Today I’m going to chat a bit about some of the intricacies of a very old game – life (oh wait, I mean poker … they’re just so closely related that it gets confusing at times…). Poker, as I am sure you have noticed, has recently made a huge come-back in the last decade or so and, for many (myself included), has actually turned into a favorite pastime. The best part about all this is what has resulted – the waters are teeming with fish. If you take the time to hone your poker playing skills a bit, finding meals has never been easier – you just need to remember to play the shark and not another fish…I’ve met quite a few people recently that seem to be a bit too hesitant to even play the game. I understand why this is – there’s basically no quicker way to lose a whole lot of money in a very short period of time than sitting down at a no-limit Texas Holdem table; there’s also no quicker way to win a whole lot of money in a short period either… You just need to play smart. Hopefully after reading these little articles you will be able to use some of my advice to muster up enough courage to be able to give the game a try – who knows? … You might like it… I also think that these articles are must reads for many of the self-proclaimed sharks out there as it is always a good idea to step back for a bit and maybe look at the game from a different perspective. More often than not, I think, poker players have a really bad habit of getting stuck in a rut with their playing style – this, of course, leads to bad things … these are the guys that I target from the get-go. The worst thing that your game can become is predictable…
Like life, poker is nothing more than a series of decisions. All of these decisions need to be made in an effort to better one’s position. The great thing about poker is that the probabilities of these choices working for or against you are knowable. In fact, situations arise in poker where you can actually be holding an unbeatable hand (the “stone cold nuts”). There are only two occasions in a person’s life that are universal certainties – birth and death. Apart from those two bookends, everything else has either known or unknown probabilities for helping or hurting you. If the human nature aspect of poker were to be removed, the game is easily seen as nothing more than probabilities playing out. Therefore, the first thing you need to understand is what probabilities actually are…
We’ll start with something simple – a coin-toss. Assuming that the coin in question hasn’t been tampered with it’s pretty easy to understand that the outcome of the toss has equal probability of ending up heads or tails. Getting heads, on average, happens once in two tosses and tails happens the other time. Of course the funny thing about probabilities is that “on average” statement – this is often what leads intelligent people to make stupid decisions. This does not mean that if a coin-toss is done and heads comes up that the next coin-toss will inevitably be tails. In fact, the odds that the next toss will come up tails never changes – it’s always 50%.
Let’s take that simple example and head a bit into the unlikely. It is possible that a coin can be tossed ten times in a row resulting in heads – extremely unlikely (1 in 1024 or approximately 0.09%) but possible none-the-less. Does this change the fact that the odds of the next toss being heads (or tails, for that matter) are 50%? Nope – although it might seem like tails are due, there’s still only a 50% chance of seeing tails on the next toss. The reason that we are inclined to think that “tails are due” is actually just a byproduct of the rarity that we’ve already seen (remember the 0.09% probability). I mean if heads came up again, how unlikely would that be? Well, it would be a 1 in 2048 (about 0.05%) chance to flop heads eleven times in a row. The thing that needs to be remembered is that the odds of flopping heads ten times in a row followed by a toss of tails is also 1 in 2048. The odds are the same for either outcome. The point that I am illustrating here is very important – probabilities do not change due to previous attempts. The coin has absolutely no “memory” of past events and each toss plays as though it were the first…
Yeah, but that’s a coin-toss. Poker’s a much more complicated animal than a coin-toss, right? WRONG! Although the math can get a bit trickier, poker obeys the same rules of probability that a coin toss does – these probabilities are laws of nature. All you need to do is figure out what the probabilities are and use this information to make your decisions. The great thing about Texas Holdem is that figuring out what the actual probabilities are is very easy – all the math is done with whole numbers and you can do just fine with close approximations. This should become evident when I explain the rule of 4&2 a bit later…
Now I’m going to assume that I don’t have to explain how Texas Holdem is played – if you’re reading this posting I’m pretty sure that you’re familiar with the game mechanics. However, if you don’t know how the game is played, I would suggest reviewing the rules (there are many web pages that you can get the rules from) before continuing on as the mechanics of the game must be understood to get anything valuable from what I am sharing. Go ahead … I’ll still be here when you return…
Okay, so now that everybody understands the mechanics of the game I’ll tell you how to win at it. Simply put, all you need to do is lose as little as you can with losing hands and win as much as you can with winners. That’s all there is to it – it’s not rocket science. The key thing is to remember that you are going to lose hands – probability just works that way. Even if the probability of losing a bet is 1 in 100, that bet will be lost 1% of the time (on average). You need to realize this. You will lose that bet 1% of the time (again, on average). You will also win that bet 99% of the time (okay, on average again – I think you get the picture so I’m going to stop reminding about the “on average” thing…). The question then becomes, “Okay, so is there any way to know whether, on any particular instance, it’s going to be a 1%er or a 99%er?” The answer to this, of course, is no. You won’t find that out until after the transaction has occurred. There is, however, something that you have complete control over that can make it so that this bet is always to your advantage – the stakes.
Now the funny thing about poker is that the odds are rarely 1 in 100. This does happen at times, but if you’re still in a hand when you discover that you only have a 1% chance of taking the pot, you did something wrong. To demonstrate this point, let’s quickly go over the procedure for figuring out your percentages at making a hand. It involves math, but don’t let that bother you – as I said, the math is very simple. On the deal, you get your hole cards. Funny thing is that this is where a lot of the newcomers to the game screw up. Regardless of how wonderful those two cards may look to you, you still need three more cards to make your hand. Not only that, but the next five cards that you get will be playable by anyone still in the hand – not just you. Remember that – one man’s garbage is often another man’s treasure. At this point, it’s extremely difficult to actually compute the odds for the plethora of hands that your two hole cards can turn into and this calculation would end up being meaningless. The time for figuring out your probability comes after you see the flop. I’ll speak a bit on pre-flop betting strategies a bit later; for now let’s talk about hand probabilities.
So you’ve called the pre-flop bet and the flop is shown. This is where the actual play begins. What you need to quickly do now is look at your hand and see what you have. Let’s use a common occurrence and say that you have either an open ended straight draw or a four-card flush. What are the odds that you will make that hand? I’ll tell you right now that the odds of making the hand on the next card are approximately 1 in 5 and making the hand with the next two cards are 1 in 3. Also, if you miss your hand on the turn, the odds for hitting on the river will be 1 in 5. How did I get these odds? It’s all about “outs”.
If you’re holding a four-card flush on the flop, there are exactly 9 cards that can hit to make your hand (if it’s an open-ended straight draw, there are 8). These are the numbers that you need to know and they will become easy enough to get with a bit of experience. (The 9 cards are the 13 cards of that suit minus the four you are holding and the 8 cards are the 4 suits of the 2 cards that would complete your open-ended straight.) Okay, so you’ve figured out the number of “outs” that you have; now you need to come up with the probability of one of these outs hitting. This is easily computed by realizing that a standard deck of cards consists of 52 cards. You are currently seeing 5 of these 52 cards (your two hole cards and the flop) which leaves 47 cards unknown. The odds of filling your flush on the next card are 8/47 or slightly less than 1/6 (for the open ended straight draw it’s 9/47 or slightly more than 1/5). Remember that approximations are good enough which makes a 1/5 probability for each case usable. The great thing is that, even if you don’t make your hand on the turn, the odds really don’t change for making the hand on the river. (Your 8/47 or 9/47 becomes 8/46 or 9/46 since the only thing that changed was that one more unknown was seen – once again, these simplify down to approximately 1/5 … pretty cool, huh?)
I also mentioned that the odds of hitting within the next two cards were 1/3. This is easily obtained by ORing the probabilities of hitting on either the turn OR river. Anyone who’s ever studied probabilities and statistics knows that an OR is easily computed by simply adding the probabilities of each outcome. In our example this would be 1/5 + 1/5 or 2/5. Keeping in mind that approximations are good enough and realizing that an increase by one to the denominator is actually being a bit on the cautious side (2/5 is more likely than 2/6), you can conclude that the probability of filling this hand on either the turn or river but staying to see both is 1/3. See how easy this is? The best part about all this is that you really don’t need to do that math. I illustrated this as a case in point to demonstrate that all you need to know in order to figure out your probabilities for filling hands is the number of “outs” available. Since many people seem to have some difficulty with fractional mathematics, you will be glad to hear that all of that can be avoided with the rule of 4&2 that I mentioned earlier. Now pay attention, things get easy at this point…
Okay, so let’s take our four-card flush and utilize the rule of 4&2 to come up with our odds. The simple trick here is all you need to do is multiply your number of outs by 4 to get an approximate estimation of hitting the hand on either the turn or river and multiplying the outs by 2 if you miss on the turn to figure out the odds of hitting on the river. It doesn’t get any easier than that. For the four-card flush remember that the number of outs was 9, right? Okay, so 9x4 is 36. That basically says that you have a 36% chance of filling the hand on either the turn or river – awfully close to the 1/3 (33%) chance calculated above. If you miss on the turn, you would then have a 9x2 or 18% chance of hitting on the river – a slightly pessimistic version of the 1/5 (20%) chance calculated above. Since approximations are good enough, this rule of 4&2 is usable. It just doesn’t get any easier than that…
Now you know how to very quickly calculate the probabilities for making hands. These tricks are known by pretty much all of the decent poker players out there and I’m sure that you can easily find this same information in pretty much any poker book or DVD out there; however this is only the beginning of my discussion on poker. I plan on covering many more of the not-so-widely-known intricacies in later posts so check back from time to time and see what I have to say. Who knows, you might find some of it rather interesting…
bis später,
Coriolis
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