Poker Articles

By Zpaceman | Published Mar 16 2007, 02:32 AM
You’ve made it heads-up in a freeroll for a million dollars; second place gets nothing. You’re even in chips with your opponent, and from the way he’s been playing, you can’t figure out how to beat his game. You limp in holding two hearts, and two more hearts hit the flop. Your opponent insta-shoves all-in. Do you call to draw for a life-changing amount of money? In another scenario with the same cards, there are lots of chips already in the middle when your opponent bets. Do you push all-in?

For my first article for PocketFives, we’re going to cover some of the criteria for making this call or this push. We all see enough bad calls or pushes with drawing hands to know that it is a big leak for a lot of players, so hopefully I can help a few PocketFivers improve their game.

The easiest situation to analyze is calling an all-in bet with a drawing hand on the flop. We just need to count our outs and use the “rule of four” to find our odds of winning the hand: our percentage chance to win the hand = four times our number of outs. The pot odds simply need to offer a better “break even percentage” (BEP) than this. Our BEP = 1 / (Pot Odds + 1). So if the pot is offering odds of 2-to-1, our BEP = 33% and we need 9 or more outs to make the call.

Here’s an example of a hand I played recently that illustrates the odds and also introduces the idea of averaging the number of outs:

http://www.pokerxfactor.com/servlet/pxf?t=hand&handid=49604

The pot is offering odds of just over 1.5-to-1 to call giving a BEP of 40%. We need 10 or more outs to make this a good call. We’ve got an open ended straight draw (8 outs) plus a flush draw (7 more outs) and a pair of nines (2 more outs to a set). All of these 17 outs assume our opponent has a single pair greater than 99 and no hearts, but we also have to factor-in some different possibilities:

1. He’s flopped a set of tens or jacks and is protecting his hand (15 outs)
2. He’s flopped a straight with no hearts (9 outs to a win plus 2 outs to a tie)
3. He’s flopped a pair of tens or jacks and a flush draw with a higher heart kicker (10 outs to the straight/straight flush or set of nines)
4. He’s flopped a higher flush draw (we’re currently ahead but he has a 24% chance of winning)
5. He’s flopped a low flush (7 outs to a higher flush)
6. He’s flopped a high flush (2 outs to the straight flush)

We don’t have time to work out all the percentages with any degree of accuracy at the table, but we can roughly assign an average of 12-13 outs here and, given this puts us well ahead of our BEP, we call. Our actual chance of winning the showdown was 53.3% equivalent to just over 13 outs, so we weren’t too far off. It’s clear that we should fold if we only have a primary draw with no overcards (i.e. an 8 out straight draw like 9s6s or a 9 out flush draw such as 5s6h), especially as its possible our opponent has a flush draw counterfeiting some of our outs. We need extra solid outs to justify a call such as a heart overcard (e.g. Ah6s: 12 outs).

This brings me to the next topic, and this is the one I often see overplayed: pushing all-in with a draw. When we push with a draw we can win in two ways: by getting called and hitting our outs or by getting our opponent(s) to fold. As such we can include a “fold equity factor” in our BEP to see if our move is +EV. It’s difficult to calculate this factor as it depends very much on our opponents, the stack sizes, the tourney situation, etc., but in some cases it is obvious when we have a large fold equity factor and when we don’t. Here is an example of a bad push that I see made all too often:

http://www.pokerxfactor.com/servlet/pxf?t=hand&handid=49603

Given the pre-flop action, I was pretty sure my A6 was ahead, and I played for a check-raise. The button complied, and I was surprised when the BB pushed. Not only was it obvious that he was pushing with a draw, but he also had almost zero fold equity. We have to call 2585 into a 6485 pot (2.5-to-1 pot odds), and the call is only a fifth of our stack. Ts8s clearly has a maximum of 9 outs = 36% chance of winning. The pot odds of this push were effectively 4985-to-4085 = 1.2-to-1 requiring a BEP of 45%. Putting ourselves in his shoes, we need to get a fold significantly more than a third of the time to make this a +EV push, but there’s almost no chance we’re getting a fold in this situation, making this a clearly –EV push.

Again putting ourselves in his shoes, if the flop was Kc4s2s and we had As8s, our push would have been a +EV move, even if we knew our opponent was holding a king. We’d already have 12 outs which is a few percent ahead of our BEP even with a zero fold equity factor. In most cases, when we push a draw, we need to have either some extra outs (like overcards to the flop) or a situation where we’ve got a lot more fold equity. If all we have is a primary draw (8 or 9 outs), then to have significant fold equity we need to have at least enough chips to make the pot odds for our opponent less than 1.5-to-1 and for a call to cost a significant proportion of his stack (40% or more). If we’re able to push in enough chips to make our opponent’s pot odds less than 1.5-to-1, this move only has to work around a third of the time to be +EV.

Let’s say there’s 2000 already in the pot pre-flop and we’re opening the betting with a post flop push holding a 9 out flush draw and no overcards. If our stack is 4000 we’re offering our opponent pot odds of 1.5-to-1. If we get called we’re betting 4000 to win 6000, requiring BEP of 40%. Our 9 outs give us a 36% chance of winning 6000 and a 64% chance of losing 4000. We lose an average of 400 if we get called every time, but we only need to get a fold 20% of the time to break-even. Assuming all 9 outs here is a little optimistic, so reducing to an average of 8.5 outs requires getting our opponents to fold 30% of the time to break even.

Sometimes we get into more complex situations. Here’s an interesting hand that happened a few hands earlier than the last example:

 http://www.pokerxfactor.com/servlet/pxf?t=hand&handid=49602

We connected with the flop in a big way with top pair and an open ended straight draw. When Annette makes a 3/4 pot bet, we can assume she has some kind of a hand including an overpair (AA/KK/QQ), or that she’d paired with the board (e.g. AJ/AT), or she was on a draw. Even if most of the time we’re behind hands including AA, KK, QQ and AJ, pushing our draw is +EV:

• We’re betting 8755 to win 12805 if called requiring BEP = 41%
• We have 13 outs versus AA
• We have 11 outs versus AJ
• We have 8 outs versus KK
• We have 2 outs versus QQ (plus 8 outs to a tie)

Even if Annette has one these hands we have an average of 10 outs = 40% chance of winning, which is already close to our required BEP. We only need Annette to be holding some other hand a small-fraction of the time to make this good push.

Annette said afterwards she had 88, and that shows what a great player she is. To the untrained eye, 88 appears to have 10 outs and a 40% chance of winning. Calling would only cost 6055 to win 12805, requiring a BEP of 32%, but Annette correctly deduced that some of her outs were counterfeited. She probably figured she had an average of less than 8 outs, making a call –EV (she actually had 6 outs).

Playing drawing hands is tricky and requires a good comprehension of pot odds, number of outs, BEP, and fold equity to make consistently correct decisions. Hopefully you’ll be able to use some of these techniques to draw for your life at the tables.