The concept of Expected Value.

[Don Pedro Dinero]

I’ve been thinking about writing this post for a while and I haven’t done it before because I know that explaining this to most people in the gambling section will be like talking to a wall.

However, I have finally made up my mind and I hope that this post can improve some people’s gambling behavior and maybe bring a healthy discussion among those who understand it.

The Expected Value (hereafter: EV) of a certain random event is the number that represents better the average value of that event. This is in general. If we apply the concept to gambling, the EV of a bet is the average win or loss of that bet if we take into account all the possible results and their chances.

I think most mistakes gamblers make come from not understanding this concept.

EV applied to poker.

Most poker players who have studied poker know the concept. Those who haven’t studied it deeply but have read about poker have a grasp of it.
EV is relevant all through the play (preflop, flop, turn and river) but differences in EV are only relevant before river.

I’ve seen people in this forum complaining about losing versus bad players who always complete their projects in the river (last card) and similar comments. What usually happens to these complaining players is that after seeing that they lose versus players worse than them, they get angry, they start playing emotionally and end up losing all and giving up poker.

What they don’t realize is that even if you are a very good player and you very frequently bet your money when you have a better hand than weak players, you will have streaks when you will lose, because losing hands have also a percentage of winning.

For example: if you go all in preflop with AA vs a shitty hand like 22 and you win, what you are no realizing is that you have been 20% more lucky than you will be on average, so you “owe” 20% of those chips you have won to the expected value.
 
I’ve taken a sample of my stats to visualize what I am saying:



That image is showing that I was being luckier than I should, even though I was playing versus players worse than me. So, if the opposite happens, you shouldn’t get emotional, because the green line and the orange one tend to be equal in the long term.

EV applied to Casino Games.

Many people think of gambling in casinos as a solution of their financial problems but what they don’t realize is that they cannot have constant profits, the way it is possible in poker:



I don’t have a program like Holdem Manager for casino games, and I doubt it exists, but I can assure you that if it existed, the orange line, which represents EV, would go constantly down, being the angle (i.e. speed of loss) dependent on house edge and type of game played. The green line, that of the actual money won, would have some spikes up but would tend to match the orange line in the long term.

I am not saying here that nobody should play casino games because I’ve sometimes played them, the same way that I sometimes buy lottery tickets, although I know lottery is also an EV-game. Rather that people playing should learn and know about the mathematical reality behind it.

[BlockEye]

I understand what you are pertaining to this case study. And I'm also certain that most of the poker players know what is the probability of winning and losing especially on poker which we can't guarantee our winning unless all cards reveal. But can you explain further the 20% part that I owe to EV? That something confusing to me.

[tokeweed]

The thing is with poker, you have the control whether to put money in the pot or not depending on what you think your EV is.  Plus there's also the possibility of fold equity, making your opponent fold the winning hand anytime you have -EV.

In casino games you don't have that 'control'.  All you do is put your money in and hope the gambling gods are in your favor.

[rjbtc2017]

In my opinion EV-technique is not for weak people who have easily dominates by their emotion and not by their mind. EV is not a 100% technique based only but also it is based on pure luck. There is losses on your graph but it shows that the profit is getting higher which is good. EV is probably is a good technique for a professional gambler rather than to normal gambler who cannot even control his emotions.

[LuanX3]

Good read. This should be an eye opener for any newbie reading it. Unfortunately, most people that gamble and want to profit do not care about gambling concepts, what they only care about is "will I win money here?" That is a fundamental error of most new gamblers and they end up losing more than they should. People that want to get rich quick turn to gambling but since they are lazy, they do not want to read up on all of these concepts because it would take time and they think that will defeat the purpose of why they want to gamble, which is to get a quick buck.

[YuginKadoya]

Good read. This should be an eye opener for any newbie reading it. Unfortunately, most people that gamble and want to profit do not care about gambling concepts, what they only care about is "will I win money here?" That is a fundamental error of most new gamblers and they end up losing more than they should. People that want to get rich quick turn to gambling but since they are lazy, they do not want to read up on all of these concepts because it would take time and they think that will defeat the purpose of why they want to gamble, which is to get a quick buck.

Well the mindset of every gambler should change, the way they think about just winning in every bet is not good at all and if they end up addicted to gambling then nobody can do a thing even if we spout good reason why not to gamble or giving an advice to be a great gambler they would just think about winning more, but as the bet goes on there will be a lot of risk involve if you don't change your mind set.

[eternalgloom]

In my opinion EV-technique is not for weak people who have easily dominates by their emotion and not by their mind. EV is not a 100% technique based only but also it is based on pure luck. There is losses on your graph but it shows that the profit is getting higher which is good. EV is probably is a good technique for a professional gambler rather than to normal gambler who cannot even control his emotions.

That's the thing, for amateurs it could actually be a bad thing to play games like poker and thinking that they're good at it because they've heard that poker is a +EV game.
Then they fail to actually monitor their wins and losses in the long term and get totally blinded by their perception that they are a supposedly good player.

I really think that there are a lot of unsuccessful poker players that are just making themselves believe they're +EV when they're not.

[Aleister Crowley]

Good read. This should be an eye opener for any newbie reading it. Unfortunately, most people that gamble and want to profit do not care about gambling concepts, what they only care about is "will I win money here?" That is a fundamental error of most new gamblers and they end up losing more than they should. People that want to get rich quick turn to gambling but since they are lazy, they do not want to read up on all of these concepts because it would take time and they think that will defeat the purpose of why they want to gamble, which is to get a quick buck.

Well the mindset of every gambler should change, the way they think about just winning in every bet is not good at all and if they end up addicted to gambling then nobody can do a thing even if we spout good reason why not to gamble or giving an advice to be a great gambler they would just think about winning more, but as the bet goes on there will be a lot of risk involve if you don't change your mind set.

when a person goes straight to gambling without knowing any ground and at that moment they are defeated. and that's when they start losing their minds to gamble .. and then they will not care about anything just will try to restore all the defeat they suffered ..

[Don Pedro Dinero]

I understand what you are pertaining to this case study. And I'm also certain that most of the poker players know what is the probability of winning and losing especially on poker which we can't guarantee our winning unless all cards reveal. But can you explain further the 20% part that I owe to EV? That something confusing to me.

Yes, of course. I think many people don’t understand that part and it is very educational to explain it.

As I’ve said, the probability of winning when you go all in preflop holding AA vs your opponent holding 22 is 80%.

“Owing” is a metaphor I use for saying that, when you win that hand, you are being 20% luckier than you will be on average, because if you play that AA vs 22 a million times, you will win 800.000 times and lose 200.000 times. 

The average return of that bet is just 80 big blinds, whereas you have won 100 big blinds because you have won that particular bet. But play long enough and you will give back EV what you “owe”.

So, after winning that hand, if you see a graph made with a program like Holdem Manager (the one I use), what you will see is the green line (the winnings one) going up 100 big blinds but the orange one (the EV one) going up just 80 big blinds.  So that gaps shows you what you “owe”, 20 big blinds, 20% of what you have won. (Here I am assuming that we are playing a tourney, for example, where there is no rake. If it was poker cash, we would need to deduce 4 or 5 big blinds for each due to rake that casino takes.)

Above I put an image representing a poker session where I “owed” 200 big blinds (first image), although I was probably always betting when I had more chances to win than mi weak opponents. But if you have a look at the second image you will see that it is EV who “owes” me some hundreds of big blinds. The important thing is play well, making EV+ movements because what you “owe” and what EV “owes” you will get equal in the long term, so there will be no “debt”.

This takes me to another concept. That of variance. This can be applied to poker and casino games, as it is a mathematical concept as well.
In poker what is normal is having long streaks where you “owe” big blinds and other where EV “owes” big blinds to you. Which means that in, like, 50.000 hands samples, sometimes you are being luckier than the average mathematical expected result and sometimes you are having less luck than that average. But the higher the sample of hands or bets, the closer the lines get: the winnings line and the EV line tend to stick together.

[pixie85]

AA is very rare and you have to be prepared that if the game takes longer the opponent might get it and win their money back. I guess that's how it usually plays out if you go on long enough. Just like you can never continue to get good cards your opponents can't keep getting bad ones. The only thing that distinguishes a bad player from a good one is that a bad player won't know when to fold and when to push on with cards that are looking weak but have a potential.
It's not that hard to play with best cards, much more difficult is to know what to do when you're holding something a bit lower like KK or AK and facing an all in from someone else. Go yolo or fold? 

[allthebitandbobs]

the only people who make money at poker or the casinos the goverment and maybe 3-5  % of the every best players .Unless your playing a very low rake private game where you dont have to pay tax on winning your wasting your time (unless your palying for the fun) 

[BlockEye]

I understand what you are pertaining to this case study. And I'm also certain that most of the poker players know what is the probability of winning and losing especially on poker which we can't guarantee our winning unless all cards reveal. But can you explain further the 20% part that I owe to EV? That something confusing to me.

Yes, of course. I think many people don’t understand that part and it is very educational to explain it.

As I’ve said, the probability of winning when you go all in preflop holding AA vs your opponent holding 22 is 80%.

“Owing” is a metaphor I use for saying that, when you win that hand, you are being 20% luckier than you will be on average, because if you play that AA vs 22 a million times, you will win 800.000 times and lose 200.000 times. 

Now I get it. That 20% is the assume gap for your winning based on your sample cards in hands of both players. Sorry for noob question, Hahaha. BTW this whole explanation is just for telling that there are no guaranteed winning even if you have the strong hand due to many variances in the result at the end of the game. Thanks for knowledgeable explanation mate. Kudos!

[Don Pedro Dinero]

I understand what you are pertaining to this case study. And I'm also certain that most of the poker players know what is the probability of winning and losing especially on poker which we can't guarantee our winning unless all cards reveal. But can you explain further the 20% part that I owe to EV? That something confusing to me.

Yes, of course. I think many people don’t understand that part and it is very educational to explain it.

As I’ve said, the probability of winning when you go all in preflop holding AA vs your opponent holding 22 is 80%.

“Owing” is a metaphor I use for saying that, when you win that hand, you are being 20% luckier than you will be on average, because if you play that AA vs 22 a million times, you will win 800.000 times and lose 200.000 times. 

Now I get it. That 20% is the assume gap for your winning based on your sample cards in hands of both players. Sorry for noob question, Hahaha. BTW this whole explanation is just for telling that there are no guaranteed winning even if you have the strong hand due to many variances in the result at the end of the game. Thanks for knowledgeable explanation mate. Kudos!

Yes, it is exactly like that. But what seems a noob question after realizing about it, is what many people don’t realize. 

And the side lesson of it is that you shouldn’t get angry and play emotionally when losing with AA vs 22, which is something I see every day. Keep playing like that, and profits will come.