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Betting Against Draws in No-Limit Hold’em

On the 3/25/2011 edition of Killer Poker Analysis, I addressed some theoretical questions about bet-sizing in no-limit hold’em. During the discussion, I said that I’d throw some supplemental calculations in my blog on Saturday. Final tabling the 7:00PM $120 tournament at The Venetian on Friday night and a late dinner with Thrash370 resulted in me staying up way later than I like to now that I’m old and in my 30s – especially since I had to do a coaching session with someone in the UK at 10:30AM Saturday morning. After a long, exhausting, but good weekend, it’s now Monday. To my loyal listeners, my apologies for the delay!

GeeBeeQED, who’s been asking me some awesome questions, posed the following three questions to me:

1) Is it always correct (pre-river) to get opponents to put the maximum number of chips in the pot when we know they’re behind?

2) If there is no folding an opponent that is drawing, is it ever improper to put him all-in prior to the river – blocking his ability to fold a missed draw?

3) Is it ever correct to make a bet that is designed to fold an opponent that is apparently willing to draw against pot odds and is currently behind? (Does it make sense to let an opponent draw against pot odds on every street if he’s willing to put his money in bad?)

When playing no-limit hold’em, it’s important to realize that you should always be playing against your opponents’ ranges rather than making plays to target specific parts of their ranges. But even though these questions focus only on opponents who are magically known to be only on drawing hands, I do think that understanding the answers to these questions is important. (Note that I’m assuming that you’re playing purely with respect to cEV)

Question #1:

If you’re ahead of your opponent, it’s not always correct to get your opponent to call the maximum possible. I attempted to do a bunch of algebra to prove a general point; however, I think a specific example is much easier to understand. Suppose you have AcAd against an opponent with KhQh, and the flop is 7h4h2s. The pot is $100, and you and your opponent both have $40 remaining. Your opponent has 36.566% equity and the flop, and he’ll therefore call an all-in on the flop. Your $EV for going all-in on the flop is:

(Your Equity)(+$140) + (Opponent’s Equity)(-$40) =

(.63434)(+$140) + (.36566)(-$40) = $74.18

Meanwhile, if you check to your opponent with the intention of shoving a non-heart, your opponent will be forced to fold when he doesn’t hit a pair, and he’ll be forced to call when he has a pair. The EV of checking the flop with the intention of shoving the turn on a non-heart is:

P(Non-heart and non-pair)($100) + P(Non-heart and pair)[(Your equity)(+$140) + (Opponent's Equity)(-$40)]

(30/45)($100) + (6/45)[(.68182)(+$140) + (.31818)(-$40)] = $77.70

The EV is checking the flop with intention of shoving the turn on a non-heart exceeds the EV of shoving the flop when stacks are $40. As stacks get deeper, things change. Suppose stacks are $100. Your opponent will still call a shove on the flop because he’s getting proper odds to do so (assuming he’s card omniscient like you are). If you shove on the flop, your EV is:

(.63434)(+$200) + (.36566)(-$100) = $90.30

Meanwhile, if you check the flop and shove a non-heart, your opponent will be forced to fold…even if he hits a pair on the turn. Therefore, the EV of checking the flop and shoving a non-heart on the turn is now:

(36/45)($100) = $80

The general concept here is that if stacks are really short – but deep enough to shut your opponent out of the turn, checking the flop and shoving the turn can be best when you know you’re ahead of a drawing opponent. However, as stacks get deeper, simply shoving the flop becomes preferable to checking the flop and shutting out on the turn.

Question #2

You should always get all-in against an opponent who won’t fold a draw that’s less than 50% to hit. Checking down to the river minimizes your EV in this situation, and your EV is maximized by getting your opponent to put as much in as possible. Note that this question is different from question #1 because we’re now assuming an opponent who’ll never fold – regardless of the odds he’s getting.

Question #3

I was able to think of one particular case where you’d rather fold out an opponent. Let’s change up the example from before slightly. Suppose you have KcQc, your opponent has 8h7h, the board is KhQh5s2s, and both you and your opponent are omniscient. The pot is $100. If you make a bet that clearly doesn’t give your opponent straight-up pot odds, he’ll fold – making the EV of such a bet $100. Your opponent only has 20.455% equity in the pot, but let’s say he’s willing to call a bet of $30 on the turn – a bet that your opponent needs at least 23.077% equity to call. The EV of this bet is:

(35/44)($130) + (9/44)(-$30) = $97.27

Even though your opponent is making a mistake by calling, this bet costs you $2.74 in $EV against an opponent who’s willing to fold to a larger bet. The moral here is that it’s not simply enough to deny your opponent odds – you need to bet large enough to profit more than you would by simply shutting your opponent out of the pot.

Now that you know how best to deal with opponents on draws, note that putting opponents solely on draws is typically a big mistake. Maximizing your performance against the drawing portion of your opponent’s range ultimately needs to be balanced with maximizing your performance against the non-drawing portion of your opponent’s range (which consists of hands your beat as well as hands that beat you). Nonetheless, the ideas presented here should at least give you a rough idea as to how you should consider approaching your bet sizing in no-limit hold’em.

May Your EV Always be Positive!

Tony Guerrera


Feel free to repost this as long as you include the following author box (including hyperlinks):

Tony Guerrera is an established poker author, an instructor at PocketFives Training, a member of Team Moshman, and host of the popular poker strategy podcast, Killer Poker Analysis. Tony blogs about decision optimization on and off the felt at


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