Preflop pot odds and equity

Hi,

I’m trying to develop a +EV opening range for playing low stakes on RP. I’m really just trying to check if my maths is correct for the moment.

First, I’m considering opening with 3.5BB from UTG with an expectation that the big blind and at least 2 others will call the raise. If I raise and get called as expected, I will have bet 3.5BB into an expected pot of 11BB + my bet.

(My bet) / (Potential Return) = 3.5 / 11 = 0.3182.

I have conjured up a range for low stakes RP players that I think represents the absolute tightest that will call a raise. Is it correct to say that my opening range, under these circumstances, should have ~32% equity against the other players?

Many thanks for your time.

Regards,
TA

I don’t understand the logic here. The point of raising is to limit number of opponents on the flop, and preferably being in a heads-up situation. Expecting at least 3 players to call your action will make post-flop play incredibly difficult. With that many people in the hand, you will lose more often than not, unless your opening range is something like JJ+ and AK. In other words, your chances of realizing that potential return are low.

Moreover, what you describe (inflating the pot) is unrelated to expected value. Expected value has to do with a long-run outcome. In essence, it’s about how profitable making a call (in a specific scenario) is expected to be in the long-run.

I appreciate that you are thinking about ranges and math.

More should go into determining your range than simple equity. Your calculation doesn’t include fold equity (you can win the pot outright) and the value of being the preflop aggressor.

Two other factors are implied odds and reverse implied odds. Implied odds means you can win more later in the hand than what initially goes in the pot. Suited hands are more likely to make flushes and connected cards are more likely to make good straights, so they can help “crack” your opponent’s hand to win a big pot (although small flushes have reverse implied odds as well). Reverse implied odds is when you are more likely to lose more later in the hand. Hands that are more likely to be second best in a huge pot (for example, Q9) can have reverse implied odds. You are less likely to have the nuts and more likely to have a hand like top pair with a mediocre kicker that can lose big pots.

You also want to play hands that flop well versus hands that don’t, and that means not playing some hands with high overall equity (eg A6o) and instead playing hands with much lower overall equity (eg 54s). You want hands that flop monsters and draws and that hit a variety of boards instead of playing every ace and king with bad kickers because they have more equity.

And finally, play hands you know how to play. Some players may be +EV with suited connectors and others may be massively negative. It’s easier to set mine than try to figure out what to do when your A9o misses. So, everyone’s range will be somewhat different. I recommend playing a range including Axs, suited connectors and some gappers, broadways, pocket pairs, but at low stakes you can probably only play 99+/AQ+ and still be a winning player.

Hi @JoeDirk,

Yes, I understand that I shouldn’t just grab a list of starting hands from Equilab and restrict myself to just those hands. If, following your example, A6o was in the starting range calculated by Equilab, I most certainly would swap it out and put in a medium suited connector. That would have very little effect on the equity of my overall range and it would, as you say, increase my chances of hitting more boards, more often.

I’m comfortable with the concepts of implied odds, fold equity and reverse implied odds. My experience on the low stakes tables is that fold equity is mostly non-existent pre-flop and goes through the roof on either the flop or turn. I am reasonably successful at running 3 barrel bluffs as well.

I don’t think that I will change my game significantly but I think it would help if I started playing more hands that had more value than thin air on the flop!

For example, if 32% raw equity is the “magic” number, then it might be profitable to raise those hands, as appropriate to my table position, more strongly than my other hands. The number of players at low stakes who have even heard of “a balanced range” is so low that provided I occasionally raise QQ+ to 3.5BB instead of, say, 10BB, I will be sufficiently balanced!!!

Many thanks to you and @AKFolds for your time and comments. You are both people that I always pay attention to.

Kind regards
TA

@AKFolds, yes, you are right, but it has probably been a long time since you played low stakes?

It is not possible, with “realistic” raises to “limit number of opponents on the flop”. It is very well known that even with a 10BB raise, 2 or 3 callers is not at all unexpected.The fact of these players calling such a large raise is, most of the time, no indication of their hand strength.

I suppose I have reduced the field a bit, partially achieving the objective of the initial raise, but I am always surprised if I go the flop less than 3 handed.

I apologize if my response was basic, it’s tough to know how experienced people are with terminology.

If you want to proof EV math, here is a handy calculator (https://redchippoker.com/simple-poker-ev-calculator/)

As far as opening ranges go, I am not an expert on low stakes here (and frankly don’t get why it is enjoyable), but I would lean towards playing a tighter, stronger opening range. Because you don’t need to bluff (and it can actually be a huge mistake because players call too much), I would probably not play suited connectors/gappers or even weaker unsuited broadways. Obviously, it varies by position, but against low stakes opponents and calling stations in general you want hands that flop big, like top pair top kicker, sets, or better. There’s no need to maximize thin value, especially as you will face many multi-way pots.

Thanks again Joe, there is no need to apologise. One of the many reasons that I enjoy your answers is because you are careful to explain the basic principles. Maybe my response came across as snarky? If that is the case, I wholeheartedly apologise.

The reason I, and many others play low stakes, is because we are bankroll limited. My particular case is that I’m cash limited as well which puts buying a “decent” amount of chips beyond me.

There is no pleasure in playing with people who will call or even raise with, literally, any two cards. Having said that, surely that is the ideal situation to be in? I know that with a limited bankroll, I’d much rather not play against someone like you. That is not because of your bankroll, it is about your knowledge.

Regarding your starting hand suggestions, I find that AXs plays well multi-way along with JTs+. These are hands that I don’t need to raise big with preflop simply because of the number of people who will call. A 75% - 150% pot raise on the flop very quickly gets rid of the dreamers.

I currently set mine with 22+ - limping from early position and raising quite large from middle and late position. My principle of “no set, no bet” tends to keep me out of trouble even in multi-way hands and I certainly bet big when I hit - there are too many ways a set can be outdrawn in a multi-way hand!

To conclude, based on your advice in both of your answers here and from reading many other comments and that suggestions that you have made, it seems quite likely that I already have a “JoeDirk” approved range (laughing!) and need to learn to play those hands better in a multi-way pot!

Many thanks again for your time,

Regards,
TA

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No worries. It sounds like you are playing good ranges and have put some thought into it.

My advice to you (and anyone who is having trouble maintaining a substantial winrate) is to really critically look at your game for leaks. If you are playing the right hands, are knowledgeable about the math involved, and just generally thinking through each hand logically, there is no reason why you should not be able to pile up millions of chips.

Buying chips is not necessary, and it is possible to go from the original 10k (or is it 5k?) to several million chips in a few thousand hands without being an aggro crusher. If you want to move up stakes to avoid people who call with any two cards (although they are everywhere) you can do it! What was helpful to me was to look at hands (either as I played or going back later) and think about how I really expected it to be profitable. This enabled me to identify and eliminate several leaks that were costing me chips that seemed relatively minor but actually took a big bite out of my winrate.

The most common leak on Replay is just calling because you like your hand and want to see a flop. So many players open limp, limp behind, or call raises because they see a hand they want to play and that’s it. Then they flop some piece of the board and keep investing more chips or just give up and fold their equity. If you have a clear plan that a certain player will pay you off when you hit or will fold too much when they miss, these individual decisions can make sense, but without a plan many seemingly reasonable decisions become massively -EV.

Other leaks that I specifically had were things like opening suited connectors and hands like JTs from EP in full ring. These hands really struggle out of position against calling stations and are unlikely to be profitable in the long run because you will end up running too many bluffs or just giving up. The other leak was a similar thing with Axs, especially from the blinds. I want to punish limpers and thin the field by taking the initiative, but these hands flop too many draws or outkicked top pairs to be profitable against a field that calls too much. I don’t know what leaks you may have, and would not tell any individual player never to play a certain way, but evaluating individual decisions for long-term effectiveness is the key to improving.

Just some food for thought.

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