Expected Value

[roo27]

Expected Value
POKER STRATEGY

If you comb through poker strategy books or articles written on this website, you will repeatedly find assertions that poor poker players may win money in the short run but will lose money in the long run. The converse is true for professional and very good players. They may lose money in the short run but will generally win in the long run.

Why is this exactly? It is because of a concept known as expected value (EV). Expected value is your expected return on a wager. For example, suppose you made a bet with me on a coin flip. If it is heads, I give you £100. If it is tails, you give me £1. Should you theoretically take this bet (assuming that the coin is fair and has a fifty-fifty chance of landing on heads or tails)?

Definitely! There is a 50% chance of it landing on heads, meaning you win £100. Thus, your expected win is £50 (0.50 * £100). If it lands on tails, you lose £1. Thus, your expcted loss is £0.50 (0.50 * £1). Your expected profit is the expected win minus the expected loss. Thus, your expected profit is £49.50.

Obviously, you will not win £49.50. You will win £100 or lose £1. However, you should view the bet as "winning" £49.50. Outcomes in gambling are influenced by chance in the short run. However, in the long run, your outcomes will very closely reflect your expected value. If we did the coin flip example a million times, your final profit would be extremely close to £49.5 million.

So how does expected value play out in a poker game? The most clear manifestation of expected value is pot odds theory (pot odds, as well as implied odds, reverse implied odds, etc.). The whole idea of pot odds theory is that you should only draw to a hand when you have a positive expected value.

Other examples of expected value are demonstrated in the advanced moves below.

AcTc
Your Hand

8c7c2h
Board


There are 8 players in the pot and you are the small blind (first person to bet). You check, and the player in the big blind position bets. Three players call. Should you call?

No, you should raise! Why? There is a 35% chance you will hit a flush on the turn or the river. If you hit this flush, you will more than likely scoop the pot. If you raise, 4 players will call, meaning you will only be putting in an additional 20% of the pot. Thus, if this was a £1-£2 game, you would have an expected value profit of £.75 (0.35 * £5 - £1).

Please realize that this is an imperfect example. The expected win only considers the flush draw. You also have overcards, which means you could easily win if a ten or an Ace falls as well. However, there is also the chance that someone may hit a full house, so you'd have to decrease it by that. Someone could also reraise behind you and knock others out, which may decrease your expected value. Nonetheless, hopefully this example shows why some fancy plays are used.

Bluffing and calling bluffs depend on expected value. When you make a bluff, you should have some estimate in your head about the bluff's chance of success. This chance of success should meet with a positive expectation. For example, if the pot is £100 and I make a bluff of £50, I need at least a 33% of the bluff's working (assuming I have 0% chance of winning if I am called). This is because I need to win 1 out of 3 times in order to break even.

Expected value also helps clarify the differences between big mistakes and small mistakes. Big mistakes occur when a player makes a decision that has a very high negative expected value whereas a small mistake is when one gives up a small amount of expected value.

If you plan on playing poker a lot, you should eventually be able to know your expected value of an hour of play. In order to do this, you need to keep accurate records. You should record the amount of time you spend playing, the type of game, and the place where you played. After a while, you will be able to reasonably estimate your expected win or loss per hour of play

Expected value is another reason why you should never play in a poker game that you cannot afford. If you play with scared money, you will be reluctant to play when you have a small edge. You will give up a lot of expected value on some hands, which will probably turn you into an overall loser.

[RedRaven]

roo - thank you. You always give us something to think about - it's because you are a rock star (ok - a poem star)

[Kingcard]

Think about?Who thinks?
Lol...
All i know is if roo's at the table,my "expected value" is one heck of a good time!
Ha!

[miataguy]

NO ONE SAID THAT THERE WOULD BE MATH!!!!!!

[2Shey]

Roo..Could you put that in poem form I can't understand..!!..lol
Your baffeling me ..

[baby]

thanks for the read

[Mac46]

Interesting one Roo. I shall have to think about this..

My initial impression is that is seems wrong as I will always try to see a drawing card as cheaply as possible. However I can see you're arguments in terms of investment strategy.

However what about this..in terms of your example.. If I have 8 7 diamonds or even top pair and raise under the gun a pot sized amount, what do you do there; You are then needing to put in 50% of the pot at 2:1 odds. On the basis of your example you should fold?

Cheers

Mac

[roo27]

Originally Posted by Mac_46

Interesting one Roo. I shall have to think about this..

My initial impression is that is seems wrong as I will always try to see a drawing card as cheaply as possible. However I can see you're arguments in terms of investment strategy.

However what about this..in terms of your example.. If I have 8 7 diamonds or even top pair and raise under the gun a pot sized amount, what do you do there; You are then needing to put in 50% of the pot at 2:1 odds. On the basis of your example you should fold?

Cheers

Mac

now i think this would be a personal chouse and or dependent on your chips stack in relation to the rest of the table ( i'm talking torny play here ) but yes if you play a maths game then yes fold would be the play as the odds on me cathing my cards are out wayed by the pot odds on the chips in play