K9s+, A9s. We can evaluate how often he continues using Stox Combo.

Using SplitSuit's calculations:
28% he folds
72% he continues
31% equity when we shove and he calls vs his given range

$profit = $pot(%win) - $bet(%lose)
$profit = (.28)(66) - (.72)(.31)(134) - (.72)(.69)(68) = 18.5 + 30 - 34 = +14.5
(.28)(66) = times he folds and we win the pot right there
(.72)(.31)(134) = times he calls and how much we stand to win given our equity
(.72)(.69)(68) = times he calls and we lose our turn shove

So according to SplitSuit's calculations, the shove will make us a profit.

Practice Problem:
Villain 15/13/4 over 850 hands
WTSD 20% W$SD 48%
CBets 85% Cbets turn 65%

50NL all involved 125BB stacks
Hero on the Button is similar holding 99.
Villain opens MP1 4X and we call for set mining value. all fold.

Flop (9.5BB) Tc 8d 7h
Villain bets (8.5BB). Hero calls

Turn (26.50BB) 2s
Villain bets 22BB.

Hero considers options based on equity calculations.

Answer by 2p2er:
Option: Shove

Hero is dealt 99
Villain’s PF range = 22+, ATs+, KJs+, QJs, JTs, T9s, 98s, AJo+, KJo+, QJo, JTo
On the turn: Tc 8d 7h 2s

48.5 BB pot after villain bets 22 BB
Villain has 90.5 BB behind

Option: Shove
Villain’s turn c-bet range = AA - 77, 22, AKs, ATs, ATo, QJs, QJo, JTs - J9s, JTo - J9o,
T9s, 98s,

I am adjusting the pre-flop range to include the J9 straight here since villain is willing to fire a double barrel on a connected board. I have removed a lot of the overcards that would most likely not fire again, but left a few in (AK) because he will do this once in a while. I’m deriving this range based on PF range + board texture + postflop tendencies (65% turn c-bet in particular).

Villain will continue with straight, OESD (T9), sets, and overpairs. He folds 56% of the time.
Hero has 23% equity versus villain’s
continuance range.

Profit (BB) = (0.56 * 48.5) + 0.44[(0.23 * 139) – (0.77 * 90.5)]
Profit (BB) = 27.16 + 0.44(-37.72)
Profit (BB) = 10.5

Since shoving is profitable, I am assuming that is going to be the best option as opposed to calling. We do fold out all worse hands and only get called by better. BUT we can also fold out some better hands, and we are not going to gain any more value out of worse hands on the river by calling the turn anyways unless those worse hands improve to better hands and end up beating us. And if we end up calling and hitting our straight, we are not getting anymore either since our hand is obvious.

And shoving is even better if we can ever get him to lay down over-pairs. I think he may be capable of folding JJ/QQ in this spot.

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