The Mathematics Behind 3-Betting - Strategy Article

One of the things I worked on at my 50NL experiment was becoming far more liberal with my 3-betting preflop, especially when I am out of position against position raises. Not only is this good for getting paid off with your strong hands, and establishing a dominant image on the table, it also has a very sound mathematical basis.

I'm going to discuss several scenarios and the mathematics behind them.

First scenario - you have AQ in the BB, and it's folded to the button (decent-ish 22/16 player). He raises pot, with 55. Standard stuff.

You should always be 3-betting here.

Imagine if you called his raise...The flop comes K 9 6 rainbow - you'd obviously check, and he'd make a standard continuation bet and you'd fold, thinking little more about the hand. This, in effect, has reduced about a 50/50 confrontation to about a 66/33 confrontation in his favour, as this is your approximate chance of hitting the flop. You are out of position, without the betting lead, and need to hit the flop to continue.

However, if you were to 3-bet, he'd be calling only for set value and obviously he'd only hit this about 1/8 and suddenly your hand turns to about an 80/20 favourite because he'd almost always check/fold to your continuation bet if he misses his set.

So by raising you have dramatically turned the tables on your opponent and made yourself a huge favourite mathematically, just by making another raise preflop - plus you give him the chance of folding and taking the pot preflop as well.

Second scenario - you have 22 in the BB, and it's folded to the button (same decent player) who raises with 65s. Standard stuff again.

If you call his raise, he'd continuation bet a Q 8 3 rainbow flop for example, and you'd be folding the best hand. Everything is against you - you are out of position, without the betting lead and missed your 7/1 shot to hit a set. And even if you do hit, would you get paid? Unless your opponent has a big hand himself(or loses his mind in this example) then the answer is firmly no. There is obviously a huge chance that a semi-lag or even TAG player would be open-raising his button with a wide range, so why should you just call with 22?

Turning the tables, if you were to 3-bet with 22, which is what I advocate, then he'd either fold preflop, which is fine, or he'd call, you'd c-bet the same flop and he'd fold. So you are forcing him to hit the flop in order to win the pot, not making you hit a hand so you are winning the pot with the best hand, not losing it with the best hand. Even if he picked up second pair or bottom pair he'd likely not continue with the hand.

Obviously your opponent's tendencies are very important when considering your options - a player who raises less than 5% of hands wouldn't be raising his button light, for example, but a 35/25 or a 20/15 even would be doing this a lot. Against a player who raised rarely, I'd be much more inclined to call and see a flop and hope to flop a set because there's more chance he'd have a geniune hand such as a strong overpair which could pay me off when I hit. As I said, even if you call with a hand like 22 and hit against a semi-lag/lag player then he almost always won't be paying you off anyway because he raised light to start with.

Your own image is also important - if it is one of getting out of line then you may start facing 4-bets a lot more because they too realise you are 3-betting far from premium hands yourself.

I hope you enjoyed reading the article, and as always I'd be grateful for feedback.

Dan.