Theorem of Blind Stealing - by MJ

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Introduction

To be perfectly honest, I didn't really want to write this article. It's such a simple concept yet such a strong tactic in single table tournaments, that it can seriously be -EV for myself if a lot of people start playing this way at Party Poker or any of the other sites I play at.

But, oh well. I know certain people have figured this tactic out already and that smart people will figure it out eventually - so I might as well write about it. I think a lot of people who read this strategy won't follow it anyways, thinking that I'm crazy, so no loss there.

Single Table Tournament Overview

Most people who are solid single table tournament (STT) players already know that the game is really composed of three parts: early game, late game and heads-up. Each stage is generally very straightforward, with very tight early game play, followed by aggressive late game play, then culminating into a heads-up game (usually aggressive as well).

As many solid players know as well, the majority of the chips are going to be won during the late game phase, where blind stealing and coin flips is pretty much the norm. While you can accumulate a stack early game, it often involves hitting a monster and having a loose player pay you off. Because of this, I would say that late game, including heads-up play accounts for 80% of how well you do in STT games, with the early game only accounting for 20% of your game.

When most players mention their STT ROI, it generally ranges from 50% (lower buy-in games) to 20% (higher buy-ins). So, if there is a late game tactic that could increase your late game by 10%, this would be be the equivalent of a 8% increase in your ROI, a rather large sum. I think this theorem of blind stealing can improve your late game along these numbers (depending on your existing skill level), so it is a very deadly weapon.

Blind Stealing and Folding Equity

Folding Equity is a term used to indicate the value of a play based on the chance that your opponent will fold. Blind stealing and folding equity are often used in conjuction, because blind stealing is all about picking up the blinds by forcing your opponents to fold.

Here is a table that I have constructed that shows what different types of players are willing to call a pre-flop raise with late game:

Now, take a look at the upper-right table, where it shows the percentage of hands played by each player type. This number can be used as a quantitative figure to figure out the folding equity of stealing from this type of player. The following table will illustrate how the calculation of folding equity works. This chart assumes that you are in the small blind, attempting to steal the big blind.

From a very quick skim, we can see here that it's worth it pre-flop raise any tight player with any hand based solely on folding equity. The reason is that even if you lose every single hand that you are called or raised on, you will still make a profit. The reason you will make a profit, as the chart shows, is simply because the very tight and tight players will give up their blinds much more than they are willing to defend it. If you raise by 3BB, you have a guaranteed profit if they are defending less than a third of their hands

Another important thing that we see here, is that our minimum profit drops significantly starting with semi-tight players, because they are actually calling or raising enough raises that it offsets the amount you are making from pure steals. Does this mean we shouldn't raise against looser players? Not necessarily, as it only means that we are break even at worst. To determine if we should raise, we need to examine how well our 'caught chips' fare.

Caught on the Blind Steal

In the chart, I had a column titled 'caught'. Caught is which is what I refer to as chips that have been called or raised in a blind steal attempt. Let make up a scenario and say that your opponent has 10BB in chips and re-raises all-in on your steal. It takes 7BB for you to call, while the pot is at 14.5BB, which gives you 2.1:1 pot odds.

For those of you who know your odds, you will know that 2.1:1 pot odds is almost always good enough to call. In the chart below, I've illustrated how a completely random hand stacks up in this scenario, if you call the re-raise.

The call equity shows that if we go on a blind steal by raising 3BB with any hand, we can call any re-raise up to 10BB (and in reality, up to about 13BB), with the exception of a re-raise from a very tight player. For those of you who have read about the concept of pushing all-in when you have 10BB or less, you can see the exact math here for why this is the case, as you have pot odds to call most players after already committing 3BB into the pot.

The caught equity column shows the actual equity of our play, since in reality, we put 10BB into the pot instead of 7 BB. The data also shows that when we do get called, it is a negative -EV play. However, what we really want to know is if our folding equity can offset our losses by being caught.

Combining Folding Equity with Caught Equity

If we apply what we just learned from Table #3, we can figure out that if we have 10BB or less or our opponents have 10BB or less, we might as well push all-in since we would be correct to call any re-raise after putting 3BB into the pot. Not only is this correct in terms of pot odds, but it also increases our folding equity, since most players are more reluctant to call all-in as opposed to calling two more big bets.

So, in Table #4, we will assume this type of push situation and see what numbers we get.

Table 4 can be a little bit confusing, so I will show a calculation below on how Total Equity is calculated from the beginning. In this example, we're going to assume that we are playing against a Semi-Tight opponent raising all-in with 10BB:

Fold Equity   = Blinds * Fold%
              = 1.5 BB * 72%
              = 1.1 BB 

Caught Equity = (Win% * Pot) - Total Cost to Play
              = (38% * 21.5 BB) - 10 BB
              = 8.2 BB - 10 BB
              = -1.8 BB

Caught Result = Caught% * Caught Equity
              = 28% * -1.8 BB 
              = -0.5 BB

Total Equity  = Fold Equity + Caught Profit
              = 1.1 BB - 0.5 BB
              = 0.6 BB

Though I'll admit my explanations so far have been a little dense, upon seeing the Total Equity column, there should be a spark of light among many of you reading and interpreting that data. The data shows that a random pre-flop hand raising 10BB to steal the BB from the SB, will always generate positive long term equity. In English, this means you can always push any two cards when you or the BB has less than 10BB (and if you look ahead, 13BB).

Raise Range on Blind Steals

Since we're all about finding razor edges in any situation, we can also look at how increasing our pre-flop raises affects our overall equity in these steal situations.

Intuition should give us the same conclusion as the data, which is that as you increase the value of your raise pre-flop, your overall equity goes down. The important thing to note is that equity is positive across the board for all player types, but begins dipping the most after about 10BB.

A good side-effect that may occur from raising over 10BB pre-flop however, is that your opponent is most likely going to tighten his calling requirements in order to call your raise. This would mean that most players will probably go up in level, so a semi-tight player would only call tight hands, and a tight player would only call very-tight hands. The effect of this of course, is that it improves your folding equity and thus, your overall equity as well.

The Effect of Variance

One thing about applying this theorem is that you will experience much greater variance than you are probably accustomed to. For the solid players, this should not be an issue. For players who multi-table, this strategy is extremely useful, as multi-tablers are already accustomed to variance, but essentially provides a logic for auto-playing steals in certain situations.

I will repeat once again that variance will naturally be very high with this type of strategy. Your opponents will think you are a maniac or a fish. Solid players will question your logic. You yourself may question the play after pushing dominated hands time and time again. If this is not acceptable to you, then you should not play with this strategy.

Strategic Adjustments to Stealing

As mentioned earlier, if you are caught and survive on a push, your opponents will most likely view you as a complete maniac - and quite likely lower their calling requirements for you. This doesn't matter however. You can see that even if they loosen up their requirements, you still have positive EV on them when stealing. The worst they can do is lower your EV, but even then can never make it go negative (unless you are raising over 14BB).

If you are seen as a maniac, you can exploit your own imagine to an absolute advantage over your opponents. For instance, you are playing this strategy and pushing everytime you or the BB has 10BB or less. When you finally accumulate up to 13BB, you decide to slow down and play normally again. Upon getting a strong hand such as KK, you then push in any position. Your opponents who have seen you push with rags will not give you any respect and are much more likely to call your overbet.

Another adjustment to make, is to pre-flop raise 3BB when you hold a monster. The BB who is sick of your all-in raises will likely see this smaller raise as a weak play and come back at you, which in case you can then call and likely dominate his hand. A 3BB bet can also be used against very tight players, as it still retains a high degree of folding equity and minimizes your loss when you are re-raised by them, as you are fairly certain to be dominated.

Independent Chip Modeling

Personally, I don't put a lot of value into ICM, but regardless of what I think, it's good to know. In short, ICM is the concept of putting a real dollar value on your current stack, relative to your opponents and the total payout in the tournament.ICM is an important early on (and even in mid-stages) of a tournament because it dictates that you shouldn't make any extreme or risky plays to win a few chips, when you aren't getting a true money return on your play.

For example, if you have pocket Tens and someone who you absolutely *know* has AK pushes all-in early game, ICM dictates that you should not call this bet. In the beginning game, your stack in dollar amounts is worth your buy-in. However, if you double up, your stack is only worth 184% of your buy-in (according to ICM). So, while TT has about a 5% edge over AK, ICM actually states that by calling, you are risking more "real money" than you are winning with your edge (as opposed to just tournament chips). As such, ICM dictates that you shouldn't call with small edges.

ICM applies to the theorem of blind stealing, because from reading this article, you may get the idea to push in every single situation where you are heads-up with the BB. This will be incorrect at times however, because you don't always want to risk many chips - especially early game. In a late game situation, my feeling is that aggression is far more rewarded than timid play, so ICM does not play as big a role. So, the general rule of thumb is - don't start stealing until the blinds are at least 50/100.

If you want to explore ICM more, here is an ICM calculator.

Heads-up Play

The writing is on the wall, so I'll let you figure this one out...

Defending against this strategy

If you understand all of the math involved, you will understand that there is no way of truly defending against this tactic. If you are on the BB and your opponent raises on every hand, your only option is to gamble with him and call every hand that he raises as well. This is actually an +EV play for the both of you, since the blinds are 'dead money' and you are both eventually splitting them.

The only real defense that you can mount, is reducing the amount of total equity that the attacker can obtain, by widening your push hands substantially to defend against steals. If you increased your range of hands to a set such as all pocket pairs, Ace/x, King/x, Queen/7+, Jack/7+ and Ten/7+ - you can effectively reduce your attacker's total equity to 0.4BB. This would be the equivalent of letting them keep their SB and you keeping your BB.

Conclusion

Hopefully (or not if you play at my tables) this article will have made something click inside your head. Because if it did, you can see how extremely effective this strategy is to use in any tournament situation, but especially Party Poker STT games. In the Party Poker $30+3 games for example, with starting chips of 800 per person, mathematical strategy can and will completely take over the end game. This is one of the reasons that any of the Party Poker STT games can be crushed by anyone who knows what they are doing.

Anyhow, I regard this as a big trick being let out of the bag. If it turns your game around, I'd always like to hear it on the forums. Good luck - although it's not really luck.

Conclusion - Part Deux (Added: 10/24/04)

There has been a number of analysis and discussions as a result of the article which you should know. The foremost is that the article did not emphasize enough that the averaged EV of random hands will be profitable over the long term, but any particular hand may not necessarily be profitble. An example is 23o, one of the worst hands in poker, would not be +EV in many situations, because it simply fares very badly vs any hand. This can apply to other rag hands as well.

The conclusion to draw from this, is that against players who are more apt to call your all-in bet, you should be more discriminate in the hands you will be pushing with. If they're loose enough to call you with 64% of their cards, you can wait for a good hand, then punish them for calling you when you have them dominated.