Say we have a $1 million raffle that has only two tickets: a winner and a loser.

I give you a random ticket and tell you that you MUST sell it. How much money should you sell it for? (I.e. how much is it worth?)

**A. $1 million?**

No, because it could just as easily be worth $0.

**B. $0?**

No, because it could just as easily be worth $1 million.

**C. $0.5 million?**

Yes. This is the expected value of the ticket.

Notice that the holder of the winning ticket will never actually get $0.5 million. They will either get $0 or $1 million. We just use $0.5M as the expected value. If you sell it for more than $0.5M, you made money on the deal. If you sell it for less than $0.5M, you lost money on the deal.

Note: We got $0.5 million by multiplying the odds of winning (0.5) by the amount of money you would win ($1 million).

You would use the same strategy in poker, where the "value of the winning raffle ticket" is the money in the pot, and the "odds of winning the raffle" are the odds of your poker hand winning.

Another way to think about this is from the point of view of the raffle creator.

Say I am giving away $1 million in my raffle again with two tickets. How much should I sell each ticket in order to break even?

Well, if I am giving away $1 million, I want to make sure that I am getting $1 million back, otherwise I will be losing money (if I sell it for less), or making money (if I sell it for more).

**A. $1 million per ticket?**

No, because then I will take in $2 million total (2 tickets * $1 million each).

I would make money in this case.

**B. $0 per ticket?**

No, because then I will take in $0 total (2 tickets * $0 each).

I would lose money in this case.

**C. $0.5 million per ticket?**

Yes, because now I will break even by getting back $1 million (2 tickets * $0.5 each).

1I just hit +1 just by reading the title. Very good question. – Radu Murzea – 2013-09-01T06:41:24.650

This is too short, so here is my quick "answer". Try explaining to yourself, simply but no simpler than is necessary. Write it down, keep honing and refining it. Put a few attempts up on the "chat" area, and maybe we can help. I'd be pleased to. – Toby Booth – 2013-09-01T20:09:54.593

EV = The average amount you expect to win or lose on the hand you are playing or the play you are making – RowdyDDD – 2013-10-03T09:38:12.573

Have you already taught them how to calculate simple probabilities like OESF draw on turn, hitting a set with underpair, 8-outer

2#of streets remaining type stuff? Because without being able to calculate the basic hand outcomes it's impossible to fully grasp EV. – Matt Langan – 2014-01-15T13:13:42.917@mattatmusiclist I have filled them in on basics, and crude math (not technically correct rounding and approximations), such as how to figure out how many cards they can hit, how much each card is worth (2% for simplicity and ease of understanding) and how to figure out their chance of hitting it (basically double your odds if there are two cards to come etc). I don't expect them to grasp advanced poker concepts overnight, so I'm just trying to inform them sufficiently and send them off on the right path to becoming a decent poker player. – Dom – 2014-01-15T15:42:43.760

Yea that's absolutely a sufficient starting point for this, and my own math isn't much more advanced than that. – Matt Langan – 2014-01-15T16:36:25.460

P.s. Is it necessary to calculate evs to be a good poker player? – ghosts_in_the_code – 2016-03-07T15:02:28.877

@ghosts_in_the_code it's an additional tool for decision making. Sometimes, when you think your cards are too awful to call a bet, calculating EV tells you that regardless of your cards you should make the call. Conversely, when you think your straight and flush draw are worth calling any bet, calculating EV tells you to fold. It ties your decisions to pot size and probability which is better than probability alone and/or gut feeling. – Dom – 2016-03-07T18:29:01.870

@Dom But then doesn't it take time to calculate the probability of, say getting a higher 2 pair than the opponent. How does one do that mentally in the middle of a game? – ghosts_in_the_code – 2016-03-08T03:41:23.403

@ghosts if you think they've got a higher two pair you should be folding to any bet. You can't know their cards before you see them, you can only guess based on their actions. Thats why I said an

additionaltool, because you need to employ various methods simultaneously. Calculations don't have to be exactly right, just within a few percent and after doing them a few times it gets easier and quicker. – Dom – 2016-03-08T07:51:25.230