Here it is, the latest free online poker article looking poker math and how it’s used in the the young aggressive style of play known to many as school 3 poker. Read and learn my friends
Hi again, everyone! Sorry for the delay in this article, what with Thanksgiving holidays, some gift shopping, getting sick, and setting up a new computer I’ve been relatively busy recently and haven’t made time to write another article. My apologies! Hopefully things will quiet down now and we’ll be getting back to roughly 1 article per week.
Today’s article is going to focus on some basic poker math, from basic tips and tricks to applying math at the table to help you make profitable decisions. I don’t really want to waste more time on the intro, so on to the poker!
Some people may be surprised that poker is a math-based game.
When it comes down to it, poker is all about percentages, frequencies, and concepts like implied odds. Sure, there are elements of chance in poker. The best player in the world can lose for 10,000 hands, and even the worst players are sure to win big pots at times.
But making profitable decisions all boils down to the math. Odds of hitting your cards, weighting your opponents’ ranges towards certain hands, and understanding how to exploit your opponents based on their tendencies (which can be broken down into percentages).
As with any topic (in poker or in general), we should thoroughly ground ourselves in the basics of poker math before moving on to more complex mathematical topics (things like balance, ICM, and equilibrium play (and no, I don’t expect you guys to have any idea what those mean! Don’t worry!)).
Fortunately, basic poker math is very simple, and there are several easy-to-remember tricks to help you with your calculations.
2 Core Concepts
The two most basic math concepts in poker are calculating your outs (and consequently your percentage chance of hitting one of them), and calculating pot odds.
For those who don’t know, an “out” is a card that you feel will improve your hand to the best hand.
> Let’s say you know your opponent has top pair on the flop, and you have 4 clubs (2 in your hand and 2 on the board).
>There are 13 cards of each suit in the deck, and you know that if you hit a pair your opponent will still have a better hand than you.
> There are 9 (13-4) clubs left in the deck – for now, we’ll consider it irrelevant that your opponent may hold a club – out of the 47 cards left unknown (you know 5, your 2 hole cards and the 3 on the flop), 9 are clubs.
> You also know that since your opponent has top pair, if you hit a club you’ll improve to the best hand, so the 9 clubs are your outs.
Here’s a simple rule of thumb which is very very important.
> On each postflop street, any given card has about a 2% chance of coming (1/47 on the turn, 1/46 on the river).
> Therefore, you have approximately an 18% chance to hit on the turn, and another 18% chance to hit on the river.
If you’re placed in a situation where you’re forced allin, you realize the 36% chance to hit one of your 9 outs (18% on 2 streets), but remember that you may face another bet on the turn if you’re not allin, so you may have to fold before seeing the river.
For the sake of simplicity, we’ll assume the odds of hitting runner-runner 2 pair, a runner-runner straight, etc is negligible (in reality you maybe have 9.25 or 9.5 outs as opposed to just 9).
Are also extremely important, as without understanding the concept of pot odds we really have no idea if a call will be profitable (in postflop spots and allin spots especially).
Let’s say we’re HU and each player has 10bb stacks.
> Player 1 goes allin preflop. Player 2 has to decide whether to fold or call.
> The pot is now 11bbs (10bb from player 1 and the bb posted by player 2), so player 2 has to decide whether or not to call 9bb for the chance to win 11bb.
This is generally expressed as a ratio, the size of the pot to the size of the call needed. In this instance, the pot odds would be 11:9 (11 to 9). Simplified, this is approximately 1.2:1.
This means that for a profitable call, player 2 has to win 1 time for every 1.2 times they lose (or, in other words, once out of every 2.2 times).
When a player is getting 1 to 1 on their money, they need to win the pot 50% of the time to break even calling. They’re profitable if they win any more than that.
Getting 2 to 1, a player needs to win only 33% of the time to break even calling (1 win for every 2 losses, or 1 win out of every 3 pots). This is why when we’re short stacked it’s correct to go allin lighter and call allin bets wider.
The blinds represent a large percentage of our chipstacks, giving us the pot odds to call (remember, if we’re even winning 35% of the time getting 2 to 1 it’s a profitable call).
The key with pot odds is to put your opponent on a range of hands and calculate the equity of your hand against that range. This is tricky, and requires lots of practice.
When faced with a call or fold situation, though, it comes down to estimating your outs against your opponent’s range (count your outs and use the rule of 2% and 4%) and compare that to the pot odds you’re getting.
In the example above where we had 9 outs on the flop with a flush draw, our call is profitable if we’re getting roughly 2 to 1 or better.
We have ~36% chance to hit our flush and win the hand, and getting 2 to 1 pot odds we need to win 1 time in 3, which is 33%. So we should call, as we make money long term even though we win the pot well under half the time.
If we’re getting 1 to 1 odds, though, we need to win half the time. We only win ~36% of the time, so we can easily fold.
It’s important to remember, though, that pot odds are only perfect in call-or-fold spots when our calling ends the action in the hand, either because our opponent is allin or it’s on the river and our call or fold will end the hand.
When there’s future action (we decide to call on the flop and there’s turn play), pot odds won’t be perfect for our turn decision, even though it’s rarely if ever wrong to fold when we’re getting direct odds to call (we have 9 outs on the flop and are getting 8 to 1 when we only need about 4 to 1 (20%, we have ~18% equity) to continue, for example).
Warning, now it gets more complicated.
If you’ve grasped everything up to this point, you’ve already learned some important concepts from this article.
If you have trouble understanding this, feel free to contact me (details at the end of the article) or come back to it at a later point. This is an intermediate concept in a series geared towards beginners.
For spots where there’s future play, there’s another (slightly) more complex concept, called implied odds.
Calculating implied odds is an attempt to estimate how much future value we get out of our hand when we do hit. While calculating outs and pot odds are an exact science (we have a 36% chance to hit by the river and are getting 2 to 1 on an allin, so we call!), implied odds are just an estimate and are imperfect at best.
The best way to illustrate the concept of implied odds is by setting up an example with super deep stacks.
> Let’s say we’re HU against an opponent and we’re each 10,000bbs deep.
> Our opponent raises to 3bb preflop and we call.
> We flop a 4 flush.
> Our opponent bets pot (6bb).
> We’re only ~18% chance to hit (assuming our 9 flush outs are good) on the turn and we’re getting 1 to 1 (need to hit 50% of the time for our call to be directly profitable), so according to pot odd calculations we should fold.
Implied odds, however, are attempting to estimate our future value when we do hit.
> Let’s say we call and hit the turn.
> On the turn, our opponent bets pot again (now 18bb, 6bb due to preflop action plus his 6bb bet on the flop and our 6bb call).
> We flat again.
> Our opponent pots river (now 54bb due to the 18bb pot on turn plus the 36bb bet and call), and we raise to 150bb and get called by our opponent’s top pair.
Even though we weren’t getting the pot odds (also called direct odds) to call on the flop, we called 6bb on the flop for the chance of winning a much larger pot when we do hit (due to our opponent’s turn and river bets).
Against an opponent who will be aggressively betting the turn and river a high percentage of the time, we can definitely call the flop bet (and maybe even the turn bet) even when we know we don’t have the best hand.
> In the example, calling 6bb on the flop allowed us to win a ~300bb pot on the river.
> That’s ~300:6, or ~50:1!
> We effectively got ~50:1 on our money, and we only needed ~4:1 (remember, 9 outs = ~18% to hit on each future card).
But this is where implied odds is an imperfect science.
While in the specific example I gave we did effectively get 50:1, let’s say our opponent pots turn and river with any hand, but only calls our river raise with top pair.
> Let’s also say our opponent has top pair 20% of the time (just making up a number here).
In that case, our calculation becomes more complicated.
> On the turn our opponent puts in another 18bbs every time, and on the river our opponent puts in another 54bbs every time, but our raise to 150 is only called 20% of the time.
> This means that the value of our raise is 30bbs (150x.2).
> So long term, we have to call 6bbs on the flop to win 102bbs (18 on turn + 54 on river bet + 30 from our river raise).
Our implied odds aren’t 50:1 here, they’re 102:6, or 17:1. This is far better than the ~4:1 we needed to call the flop, so it’s still profitable of course.
But in reality the calculations are far more clouded.
> Let’s say our opponent is only betting the turn with top pair and is shutting down on the river without top pair top kicker?
> Or our opponent is betting top pair on the turn only 70% of the time and is betting the turn as a bluff 15% of the time (with his bluff range)?
> It’s not really feasible to sit at the table (or at your computer) trying to calculate the exact implied odds of a play.
Implied odds are at best only an estimate, and in reality will never be perfect. This is unlike pot odds, which are just a brute mathematical concept.
To try and more accurately “guess” implied odds, we need to think about our opponent’s tendencies (as usual).
> If our opponent is loose and aggressive, our implied odds are usually much higher than our direct odds.
> If our opponent is tight and nitty, our implied odds and direct odds are usually closer.
Generally, though, the concept of implied odds teaches us that it’s often profitable to draw even when we don’t have the direct odds to do so.
We have to estimate our implied odds to know what the “true” cutoff is for when chasing our draws is mathematically unprofitable, but this is informed guesswork at best and it takes a lot of practice to even be passable at.
It has to do with putting our opponent on an accurate range and accurately assessing what they’ll do at each future action with each part of that range.
Reverse Implied Odds
The last concept I’ll introduce here is called reverse-implied odds.
We have to take into account those times when we hit our outs and we still don’t have the best hand.
This can be through our (assumed) out either improving us and our opponent (ex. we hit our flush out but it gives our opponent a higher flush), or our opponent still having a better hand than us if we hit (ex. we turn top pair but our opponent has a set).
In general, calculating reverse-implied odds is much simpler than calculating implied odds.
When we put our opponent on a range, there will be hands that improve when we improve, and this is easy to account for.
> Let’s say we have a queen high flush draw on the flop and our opponent’s range is top pair+ (top pair, overpairs, any 2 pair hand, any set) and any flush draw.
> We should realize that this range includes ace high and king high flush draws as well as 2 pairs and sets which can improve to boats even when we hit our flush.
If you were able to grasp the math presented in the implied odds segment, you’ll definitely be able to figure out the math behind this (hint: relate implied potsize to percentage that villain’s range improves to beat your hand when you hit and subtract this from implied potsize, then recalculate implied odds with the new potsize), so I won’t delve into that too deeply.
Again, the degree to which reverse-implied odds affect your implied odds varies greatly.
> Against a wide, aggressive opponent it will generally be pretty negligible
> While against a meganit who only raises with the nuts it will be quite substantial (at times even making your implied odds less than your direct odds, although extremely rarely).
Complex section over, closing and some advice
I know the implied odds and reverse-implied odds sections were quite a bit to handle and were a bit beyond the scope of a beginner series.
That said, they’re important concepts to understand (even if you don’t utilize that understanding effectively at first), and a free online poker site like NoPayPOKER is a great place to play until you have a solid understanding of the game and can make the jump to real money play.
> I would also suggest downloading pokerstove (http://www.pokerstove.com/) or Equilab (http://www.pokerstrategy.com/software/10/), both of which are free, and messing around in them to see how the equity of different hands matches up against various ranges.
I’ll probably write an article on these (and other) tools at some point, but for now just mess around and see how hand strength changes with regard to board texture, against different ranges, in multiway pots, etc.
In order to use pot odds and implied odds, you need to be able to accurately estimate your equity against your opponent’s range, and you might learn some things that surprise you!
If you have questions about any of the concepts in the article (estimating outs, pot odds, implied odds, reverse-implied odds) or about the tools I recommended (pokerstove and equilab), feel free to comment on the article here, on the NPP facebook page, talk to me (gloves22) in NPP chat, leave me a NPP pm, or email me at firstname.lastname@example.org
Good luck at the tables!
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