Irrefutable Southern Logic - Sometimes doubling up doesn’t mean you have twice as much

It is always cool to make a final table. Our goal is always to win the tournament, and if we cannot win the tournament then our goal should be to win the most money possible. It doesn’t matter how many antes we steal, how many pots we bluff, how many chips we have or once had, it only matters when we lose our chips unless we win all the chips. Never forget that those colored discs in front of you represent life and survival, nothing else. If you have some, then you may continue to play in the tournament. If you do not, then you cannot, and then you cannot collect money. The only thing the biggest pile of betting discs means is that you are most likely to win the tournament and least likely to go broke next.

I often mention the theory of ICM, or Independent Chip Model, as justification for an action in a tournament. I generally reference it like some deity, like I can’t call here because of ICM, or there’s no way he can call here because of ICM, and what I am really saying is that it is harder to call either way because going broke in tournaments sucks more than doubling up is awesome. This is all because of the mathematical fact that doubling up in a tournament does not double your chances of winning the tournament.

I’ve written over a hundred articles for Card Player magazine since 2008 and I’ve smoked at least three ounces of legal Colorado pot in 2014 so I can’t remember if it’s time to talk about ICM again, but we’re going to anyways because ICM is such a big, scary, mathematical monster. I could probably dedicate the entire next year of columns to ICM and keep talking about it in 2015. There are so many different spots where it’s profitable to shove with any two cards and so many other spots where it’s profitable to fold with 60 percent equity.

Let’s break this down into a simple example. Ten-handed final table, all players have equal chips, and payouts are $1,000, $700, $500, $400, $350, $300, $250, $200, $150, and $100. Granted this payout structure is bad, but we’re making simple examples here. With $3,950 in the prize pool, each player has $395 in equity. It folds to the small blind (SB) who shoves into our big blind (BB). What equity do we need to call profitably in this spot?

First, in a cash game, this problem would be easy. Estimate the opponents shoving range. Using a program like PokerStove, compare your hand to your opponents shoving range. Using the above example, let’s say that stacks are 20,000, blinds 500-1,000 with a 100 ante. Therefore there is 20,000+1,000+1,000 in the pot, it is 19,000 to us. Since we win 22,000 by risking 19,000, our equity needs to be 46.34 percent (19/41) to call. Anytime our equity is 46.35 percent or better, and we fold, then we are making a mistake, anytime we are worse and we call we are also making a mistake. In cash games, chips are worth what you can trade them for at the cage. Their value is constant and it never changes.

With the exception of the occasional hooker in Vegas, tournament chips don’t do anything except say that you can still be in the tournament. Their value is dynamic, with one chip being worth the most and lots of chips being worth the least, at least on a per chip basis. Once you run out of tournament chips it means something, and you’re generally not happy about it. I’m really glad that the WSOP changed its policy on cashing. Several years ago when a player busted in the money, the dealer would yell, “WINNER!!!” Somebody finally turned a table upside down or something and now they simply say “payout” thank goodness. So it’s 19,000 to us, chance to win 22,000. We know that we need to be 46.35 percent to make a +cEV (positive chip expected value) call, but what must our equity be to make a +$EV (positive REAL MONEY expected value) call? Well, if we call and lose then we collect $100 in real prize money, meaning that we lost $295. What happens to our equity if we call and win?

Using the calculator at icmpoker.com, an excellent resource for ICM data, it turns out that if we call and win our equity in the tournament is now $555.47 while our eight remaining opponents earn $16 each, climbing to $411.82 in equity. Nifty, we’re a favorite. But, we sure risked a lot of real dollars to earn this equity. If we call and lose it costs us $295, if we call and win it earns us $160.47. Pretty hefty odds to lay, don’t you think? They are so hefty in fact that to lay $295 to win $160.47 we need to be at least a 64.77 percent favorite to make the call! Wow!

So, breaking this down even further, let’s give our opponent an optimal shoving range for 20 BBs and assume that this range is balanced. That range, since we have to be 64.77 percent to call, consequently is wide: 2-2 plus, A-x plus, K-2 suited plus, K-4 offsuit plus, Q-2 suited plus, Q-8 offsuit plus, J-3 suited plus, J-7 offsuit plus, 10-3 suited plus, 10-7 offsuit plus, 9-5 suited plus, 9-7 offsuit plus, 8-4 suited plus, 8-6 offsuit plus, 7-4 suited plus, 7-6 offsuit, 6-3 suited plus, 5-3 suited plus, and 4-3 suited. Know what all that means? It means that I am barely calling with A-K suited and reluctantly folding A-K offsuit, since A-K offsuit has equity of 64.5 percent versus that range. Nines are a call versus this range but eights are a fold.

The lesson here is that you gotta be awful confident in your read when calling it all off in big ICM situations. Also, you should be shoving much more than you are right now, but you probably knew that already. And as always, the most important part of your skill in these situations is evaluating opponents’ ranges because the rest is all a math problem. If the opponent is only shoving a range like any ace and any pair, it makes folding any ace-king optimal even though you are so far ahead of their range. It is important to note their calling ranges too, since opponents will usually fall into a calling or folding too much category rather than an optimal one.

More talk about the final table next issue. See you then. ♠

Bryan Devonshire has been a professional poker player for nearly a decade and has more than $2 million in tournament earnings. Follow him on Twitter @devopoker.