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.
Mriya, on Saturday, April 8th, 2006, 10:43 PM, said:
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: $488.642nd run: $477.27Here 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.