This is really one of my chief money makers in our live games, and thus very -EV explaining the mistakes I've seen many of you make with this seemingly easy to apply rule. Still, in the interest of improving everyone's game, let's take a look at the common mistakes a lot of you make.
Defination
The rule of four and two state that the chances of you winning on the hand is roughly equivalent to the number of outs you hold multiplied by 4 on the flop and 2 on the turn.
Easy enough to remember? Chances are, you have been applying this rule wrongly.
Let's start by understanding how we get 4 and 2 in the first place.
On the flop, there are 52-3-2 unknown cards. That's 47 cards that are mucked, burnt, dealt out or left in the deck. Since the cards are in a quantum state, the fate of each individual card doesn't matter. On the flop, there are two cards to come. that's 1/47+1/46 chance of hitting each of your outs. Add that together and you get roughly 4/100 = 4% per out. If you have 5 outs, your chances of winning by the flop is 4X5 = 20%. Simple enough. You can work out the rule of 2 yourself.
Let's take the most common misuse of this rule, the nut flush draw. What most of you have done really, when holding the nut flush draw is apply the basic concept of the rule. If 20 dollars is in the pot and someone bets the pot, you quickly apply the rule and decide you're getting correct odds at 1:2 to call the flop and see the turn. Now we know that calling a pot sized bet with a flush draw can't be correct, so where did the problem arise?
That's where most of you guys lose money. You took the rule and never bothered to understand how it worked. This rule only works if you are ALL IN on the flop or turn, respectively. You can't call 1:2 on the flop and 1:5 on the turn. That's only for all ins! You don't magically have twice the chance of drawing to the flush on the turn card than on the river. The double odds are because you are already all in and paying for TWO cards and not one.
Sunday, April 6, 2008
sunk costs and you
I've been meaning to write about this really cool topic for awhile now. I've procrastinated because I know it's going to raise many questions and take a long time to explain, but here goes.
I'm kinda hoping everyone here knows what sunk costs are, and how they relate in poker. Here's a brief explanation : When you put money into the pot to raise, call or bet, that money is considered your sunk cost. It's money you won't get back again unless you win the pot(investment pays off). In gambling circles, it is considered wise to think of money put into the pot as no longer yours. This helps the average player understand the line drawn between sunk costs and available capital. Inexperienced players lose more money because they consider the money put into the pot as still theirs and thus necessary to protect.
But I digress.
The point of this post is really to discuss two really cool concepts every poker player needs to understand : The sunk cost fallacy and sunk cost dilemma.
Sunk cost fallacy
This is the more common problem. As discussed above, the sunk cost fallacy is the phenomenon of throwing in more good money after the bad. Say you have AK, and re-raised original raiser 15XBB pre-flop and got a caller. You miss the flop, and it gets checked to you. You C-bet about 25XBB and get raised. At this point, let's assume you know you're beat. You've just put in 40XBB into the pot and you're facing a 40XBB raise. The weaker players will occasionally succumb to the sunk cost fallacy. They're thinking : I've put in so much money already, it's just silly to throw this hand away. Especially when there's still a chance I can draw out!
It's easy to kid yourself in this scenario. Hell, I've seen even above average players succumb to this temptation on occasion. I would not be honest if I claim never to have done it myself. Still, if this is a major leak in your game, it would do you well to plug it ASAP. It's not hard to identify, and more often than not, throwing the hand away could make the difference between a winning session and a losing one.
The sunk cost fallacy is not unique to poker players, or even gamblers. One of the biggest fiascoes in recent history demonstrating this mindset was the Concorde experiment. Millions of dollars poured into the development of a super sonic passenger jet before it was determined that the idea was unprofitable. But because millions had already been spent, the sunk cost fallacy clouded the minds of the government entities behind the project. It was more than a decade later before mounting losses forced them to pull the plug.
Sunk cost dilemma
This is the juicy one. It's also the more dangerous of the two, because it happens so often in poker. First, a description:
The sunk cost dilemma is the situation whereby an opportunity is given in various timeframes to decide on the action to proceed or withdraw...and the optimal solution at each of these steps while being to proceed, will actually lead to an overall loss in value. It is in essence the direct opposite of the sunk cost fallacy. Because sunk costs are not taken into consideration, every decision made appears to be optimal, but ends up being detrimental to the overall project.
Now let's consider this in a poker situation(and you'll soon see why this is the more dangerous of the two in poker).
Consider yourself holding KQ of spades on the button. Someone raises preflop and you smoothcall. Flop comes A68 with 2 spades. The guy bets about 1/2 the pot. Assuming you know for certain he has an ace, and your only real chance of winning is hitting your flush, we know your odds of winning this hand is about 33% at best. This is a common situation. You do a quick mental calculation, and realise you will need real odds of at least about 1:6 for a call to be profitable. You already have 1:3 currently, and you believe your implied odds will make up for the rest, so you call. The turn doesn't make your flush, and now he continues to bet 1/2 the pot. You look at the rest of his stack and determine he's going to pay off the flush if you hit. You still need 1:6 real odds, and you think you have it, so you call.
Ok, what was wrong with that?
Conventional poker wisdom(ABC poker) says that so far, you've been playing good mathematical poker. You've been playing the odds correctly. But alas, you have already fallen for the sunk cost dilemma. This may sound really wierd to those of you who play poker mathematically, because this runs counter to the conventional theory. But let's look at what's happening again, this time with a slight twist.
Let's assume the pot was 30 dollars on the flop. Calculating forward, we know the effective stacks here were 120 on the flop after he bets the 15 dollars(half pot). In the scenario above, we are HAPPY he has the 120 left, because that allows us to draw profitably on the turn after we missed. But what if he had shoved on the flop instead with his 135 dollars into the 30 dollar pot? You most certainly would not have had the odds to call it. Not by a long shot. What's the difference between the two scenarios, really? Experienced players will probably explain it away by saying the pair of aces could have got away from the hand if the flush hit on the turn. But they can't really place a value on that option. It's just a way to explain away the uncomfortable discrepancy.
The truth is, we are blinded by our insistence of not taking into account sunk costs. We know taking into account sunk costs invite trouble via the sunk cost fallacy, and so we disregard it, trading it for the lesser evil of the sunk cost dilemma. But that's just the problem. Most of us were taught to look out for the trap of the sunk cost fallacy, but how many of us were actually warned that avoiding the fallacy traps us with the dilemma? Our very confidence of having avoided the pitfalls of the fallacy makes us more vulnerable to the dilemma. It happens all the time in mid-project budgeting, and sure as hell happens often in poker.
It is not what we do not know that dooms us, but what we think we know...and are wrong.
I'm kinda hoping everyone here knows what sunk costs are, and how they relate in poker. Here's a brief explanation : When you put money into the pot to raise, call or bet, that money is considered your sunk cost. It's money you won't get back again unless you win the pot(investment pays off). In gambling circles, it is considered wise to think of money put into the pot as no longer yours. This helps the average player understand the line drawn between sunk costs and available capital. Inexperienced players lose more money because they consider the money put into the pot as still theirs and thus necessary to protect.
But I digress.
The point of this post is really to discuss two really cool concepts every poker player needs to understand : The sunk cost fallacy and sunk cost dilemma.
Sunk cost fallacy
This is the more common problem. As discussed above, the sunk cost fallacy is the phenomenon of throwing in more good money after the bad. Say you have AK, and re-raised original raiser 15XBB pre-flop and got a caller. You miss the flop, and it gets checked to you. You C-bet about 25XBB and get raised. At this point, let's assume you know you're beat. You've just put in 40XBB into the pot and you're facing a 40XBB raise. The weaker players will occasionally succumb to the sunk cost fallacy. They're thinking : I've put in so much money already, it's just silly to throw this hand away. Especially when there's still a chance I can draw out!
It's easy to kid yourself in this scenario. Hell, I've seen even above average players succumb to this temptation on occasion. I would not be honest if I claim never to have done it myself. Still, if this is a major leak in your game, it would do you well to plug it ASAP. It's not hard to identify, and more often than not, throwing the hand away could make the difference between a winning session and a losing one.
The sunk cost fallacy is not unique to poker players, or even gamblers. One of the biggest fiascoes in recent history demonstrating this mindset was the Concorde experiment. Millions of dollars poured into the development of a super sonic passenger jet before it was determined that the idea was unprofitable. But because millions had already been spent, the sunk cost fallacy clouded the minds of the government entities behind the project. It was more than a decade later before mounting losses forced them to pull the plug.
Sunk cost dilemma
This is the juicy one. It's also the more dangerous of the two, because it happens so often in poker. First, a description:
The sunk cost dilemma is the situation whereby an opportunity is given in various timeframes to decide on the action to proceed or withdraw...and the optimal solution at each of these steps while being to proceed, will actually lead to an overall loss in value. It is in essence the direct opposite of the sunk cost fallacy. Because sunk costs are not taken into consideration, every decision made appears to be optimal, but ends up being detrimental to the overall project.
Now let's consider this in a poker situation(and you'll soon see why this is the more dangerous of the two in poker).
Consider yourself holding KQ of spades on the button. Someone raises preflop and you smoothcall. Flop comes A68 with 2 spades. The guy bets about 1/2 the pot. Assuming you know for certain he has an ace, and your only real chance of winning is hitting your flush, we know your odds of winning this hand is about 33% at best. This is a common situation. You do a quick mental calculation, and realise you will need real odds of at least about 1:6 for a call to be profitable. You already have 1:3 currently, and you believe your implied odds will make up for the rest, so you call. The turn doesn't make your flush, and now he continues to bet 1/2 the pot. You look at the rest of his stack and determine he's going to pay off the flush if you hit. You still need 1:6 real odds, and you think you have it, so you call.
Ok, what was wrong with that?
Conventional poker wisdom(ABC poker) says that so far, you've been playing good mathematical poker. You've been playing the odds correctly. But alas, you have already fallen for the sunk cost dilemma. This may sound really wierd to those of you who play poker mathematically, because this runs counter to the conventional theory. But let's look at what's happening again, this time with a slight twist.
Let's assume the pot was 30 dollars on the flop. Calculating forward, we know the effective stacks here were 120 on the flop after he bets the 15 dollars(half pot). In the scenario above, we are HAPPY he has the 120 left, because that allows us to draw profitably on the turn after we missed. But what if he had shoved on the flop instead with his 135 dollars into the 30 dollar pot? You most certainly would not have had the odds to call it. Not by a long shot. What's the difference between the two scenarios, really? Experienced players will probably explain it away by saying the pair of aces could have got away from the hand if the flush hit on the turn. But they can't really place a value on that option. It's just a way to explain away the uncomfortable discrepancy.
The truth is, we are blinded by our insistence of not taking into account sunk costs. We know taking into account sunk costs invite trouble via the sunk cost fallacy, and so we disregard it, trading it for the lesser evil of the sunk cost dilemma. But that's just the problem. Most of us were taught to look out for the trap of the sunk cost fallacy, but how many of us were actually warned that avoiding the fallacy traps us with the dilemma? Our very confidence of having avoided the pitfalls of the fallacy makes us more vulnerable to the dilemma. It happens all the time in mid-project budgeting, and sure as hell happens often in poker.
It is not what we do not know that dooms us, but what we think we know...and are wrong.
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