Fold Equity and Restealing in Multi Table Tournaments
by Corndog

This will be hopefully the first of a series of posts I'll make on concepts of advanced tournament play. School is starting so MTT play will be limited, but as I try to implement or learn new concepts I will share them on this blog.

As a little bit of a background, I have a fairly nice history in online MTT play. I've made some final tables and some nice 4-figure scores against tough fields. I have made some great ballsy plays against tough opponents that amaze me when I go through my hand history. I've played players such as Rizen on final table bubbles and went deeper than him (although I can't necessarily say I outplayed him or even have the capability to). I've read opponents' cards like they were face up and picked off the most intimidating of bluffs.

I have also refused to give up on hands where I was obviously beaten, and have given up on hands where a monkey can see that I was ahead. I have gone on tilt and donked off a dominating chip lead with 80% of the field gone and only 10% left to the money. I have given up on aggression and gone into a weak-tight shell when facing quality opponents. I have made horrible bluffs with my entire stack, and made horrible calls for my entire stack when convincing myself that my opponent was bluffing. I have slow-played myself out of more tournaments than I can count.

Anyone playing a good aggressive game with ABC poker skills can have some success in MTT tournaments. Most of my big scores have been when I played fairly straight-forward the entire time, and this is the best way to play at least early on in a tourney. However, in the middle to late stages of the tournament I feel I miss out on tons of opportunities to play the situation and not the cards. You HAVE to find ways to go outside of the box to accumulate chips if you want to put yourself in position to win the tournament. We all know the importance of concepts such as blind stealing when the blinds get high and antes kick in but I want to learn and discuss some of the lesser-known issues.

I played a small MTT on Bodog ($10+1, 401 players) this week that really opened my eyes to the art of restealing. It was one of those "Aha!" moments that we poker players occasionally experience in our evolution.

Bodog won't let you save hand histories, so here is the summary as best I can recall:

Around 80 people left in tourney with 45 getting paid. Average stack is around 7100, blinds are 150/300 with 25 ante. Here (yours truly) is in small blind w/ 68s, and a stack of around 3000 left. Everyone folds around to the button, who makes it something like 1000 or 1200. Pot is now approximately 1800. I looked down at my 68s and decided they couldn't stand a raise, especially not with my stack. Big blind folds and button takes it.

The thing that bothered me about this hand is that I never thought beyond my cards. A better player would recognize that the button is most likely stealing and recognized a good chance to resteal. Many better players would probably push from my SB with any two considering the opponent I was against. I am not a better player, but am trying to become one, so pondered this hand for awhile. I should automatically suspect a steal here, and additionally my notes on the player already stated that he was a habitual blind stealer and had even shown 39o after a steal from the cutoff earlier in the tournament.

I concluded that I have to push at this point. First off, I have tremendous fold equity. For those not familiar with the term, it is basically saying that I stand to make a decent amount of money on average because my opponent will be folding. There is a very good chance here that my opponent will fold and I won't have to show the world what I'm raising with. These reasons alone are almost good enough to justify pushing any 2 cards here.

But what if he calls? I will be an underdog for sure. However, I can assume both of my cards are live and suited 1-gappers play reasonably well against strong holdings compared to complete trash like 47o. I decided to try to put my opponent on a range here. I decided that he will probably be raising on somewhere around the top 50% of hands at this point (and based on his 39o from earlier, this may be too conservative of an estimate). With so many chips in the pot I will say that he will have to call with most good holdings. A-8s, any two broadway cards, and any pocket pair might make the call. This is around 20% of all possible holdings. From here, I can determine my average gain (EV) of pushing.

In terms of chips, I expect to profit of:

F * (1800) + C * (W*3600-L*1800)

where:
F= % of time opponent folds, C = 1- F = % of time opponent calls, W = % of times I win when he calls and L = 1-W = % of time I lose when he calls. The chip amounts are based off of how many are in the pot already (around 1800), and what I would stand to gain or lose should he calls (I have to put in 1800, but will make 3600 when he calls and I win). The first term of the equation is the fold equity, the second part is the showdown equity.

Using the idea that he will raise with the top 50% of cards but only call with the top 20%, F = 3/5 = 60% and C = 2/5 = 40%. Running my holding versus his possible range in PokerCalculator I find that I should win somewhere around 35% of the time, or a little more than a third.

Running everything into my above equation I find:

Expected net = 1116 chips. When I just fold expected net = 0 chips.

Basically, every time I make this play I expect a 33% or so increase on my stack. With that kind of edge, this push HAS to be made. If he surprises me with a huge hand I'm going broke, but I can comfortably put him on a range that makes this a long-term good move.

I encourage you to use the formula above and play with it depending on different opponents. The most important thing to note is that the lower your fold equity, the better your starting hand should be. For example, against a very tight opponent the fold percentage may be around 10% or even less and his range increasingly dominates ours so that it becomes a losing move. Even against my opponent 60% may be too high since he will get 2:1 on what he calls with. My suited 1-gappers are actually a profitable move against his range even if I am 100% sure he calls, but chances are my fold equity will still be high enough for this to be profitable if I had worse cards. Check 27o vs your opponents range to see when it may be right to move.

You don't have to be short-stacked to make this move either. You can both have big stacks. The equation I gave is only applicable in the case that someone is getting all their chips in preflop, so if you are big stacked and just repop to 2 or 3 times his raise you are on your own postflop if he calls and may God have mercy on your soul should he re-raise. However, if you assume that you will give up on the flop unless you hit big or will fold to a preflop 3-bet it is good to have some kind of handle on your fold equity. If you think he has a big raising range but small calling range you have great fold equity and it may be worth taking a chance to accumulate chips. Show him your dominance and resteal it.

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