Calculating Drawing Odds

Aug 29th, 1999

In low limits drawing to flushes open-ended straights seems almost automatic. But, what about draws with fewer outs? At some point of your poker career, it becomes necessary to be aware of the pot size and the odds of sucking out. And it becomes necessary to calculate.
For a more technical info on drawing, see Abdul's Theory of Sucking Out.

The following is excerpts from on this subject. Enjoy.


From: (Izmet Fekali)
Subject: Re: Effective Odds and Draws...
Date: 23 Aug 1999 00:00:00 GMT

Gremlin writes:
> HitTheFlop writes:
> >If it's three way with only 3 sb in the pot it's right on the
> >cusp. you're getting 4:1 (3 in pre-flop + yours + opponents) on
> >a 4:1 shot that doesn't always win and doesn't always get paid
> >off. Add to it that on the turn you'll be getting only 3.5:1
> >and will probably give it up. You won't lose much or win much
> >either way. The illusion of action theory might push you toward
> >playing.

It's usually not that simple.

> >Play on the turn is str8foward.


Gremlin writes:
> It is 2:1 on the flop to make the flush by the river. You should
> only calculate it as 4:1 if you only plan to stay in for just
> one card, right? It doesn't make sense to say you're getting
> 4:1 to make your flush on the turn if you plan to stay in for
> both cards, does it??

Staying for one card only or chasing to the river is two separate things. One card only draws (draws with one card to come) are pretty straightforward (as HitTheFlop concurs), especially if one is last to act, closing the action on that round. Not so when one plans to go from the flop all the way to the river.

One has to anticipate future action, raises, check-raises, calls and folds on the current round and beyond. Doing this with a high degree of accuracy is close to impossible; approximations are usually in order. In addition, one can seldom know exactly where one stands (one might be drawing dead, have opponents beat already, some of the outs might not be good, one might win without a showdown, hit a backdoor draw, etc.).

Open-end straight and flush draws on the flop are automatic, except in some tough tight games heads-up (but I presume you are wise enough to stay away from those, right?). It's most often a check-and-call situation (or raise-for-a-cheaper-card-on-the-turn in late position). Another exception is if there are many people in the pot where ram-jam tactics are in order (see Rammin' and Jammin' on a Draw).
In case of slimmer draws (e.g. gutshots), I prefer evaluation on round per round basis. Let's say the game is $10-20, I have a gutshot draw (and nothing much else, for the sake of simplicity) on the flop in a five way unraised pot. Somebody in early position bets; there is one caller. Do I have a call?

I say yes.

Let's look at the method you describe (the "effective odds" method). There is $70 in the pot now. Odds for completing the gutshot draw by the river (two cards to come) are about 16.5% or 5 to 1 against if you plan to take your draw that far. If your opponent bets again on the turn and the third player folds, you'll invest $30 to win about $130 ($70 on the flop + $ 20 bet on the turn + $20 bet on the river + $20 call of your raise - keep in mind this is just one possible scenario). In view of this, the $10 call on the flop seems like a bad idea with 5 to 1 odds and probable $130 payout on your probable $30 investment (You might get raised by the third player if he stays in. OTOH, you might get a free card on the turn).

Yet, experienced players often call in this situation.

IMHO, it's much better to evaluate slim draws (5 outs or less) on a round to round basis:

What if you decide to take a card off and *fold* on the turn if you do not improve? The odds for hitting a gutshot on the next card are about 11 to 1 against. You are getting 7 to 1 from the pot. Not enough? Well, it's plenty enough!

Here, you're getting good implied odds, as you only plan to invest $10, but you'll get a good payoff if the turn card hits you in the nuts. You'll get the missing 4 small bets in future rounds as follows:

$20 from his bet on the turn, $20 from his calling your raise and $20 from him calling you down on the river not believing you went for a gutshot (it's usually good to know your opponents in poker), with $70 current pot, that's a total of $130. If the third player stays in on the turn, the payoff can be much better, of course.

But then again, somebody might hurt your hairy softballs with a backdoor flush on the river... you just can't be sure... but we shouldn't live in fear, either (otherwise, what's the point?).

If the turn card doesn't hit, you *must* fold, unless there are 11 big bets in the pot on the turn (quite impossible in the example above, but a common occurrence in low limit games). If you don't fold at this point (maybe you are on tilt, maybe you have a extrasensory "feeling" about the next card), the whole "implied odds" exercise above is pointless.

My point is, I guess, draws are unbelievably complicated and the kind of analysis above is best done away from the tables. There's just no time to do all this at the tables, where rules of thumb really rock'n'rule. Like, stay with good draws with 6 outs or more, take a card off on the flop for gutshots, never draw to an 2-outer, etc... Be sure to construct your own rules of thumb pertaining your particular situation. A soft no-fold'em game requires a different pair of thumbs than a Binion's $20-40 afternoon hold'em game full of retired geezers you expect to keel over the table any moment now...

Automatic bet counting as the pot grows is imperative; it should be second nature to a serious player. IMO, without this one cannot have even an approximate idea of where one stands.

And keep in mind that above examples are greatly oversimplified. What about overcards, backdoor flushes, bluffs, semi-bluffs, free cards, etc.? It's a great game.

Have fun racking those chips.

P.S. If my reasoning is incorrect, please feel free to comment or flame. I'm willingly sticking my neck out on rgp to get rid of misconceptions as soon as possible. Thanks for your replies.

Izmet Fekali
Burek Experts Ltd.
Catering the World since 1389!

From: (Izmet Fekali)
Subject: Re: Effective Odds and Draws...
Date: 23 Aug 1999 00:00:00 GMT

Gregory Raymer wrote:
> Gremlin wrote in message ...
> >It is 2:1 on the flop to make the flush by the river. You should
> >only calculate it as 4:1 if you only plan to stay in for just
> >one card, right? It doesnt make sense to say you're getting
> >4:1 to make your flush on the turn if you plan to stay in
> >for both cards, does it??
> Maybe you shouldn't make your decision (about whether or not to stay in for
> BOTH cards) until the situation on the turn presents itself.
> Let's say you're the big blind with As5s. 1 caller in mid-position, SB
> calls, you check. Flop is Ks8s6s. SB checks, you check, mid-position bets,

You flopped the nuts here, but it's obviously a typo. Read this as Ks8s6d (or something).

> SB folds. Right now, there are 4 bets in the pot. If you call here, and
> the turn card is a spade, you will probably win greater than 95% of the
> time. Plus, you will probably get at least 1 big bet from your opponent.
> So, you should call. 5 bets in the pot (2.5 big bets). Turn is 2d. You
> check, opponent bets, 3.5 big bets in the pot. Now, if you call, you only
> win 3.5 big bets, plus any money you can get your opponent to put in on the
> river. Thus, unless you're pretty sure that he will call your river bet (or
> that you can get in a check-raise), you should fold here.
> The call on the flop was +EV. The call on the turn was -EV. Even if put
> together they have +EV, it still seems that you should call the flop and
> fold the turn here.

It seems that we have a paradox here. Let's look at the situation this way:

You have better than 2 to 1 odds on the flop if you plan to call all the way to the river. If your opponent bets on the turn, you are getting 6 small bets (3 before the flop, 1 from your opponent betting on the flop and 2 from your opponent betting on the turn) for a 3 small bets investment (1 for a call on the flop, 2 for a call on the turn).

It's a clear call (both on flop and turn).

This reasoning contradicts the reasoning above. Which is correct?

> (Actually, in artificially contriving this hand, I've not played it well.
> So, please ignore how this hand should be played, especially the fact that
> you have 3 aces to hit that might also give you the best hand. It is only
> intended to be an example of calling with a draw on the flop, and then
> correctly folding on the turn, a play that is sometimes correct.)

Right, other outs severely complicate things...

Izmet Fekali
Burek Experts Ltd.
Catering the World since 1389!