Lesson 20 – Is 2 to 1 a Good Deal?

Home Poker School Lesson 20 – Is 2 to 1 a Good Deal?

The quick answer: maybe. If I were to offer you two to one odds on a coin flip, it would be a great bet, at least from a probability point of view. The math is simple; I’d be willing to pay you $2 on your $1 bet based upon an event that will happen one time out of two tries. The probability of success is 50%, but you need a probability of only 33% to break even, so that’s a great bet, at least on the surface. You can probably tell I’m hinting about a downside here, so let’s talk about it in poker terms – specifically poker tournament terms, rather than cash or “ring” game terms. Why the distinction? Because in a cash game, if you take a 2 to 1 bet and lose, you can just reach in your pocket for more $$$. In a tournament, losing the hand may knock you out of contention or even bust you. It’s like me offering you 2 to 1 on a coin flip, but you have to bet everything you own. Sure, do it often enough and you’ll bust me, but if you lose the first time we do it, you’re busted and don’t get a second chance. Does two to one still sound good?

My point here is that every bet has a mathematical value, which can usually be measured precisely and a relative value, which is more difficult to measure because it must be done in relationship to other factors. Flipping a coin for a buck is one thing; flipping a coin for your entire net worth is another thing entirely. Fortunately, none of us has to risk our entire net worth on the outcome of a poker tournament, but we do want to finish as close to the top as possible, so we have to examine our bets from both a mathematical point of view and a relative point of view. For example, let’s say you’re in the Big Blind, which is $200 and you have $3000 left in chips after posting. A player in Middle Position bets $700 and everyone, including the Small Blind folds. The pot is now $1000 ($100 SB, $200 BB, $700 from MP player) and it will cost you $500 to call, so you’re getting two to one on your money. Now remember that your $200 blind bet is gone – once it’s posted, it no longer belongs to you, so you don’t use that in figuring odds like this. It’s simply a case of paying $500 to try and win $1000, which is 2 to 1 pot odds. In Lesson 2, I showed you some basic poker math that tells us how to convert probability to odds and vice-versa. Pot odds of 2 to 1 means you need a probability of just over 33% to break even (add 2 + 1 = 3; divide that into 100 and the result is 33.33). So, if we have a hand that we think has a 34% probability of winning, the math says it’s a call.

But there are several problems here. First of all, if the raiser has A-A and we have Q-Q, our probability of winning is only about 20%, so we’re not getting a good “price” for our bet. On the other hand, if our opponent raised with, say, A-K offsuit, our probability of winning is closer to 55%, which makes this a great call with Q-Q. But what if we have to go all-in to make the call? Is the return big enough; is 2 to 1 a good deal? For me, if I were short-stacked, I’d be happy to get all my $$$ into the pot with a pair of Queens. If my opponent has A-A or K-K, I’m basically toast and as the saying goes, “that’s poker”, but I’m a favorite in most other situations. Sadly, most hands you’ll encounter are not as clear-cut as this. What’s more likely is that you’ll hold something like 5-5, K-Jo or A-4 suited (I’m assuming you’ll fold the truly “junk” hands like Q-7o,10-5s, etc.) and calling the bet won’t force you all-in, but it would be a shame to miss a chance to add to your stack. What to do?

First, of course, you have to consider the source of the bet. A Middle Position raise from a player you perceive as “tight” may well mean s/he has a pocket pair of 9s or better or maybe A-Ko, A-Js or K-Qs. Here’s how those hands match up against yours:

Opponent You Your probability of winning
9-9 5-5 19.8%
A-Ko 5-5 55.0%
A-Js 5-5 51.2%
K-Qs 5-5 50.3%
9-9 K-Jo 44.3%
A-Ko K-Jo 26.2%
A-Js K-Jo 24.5%
K-Qs K-Jo 25.0%
9-9 A-4s 33.7%
A-Ko A-4s 31.5%
A-Js A-4s 31.1%
K-Qs A-4s 56.8%

It’s easy to see that calling if you have a pair or a suited A-x is, for the most part, profitable or very close to it. The problem is that you’re really in trouble if your opponent has a pair higher than yours, or if s/he has one of your cards along with a higher kicker, like A-Ko vs. K-Jo. But even there, if the pot is paying you 3 to 1, it’s not the worst call you’ll ever make. These numbers obviously don’t cover all possible situations, but they at least will give you a feel for what you can expect when the pot is offering 2 to 1 on your money. Of course, if your opponent is a “loose” player who might raise with hands like Q-Js, A-10o or 6-6, then your probabilities will look even better, so it’s probably fair to say the percentages shown here are a worst-case scenario.

There is no hard and fast rule that can come out of this discussion because the possibility of your opponent holding a high (Jacks or better) pair skews the numbers quite bit. While every hand is different, I’d be very tempted to call with any pair; any hand with a King, face card and any A-x suited when the pot is paying 2 to 1 or more. That’s the math side of it. The “relative value” side, where I might have to go all in would find me playing any pair above 8-8 and very likely folding everything else, unless I have a stack of less than 5 times the Big Blind. In that case I’d play with any decent hand, like those listed above. If I’m short, but hold an A-x suited or a pair of 8s or better, I’ll likely re-raise to try and win the pot right there, even though my short stack will basically tell the original raiser that I’m desperate, which greatly reduces my “folding equity”.

The important thing to take away from this lesson is a feel for what hands are worth holding in a 2 to 1 pot odds situation. I’ve obviously not covered all of them, so you should continue comparing hands as I did here. My numbers come from the free poker odds calculator that’s available at www.cardplayer.com/. When you get a chance, check out the probabilities for such “classic” matchups, like two overcards versus two lower, suited connectors and a pair versus a higher card and a lower card (10-10 vs. A-9, for example). You don’t have to be exact about the percentages when you’re involved in a hand, but knowing that your hand has a 33+% probability against what your opponent may be holding can earn you a lot of $$$ over the long-term.

I’ll see you here next time.

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