Secrets of Professional Tournament Poker, Volume 1 (64 page)

0.7(3) + 0.3[32(0.38) - 15] = 1.7BB expected profit.

Your equity in the hand is 0.38 when you push 100 percent of hands and he calls with 30 percent of hands. If he calls with only 20 percent of hands, your profit is still 1.7BBs, as the equation becomes:

0.8(3) + 0.2[32(0.36)-15] = 1.7BBs.

Some opponents will only call with 10 percent of hands, in which case your equity when called dips to around 32 percent, so you have

0.9(3) + 0.1[32(0.32)-15] = 2.2BBs,

which is huge. Push everything from the small blind unless your opponent is willing to call off very wide.

As your stack dips to 6BBs in the small blind, you should still push with every hand. Even though you will be called much more often, you will still show a significant profit. Suppose you push all your hands and your opponent calls half the time. We have

0.5(3) + .5[12(0.42) - 6] = 1.02BBs.

It is tough to not profit by pushing all hands from late position as your stack gets short. But don’t get too far out of line from early position when you have 15BBs, as that can cause some costly mistakes. When I played sitngos as an 18-year-old, I would constantly push A-x from early position for 10BBs. Once some of the powerful online poker tools came out, I realized the size of that leak and quickly fixed it. From early position, you need to be tighter as long as you have a decent stack of 10BBs or so, and you can shove wide as you get short. When it is folded to you in late position, and especially the button and small blind, shove any two cards as long as your opponents are not calling with an extraordinarily wide range.

Be careful not to shove every single time it is folded to you if your opponents are quick to figure you out. You can occasionally fold the button with a total trash hand when you have 11BBs. While you may pass up a slightly +EV spot, you will gain a lot of fold equity next time you push on those players. However, if I had to choose between always pushing the button or never pushing it with 9-4 and a 7BB stack, I would push it every time as long as I had fold equity.

When There Are Limpers

From time to time, even in large buy-in events, a player will limp when everyone has a short stack. When this happens, you need to quickly figure out if he is limping with a wide range, trying to see a cheap flop or holding a monster and hoping an overly aggressive player will shove. Give a player’s first limp a decent amount of respect, but after that, attack him whenever possible as long as he is not tricky enough to balance his limping range.

Suppose someone limps from middle position, the small blind calls and you are in the big blind with any two cards and 10BBs. If you think the limper calls around 30 percent of the time with the top 15 percent of hands, and that the small blind will never call—and he usually won’t—should you push? We have

0.7(5) + 0.3[23(0.31) - 10] = 2.6BBs expected profit,

which is huge. So, if players limp often, push very wide. Now, look at what happens when they never fold and they have the top 10 percent of hands. We have

0(5) + 1[23(.31) - 10] = -2.87BBs.

So, if your opponent is always limp-calling with a strong hand, you should never push.

This should show you the importance of fold equity. If you only have a 6BB stack, you probably have much less fold equity than before, which means the push will not be as profitable. However, if your opponents fold even a tiny bit, you profit more than enough to make up for when they call. Your hand can go from a huge winner if your opponent limp-folds often to a huge loser if he always limp-calls. It is not uncommon to see a player with a skewed limping range. Get to know your opponents and take advantage of them.

Your equation should change slightly with multiple limpers, but generally push a ton if the initial limper is loose and fold if he’s tight. The second caller will often show up with a small pair in this situation, so shy away from pushing 100 percent of hands, but tend more to push hands like J-7, which are flipping against small pairs.

Assume the first limper calls 30 percent of the time with a top 10-percent hand and the second limper calls 30 percent with exactly 6-6, 5-5, 4-4, 3-3 and 2-2. You are pushing the same 10BB stack for an expected profit of

0.4(5.5) + 0.3[0.31(23) - 10] + 0.3[0.43(23) - 10] = 1.31BBs.

Notice that the second player’s range doesn’t actually matter because when you get all the money in, there are 3BBs extra in the pot from the blinds and antes, which gives you enough pot odds, seeing as you have 43-percent equity against the small pairs.

As more and more limpers jump into the pot, be more willing to push with medium-strength hands such as J
-10
and Q
-8
if you know the initial limper is loose. We know from the last paragraph that players that limp behind have negligible effect because they call so infrequently. But make sure you have around 7BBs when pushing over multiple limpers because you have no fold equity with only 5BBs. However, if there are enough limpers and you can get a lot of dead money in the pot, pushing with a wide range may be profitable.

Suppose there are five limpers and you push any two cards on the button with 7BBs. Expect at least one player to call almost every time. For simplicity, assume you have 35-percent equity when called. Your expected profit is then

0.1(9) + 0.9[(0.35(21) - 7] = 1.22BBs.

Notice that even though you only have 35-percent equity, the dead money in the pot makes this a profitable push with any two cards. Also notice that pushing is basically break-even with no fold equity at all.

Occasionally you will get multiple callers, which I ignored in the above calculation. This tends to happen more often when a number of deep-stacked players limped and you, the pusher, are the only short stack. If 7BBs is not significant to your opponents, then tend not to push over multiple limps with a very wide range because you have no fold equity and there will be little dead money in the pot.

Although I just proved that you should shove over limps a lot, you should still fold from time to time, even if you think the limper is loose. If he limps from early position and you are in second position, you should usually fold because someone behind might call. If you push over limps a few times in a row, expect all your fold equity to vanish because players will get fed up with your constant aggression. My advice is to steal pots when you are in late position and the initial limper is loose. Also, it doesn’t hurt to wait for some showdown value. This is another decent way to balance your range, although if you have a lot of fold equity, your hand is irrelevant.

When There Is A Raise

When a player raises in front of you, you must determine whether getting all-in with your hand is profitable. In general, unless your opponent is bad, you will have little to no fold equity. Because of this, you must have a hand with decent showdown value, especially once your stack dips below 10BBs.

Suppose someone raises to 2.5BBs from middle position and it is folded to you, with 10BBs in the big blind. If you push, your opponent is probably going to call between 80 and 100 percent of the time with his entire range. If you always push, assuming your opponent raises 15 percent of hands, your expectation is

0.05(6) + 0.95[23(0.34) - 10] = -1.8BBs,

for a clear loss. So, you need fold equity to profitably go all-in with a wide range.

You must determine with which hands you can profitably raise all-in here, as this situation comes up all the time. Suppose you had 50-percent instead of 34-percent equity. Your expectation would now be

.05(6) + 0.95[23(0.5)-10] = 0.3 + 1.4 = 1.7BBs.

You clearly need a hand that is better than half your opponent’s range if you are to have at least 50-percent equity. You need a hand with about 44-percent equity in order to break even in this spot. But breaking even is not good enough to make a profit, so to make a small expected profit you need a hand with closer to 46-percent equity against your opponent’s calling range, which is most of his raising range in this instance. If your opponent raises only 15 percent of hands, you need a hand with 46-percent equity against those hands to push. The range of hands with around 46-percent equity against this range is something like 7-7+, A-10+, A-8s+ and K-Qs. You may be surprised by how tight this is, but when you have no fold equity, you need a fairly strong hand to get all-in.

Most players will be raising a really wide range late in a tournament and will never fold. When I am deep in a tournament, if I raise to 2.5BBs from a 30BB stack and someone pushes for 8BBs, I am never folding because I only need to win 33 percent of the time to show an expected profit. Even if I am raising 50 percent of my hands and I know my opponent is pushing the top 10 percent of hands, I am usually getting the right price to call.

Now, say I raise to 2.5BBs and it is folded to you on the button with an 8BB stack. My range is 50 percent of hands. Which hands should you push
You have no fold equity, so that part of the equation is irrelevant. It now becomes just

19.5(}) - 8 = 0,

so you need to win 8/19.5 = 41 percent of the time to break even. All you have to do now is figure out which hands have more than 41-percent equity against 50 percent of hands. Remember, you want higher than 41-percent equity because that’s the break-even point. Also, you have to worry about the blinds picking up a hand, which will happen from time to time. So, you need around 45-percent equity against my 50-percent raise-calling range. Your range should be 2-2+, A-2+, K-6+, K-2s+, Q-9+, Q-8s+, J-10 and J-9s. Notice that this range is much wider than before because my raising range is 50 percent instead of 15 percent. Your opponent’s raising range drastically affects your pushing range.