I am glad that you have read the other post and was able to see my point. I have no objection to the conclusion that EV doesnt change when you consider the long run.

My objection is to what Andy was saying:" run as many times as you like "

That is just simply not correct.

If anyone followed my calculation would understand this:

If you are the favourite, your best chance to win the whole pot is to run it once. When you run multiple times, your chance of winning that proportion of the pot is going to be reduced. In your own example, this is to be shown by the reduced equity in the 2nd run:

1st run: $488.64
2nd run: $477.27

Here the 2nd time your equity is reduced. That is for the same 500 dollars, your equity is higher in the first run.

Sure it doesn't matter if you add them all up and talked about EV, by my point is very simple, if run it multiple times your are getting less in your chance of winning the whole 1000.

Think it this way, if you deal every card in the deck out run by run, your opponent will almost always get a proportion of the pot. (apart from rare situations where your killer card presents itself in the same run with his) In this situation, he is getting a fair shot at 'his' equity.

If now, everybody plays this way, all you have to do is to pay the exact money to get your equity and that would be a 'ultimate fair game' Because everyone makes the correct decisions and everyone gets his/her deserved equity (which is now the money they are paying), in a game like this everyone would go home with the money they brought in.

But thats not poker. That would make the game pointless.

Now, I think I have explained my point fairly simply, whether to appreciate it or not, it's up to you.

As for your remarks on statistics and other things. Let me put it this way, I am NOT just a guy who had taken a statistic course in college.

Allow me to make a couple of points:

(1) The equity of the two runs are actually equal, unlike your claim. Your claim for the equity of the second run is $477.27, which actually only includes the times when you've won the first run, and also win the second. However, your second run also includes equity from the times where you've lost the first run (an equity of $11.36), which gives you a total second run equity of $488.63. You can't simply ignore this equity here.

Now the equity of the first run is equal to $488.64 according to the calculations, which does seem to imply missing equity of a penny in the second run. This is just a particular nuance of the situation where we round to the nearest penny. As it turns out, the equity of the first run is exactly equal to 488 + 7/11, where 7/11 equals .63 repeating. Since the next digit is larger than 6, we round up, creating equity of $488.64. With the second run, the combined equity is 488 + 7/11 + 488 + 7/11 = 977 + 3/11, where 3/11 = .27 repeating, which rounds down, hence appearing to create the illusion of a missing penny.

(2) The other problem with your arguments, however, seems to be your insistence on there only being value in winning the whole pot.

In this situation, you can choose to win the whole pot 97.73% of the time and lose the whole pot 2.27% of the time.

Or you can choose to half the pot 4.55% of the time and the whole pot 95.45% of the time.

While some people find value in winning the whole pot the extra 2.27% of the time, other people find value in making sure that they NEVER walk away from the pot with nothing, which also happens 2.27% of the time.

This is the same type of argument that I would expect from someone who insists on winning the most pots, regardless of how much he loses in the other pots, because the object of the game is to win pots.

Except the problem is that it's not an argument of what's the way to win the most money in any given pot, but is what's the way to win the most money in the long term. As it turns out, it frankly doesn't matter, and it's only a question of variance.

So if you're looking for the concession, of "Yes, it's more likely that you're going to win $1,000 in that pot by running it once", then yes, you're absolutely right.

But you're wrong in your assertion that everybody would leave with the money they brought in with everybody getting "their fair share". People are still going to make decisions that have both positive and negative expected values to them, and there are going to be times in addition to those where the turn of the cards isn't going to resemble the long-term expected results. There's also the point to consider that not everybody makes the decisions that expected value would dictate.

You could play this pot, exactly the way you've said, and walk home with nothing. The odds are slim, to be sure, but the odds aren't zero. If you end up with zero, you're certainly not heading home with what you came with.

To further illustrate the point, imagine that the hand was run several times with one player ending up with a scant amount of cash based on actually hitting his hand, and the other player ending up with the majority of the 1000.

Let's further suppose that on the very next hand, the exact same situation occurred, but with the players holding the opposite player's holdings. Are we to suggest now that the player should end up even in chips?

The fact that the long run suggests that every player should be faced with situations from both sides doesn't mean that the opportunities will truly turn out to be equal, based on the players involved and based on the chip stack situations that they run into at the same time.

*first post, high everyone *

Mriya seems to be arguing simply that running it once gives you the greatest chance of taking the whole pot. This is clearly true. Mriya also seems to be assuming taking the whole pot is 'best' or 'what one should want to do'. This is debatable. So Andy is not 'simply wrong' when he says he would like to run it as many times as possible when a favourite. It's his opinion, and Mriya doesn't seem to have offered any concrete argument against it. Mriya's argument essentially rests on the assumption that winning the whole pot has some kind of intrincic value; value other than the monetary value.

There might? also be a slight change in the math needed. When something is run twice after the flop, there are 2 independent turn and river cards.

However, after the 1st run, those turn and river cards are NOT reshuffled back into the deck. Thus, if the person who is behind hits 1 (or 2) of his outs on the 1st run, he is less likely to hit them on the second and vice versa.

Here it is very simply. We are playing with a deck of 16 cards containing:
AAAA,KKKK,QQQQ,2222. No straights or flushes can come up. There are no burn cards.

Player A holds: AA
Player B holds: QQ

Flop/Turn is: A Q 2 2

8 cards remain in the deck. Only 1 of those improve Player B's hand and allow him to win--that card being the case Q. If any of the remaining 7 cards come Player A wins.

If the players Agree to run the river 8 times, Player B will win only 1 out of those 8 times.

Theory A: If the rule is that the who ever wins majority of the draws takes everything then Player A will always take everything. Player A should therefor elect to run it as many time as possible. In fact, in this particular contrived scenario, if he runs it at least three times, he is sure to win because he can lose only once out of those three times.

Theory B: The pot is split up according to the number of times a player wins the redraws. This is the same as the two players deciding the odds and splitting up the pot right there. If player A is X% favorite and B is Y% favorite then A takes X% and B takes Y% out of the pot. This scenario does not change EV. It changes the variance only. It ensures that each player will only get what they are expected to win in the first place and takes the gamble out completely.

Going back to theory A in which one player takes all, the favorite-to-win should always elect to run it as many times as possible and the underdog should clearly elect to run it as few times as possible. As I outlined earlier, the favorite-to-win will _always_ win if the hand is run only three times in that particular scenario.

That should make it very clear to understand and help you determine what route to pursue next time you are in the situation--even though it seems counter-intuitive. If you are a favorite run it twice. If you're a dog, run it once.

Who does everyone like at the final table of the main event? I think that Hachem guy might win even though he's the short stack.

Hachem won last year.... I've got my money on that Luckbox wearing the BoDog gear.

Who is this?