Would Love For Daniel To Discuss This Hand Of His

[Garn 0]

i would run it twice as a 2:1 dog. I get to see 4 cards and only one of those has to be a face card for a split. if you get a face card on both runs then you take it down

[bigesmalls 0]

Alright, my first post might as well be a stupid question. I don't feel like doing the math so I'll ask one of you. If the deck is not reshuffled and it's a situation where someone is drawing to a one-outer doesn't that effect the EV since their is no possible way to scoop the pot?

[BuffDan 0]

Alright, my first post might as well be a stupid question. I don't feel like doing the math so I'll ask one of you. If the deck is not reshuffled and it's a situation where someone is drawing to a one-outer doesn't that effect the EV since their is no possible way to scoop the pot?

Inuitively it would seem so, but what was proven in the thread:http://www.fullcontactpoker.com/poker-foru...showtopic=54819that in all situations, even without shuffling, the EV is always the same whether it is run once, twice or even n times. Ah, the power of proof.

[Andy Beal 0]

Alright, my first post might as well be a stupid question. I don't feel like doing the math so I'll ask one of you. If the deck is not reshuffled and it's a situation where someone is drawing to a one-outer doesn't that effect the EV since their is no possible way to scoop the pot?

But, if you actually do the calculations, you will find the EVs are the same even with only 1 out. Might be counterintuitive, but true nonetheless.My calculations showEV(once)=.089W-1.91LEV(twice)=.089W-1.91LHere I have assumed 45 unknown cards and 1 out. W is the amount won per run, L the amount lost per run. (Treat running it once as running it twice but act like the same cards that fell the first time fell the second time.)

[Abbaddabba 0]

However, I think human nature takes over whether you are the dog or the fav: both want a better chance of losing less even if it means sacrificing some of their chance to win more. I talked more about this here (see the 3/22, 9:06 pm post of mine).

Not necessarily.I think what you're getting at is the notion of convex preferences. Thing is - they're addicted gamblers (they arent 'problem' gamblers until they start losing ) - they enjoy gambling for the sake of gambling. While each dollar is of diminishing marginal value in and of itself (implying they ought to prefer averages to extremes), the bet itself isnt significant relative to their overall wealth (at least int he case of daniel). There is some marginal net loss, but when you're operating so far along your marginal utility curve, it's pretty inconsequential. If it's not entirely clear, i can draw out a pretty diagram in paint. If joe blow sat at the table with his life savings, he would clearly prefer the hand be run more than once. In fact, he'd probably want it run an infinite times - or in other words, that he be paid precisely his expected value. Why? Because he prefers averages to extremes, because the marginal value of each dollar declines. The first $10,000 is more valuable than the next, which is more valuable than the next. And so on - but this fall off comes at a declining rate. Even if he LOVES gambling, he's not willing to screw up his life that much to get some action. But if he was a billionaire, he'd be so close to indifferent to the risk involved that, if he enjoyed gambling at all, he wouldnt care about running it multiple times.More significant for "the pro's" is the joy they get from gambling. For whatever reason, they get off on having their money arbitrarily redistributed between each other. Mmmm... arbitrary redistribution.

[NoSup4U 0]

Hate to say it Davezz5, but Andy is correct. I understand that it seems a bit illogical because you are looking at it from the perspective of having more 'chances' to hit your outs. But trust us, the math works out even.And if you don't believe that, think of it from the favorites standpoint. Why would any player give you more chances to catch your outs if it was going to cost him money in the long run? Winning over time is why we play poker in the first place.Mark

[Andy Beal 0]

Not necessarily.I think what you're getting at is the notion of convex preferences. Thing is - they're addicted gamblers (they arent 'problem' gamblers until they start losing ) - they enjoy gambling for the sake of gambling. While each dollar is of diminishing marginal value in and of itself (implying they ought to prefer averages to extremes), the bet itself isnt significant relative to their overall wealth (at least int he case of daniel). There is some marginal net loss, but when you're operating so far along your marginal utility curve, it's pretty inconsequential. If it's not entirely clear, i can draw out a pretty diagram in paint. If joe blow sat at the table with his life savings, he would clearly prefer the hand be run more than once. In fact, he'd probably want it run an infinite times - or in other words, that he be paid precisely his expected value. Why? Because he prefers averages to extremes, because the marginal value of each dollar declines. The first $10,000 is more valuable than the next, which is more valuable than the next. And so on - but this fall off comes at a declining rate. Even if he LOVES gambling, he's not willing to screw up his life that much to get some action. But if he was a billionaire, he'd be so close to indifferent to the risk involved that, if he enjoyed gambling at all, he wouldnt care about running it multiple times.More significant for "the pro's" is the joy they get from gambling. For whatever reason, they get off on having their money arbitrarily redistributed between each other. Mmmm... arbitrary redistribution.

I'm not sure what your point was, but the math says running once, twice, 3 times, or thru the deck all have the same EV. Period. It is a mathematical fact that whether one understands it or not or believes it or not is just as true as the Laws of Thermodynamics or gravitation. Similarly, the math indisputably says that the variance is lowered each run. There can be speculation on whether a certain player would want fixed EV with higher or lower variance when he is the dog/fav, but those are probably personal preferences based on many factors.In a nutshell, the amounts of money these guys are playing for ARE meaningful (even to them). If they were not, they would increase the stakes until they were because the game wouldn't be much fun otherwise.

Hate to say it Davezz5, but Andy is correct. I understand that it seems a bit illogical because you are looking at it from the perspective of having more 'chances' to hit your outs. But trust us, the math works out even.And if you don't believe that, think of it from the favorites standpoint. Why would any player give you more chances to catch your outs if it was going to cost him money in the long run? Winning over time is why we play poker in the first place.Mark

Exactly.

[Abbaddabba 0]

I'm not sure what your point was, but the math says running once, twice, 3 times, or thru the deck all have the same EV. Period. It is a mathematical fact that whether one understands it or not or believes it or not is just as true as the Laws of Thermodynamics or gravitation. Similarly, the math indisputably says that the variance is lowered each run. There can be speculation on whether a certain player would want fixed EV with higher or lower variance when he is the dog/fav, but those are probably personal preferences based on many factors.In a nutshell, the amounts of money these guys are playing for ARE meaningful (even to them). If they were not, they would increase the stakes until they were because the game wouldn't be much fun otherwise.Exactly.

Huh?What did you mean by,"However, I think human nature takes over whether you are the dog or the fav: both want a better chance of losing less even if it means sacrificing some of their chance to win more. I talked more about this here (see the 3/22, 9:06 pm post of mine).?That's what i was responding to.

[Andy Beal 0]

Huh?What did you mean by,"However, I think human nature takes over whether you are the dog or the fav: both want a better chance of losing less even if it means sacrificing some of their chance to win more. I talked more about this here (see the 3/22, 9:06 pm post of mine).?That's what i was responding to.

After a lot of words in your post (convex preferences, etc.) you say that the pros run it twice "because of their love of gambling". Running it twice reduces variance and builds a hedge against losing the most. That doesn't sound like someone "gambling for the fun of it"---quite the opposite. It sounds to me like someone who is trying to minimize his loses. And that's all I was saying in the first place.

[canadianyanke 0]

I didnt read all of the posts but when they ask to run it twice it means if they win 1 out of 2 they split the pot, if they win both they get the full pot.

[Abbaddabba 0]

After a lot of words in your post (convex preferences, etc.) you say that the pros run it twice "because of their love of gambling". Running it twice reduces variance and builds a hedge against losing the most. That doesn't sound like someone "gambling for the fun of it"---quite the opposite. It sounds to me like someone who is trying to minimize his loses. And that's all I was saying in the first place.

I said the exact opposite.I said joe blow would prefer it be run an infinite number of times. Joe blow is no pro. He's an example of a poor shlub who, for whatever reason, got involved in a high stakes game of poker and was faced with the decision being discussed.Pro's (or at least a good portion of them) probably wouldnt care, and would just wnat to run it once if it was for a negligable amount relative to what they have. Either to save time, to save face and not be seen as 'scared', or because they genuinely enjoy gambling.... a hobby that, for many, is what drew them to playing cards in the first place.

[Andy Beal 0]

Pro's (or at least a good portion of them) probably wouldnt care, and would just wnat to run it once if it was for a negligable amount relative to what they have.

Hard to follow your logic or point here since the very first post in this whole thread is about two pros that chose to run it twice.

[Abbaddabba 0]

Clearly it wasnt negligable to them.I was responding to the statement i quoted, not the original post.Nevermind.

[Phlatline 0]

True, and I see your point. By the way, very nice theory post.I still maintain my original position. Variance is a two way street that really only comes into play in the short term. Bank roll determines the "ride" you may want to take.I agree with your first paragraph, with "small set of trials" being key here. However, in the second paragraph, I don't see how variance will help your low probibility event occur. Again, variance is a two way street. The positive swing will equal the negative swing and -EV will emerge in the end. Win less/lose less, or win more/lose more. Are you saying that when you are +EV you are willing to gamble less, and when you are -EV you are willing to gamble more? I think this is the true "human nature" of a poker player.I think the whole running it X times is probably more for pro's entertainment and bankroll security. Personally, whether I am + or - EV, I will take reduced variance any day of the week.Phlat_________

Sorry to be redundant and quote myself but I would really like to hear Andy's thoughts on this.Andy, it sounds like you are saying it is more advantageous for a player with a -EV hand to run it multiple times. I still fail to see how this is true. Advantage is measured in terms of EV. Variance is measured in terms of trials. As you know, running it many times decreases variance, and running it fewer times increases variance. In no way does the Variance/Trials outcome have any effect on the Advantage/EV. Bankroll management and entertainment value are the only considerations when it comes to running it N times.I think Abbaddabba was only stating why some people would choose less/more variance by running it once/multiple time(s). ie. someone with life savings on the line wants less variance, whereas a seasoned pro could live with more variance. A dollar means more to some than others. But this does not change our EV/Variance debate.Andy, I think you have fallen into the gamble more to catch up when -EV and preserve bankroll mode when +EV mindset. I honestly don't think there is any tactical advantage there.Phlat___________ :DPS. LOL, this is too funny. "Joe blow is no pro."

[Andy Beal 0]

Andy, it sounds like you are saying it is more advantageous for a player with a -EV hand to run it multiple times. I still fail to see how this is true.

I can see how you might infer that but let's be careful here: I offered a conjecture on why I thought a dog might want to run it twice, not a statement that running it twice is advantageous for the dog. The reason I belabor this last statement especially is because the math clearly says that it is really neither advantageous or disadvantageous---the EV's are equal whether you run it once or more. If you are an 11:1 dog, your opponent is most likely gonna scoop the whole thing if you run it once or twice or N times. On the other hand if the pot is $250K+ like on High Stakes Poker on GSN and Esfandiari turns over AA while Elezra turns over JJ, Elezra may very well choose to run it twice to give him a better chance at losing less. It just depends on the risk/reward characteristics of the individual players involved I think. Similarly if you and I are playing for a ton of money and you turn over AK to my QQ we might (implicitly) decide to "call it a tie" for all that money by running it twice since the chances are very good that we will split.

Andy, I think you have fallen into the gamble more to catch up when -EV and preserve bankroll mode when +EV mindset. I honestly don't think there is any tactical advantage there.

I'm not sure what you mean. I don't think I made any assertions in this direction. Because if I did, I would have implored the dog never to run it twice since it is much more difficult to strike the big payday a gambler would seek!

[Phlatline 0]

Well one might turn around and argue that variance is the friend of the fav since reducing variance just makes higher probability events more "likely" to occur on this small set of trials.On the other hand, one might very well argue that if you are the dog, then you NEED variance to help your low probability event "occur" and therefore should want to just run it once.

Above was your assertion in the direction I was talking about when I said "Andy, I think you have fallen into the gamble more to catch up when -EV and preserve bankroll mode when +EV mindset." Gamble more here means running once when -EV.Increased variance does not help a low probability event occur, it only increases the range of possible outcomes. Over a large sample the -EV will come out anyway.

On the other hand if the pot is $250K+ like on High Stakes Poker on GSN and Esfandiari turns over AA while Elezra turns over JJ, Elezra may very well choose to run it twice to give him a better chance at losing less. It just depends on the risk/reward characteristics of the individual players involved I think.

Becareful with your choice of words here, as Elezra does NOT have a better chance at losing less. He is simply limiting BOTH winning and losing potential, ie. variance. I agree that these considerations depend heavily on the risk tolerance of the individual player.Phlat__________

[Andy Beal 0]

Above was your assertion in the direction I was talking about when I said "Andy, I think you have fallen into the gamble more to catch up when -EV and preserve bankroll mode when +EV mindset." Gamble more here means running once when -EV.Increased variance does not help a low probability event occur, it only increases the range of possible outcomes. Over a large sample the -EV will come out anyway.Becareful with your choice of words here, as Elezra does NOT have a better chance at losing less. He is simply limiting BOTH winning and losing potential, ie. variance. I agree that these considerations depend heavily on the risk tolerance of the individual player.Phlat__________

OH, again let me be clear. I wasn't saying that high variance "helps" a low probability event occur, I was saying one might try to argue that. Of course there is nothing one can do to hurt OR help a specific probablity event occur any more than one can affect the gravitational constant of the Earth.No he does have a better chance of losing less by running it 2x (of course, he has a worse chance of winning more too). It's basically the same caluclations that I already did for the Deeb-Negreanu hand here, post #7. If they run it once, DN has a 67% chance of losing $110k and 33% chance of winning $125.3k. If they run it twice, Daniel has a 44.4% chance of losing $110k, a 44.4% chance of chopping the pot (for a modest win of $7.65k due to the dead money in the pot), and only an 11.1% chance of winning $125.3k. So by running it twice, Daniel has a considerably better chance of NOT losing the max of $125.3k.

[Shaffer 0]

In a situation where the EV is identical (as running it twice always is), I think the only variables in play are metagame effects of variance: (1) whether or not, if you bust the other player, they will get up and leave, and (2) whether or not, if you give them a beat, they will tilt.Say you've got a strong player sitting at the table that is unlikely to rebuy if they go bust, with a weaker player waiting in the wings. This pushes the advantage to running it once (whether dog or favorite), because of the chance to bust the player and lower the overall skill level of the table. Conversely, busting a weak player with a strong player waiting decreases your overall EV by making the table stronger. This situation gives value to running it twice, whether dog or favorite; keep the table weak, and increase your chances of getting your money in with better EV in future hands.On the psychological level, I can make an argument, I think, for running it only once as the dog in a situation where, if you lay a beat on a player for their whole stack, they will rebuy, go on tilt, and drastically increase your EV in the near future. In another hand, on an earlier night, DN was willing to call in what he knew was a very negative EV situation in order to put someone (I forget who off the top of my head) on tilt. While that's something I don't think I would ever do (and I don't agree with the play under the circumstances for sure), I see the logic behind it. In a situation that doesn't affect your EV, such as running it twice, I think you want to do whatever you can to bump up the variance if you feel you have a better psychological capacity for handling the swings than your opponent does.I think DN and FD's mutual decision to run it twice reflected their natural desire to lower variance as well as (possibly) a mutual respect insofar as neither one felt they would be likely to tilt the other. Maybe Freddy also felt like he had an advantage over DN so long as DN was playing hyper-aggressive, but felt that if he took 100k from him, Daniel would calm down, play tighter, and lower Freddy's EV - kind of an inverse tilt sort of thing.Who knows really? When EV is not affected, very small considerations can push the balance one way or another.

[Mriya 0]

first of all, I havent read all the replies, I just found 'Andy's' calculation is logically unjustified. Based on that, this can't be the Andy Beal who is a very good mathematician. Now, why did I say that?There is one fact, that 'Andy' ignored, and he called it 'subtlety', that there is only 52 card in a deck. Personally, I don't think this is subtle at all, nor it is a minor issue. In fact, this is the ONLY issue that matters. Ignoring this fact, which means the probability of drawing out as a underdog remains the same, the equity will OF COURSE, ALWAYS stays the same. You really dont need any calculation to draw that conclusion. Because all you did, is run the EXACTLY same hand a number of times, and each and everyone of them has the EXACTLY same probabilty of winning/losing.Now why isnt it good to run it more times when you are a FAVOURITE?NO, IT IS NOT THE VARIANCEThat is because, you are effectively giving more chances to get out DRAWN.REMEMBER there are only 52 cards in a deck, and are only a few cards that can help the DOG. As a favourite, you DONT WANT TO SEE THEM. If you ran it twice, you are given out more chances to SEE them, that is IT. The chances of hitting 3 cards when there is 35 cards left is much higher than there is 40 left, isn't that obvious?I think this is very simple to understand?

[Mriya 0]

Now because this is a 'mathematical' discussion, let's see some numbers. Lets use a rather simple example (coz I am lazy)AK vs KJ, and you are dead to a JACK on the flop: you have two chances to hit remaining 3 jacks in the deck, the estimated probability is: (considering only you and your opponent's hands)(3/45)*(39/44) = 5.9%-> one jack on the turn, a card that is NOT an ACE on the river (Situation A)(42/45)*(3/44) = 6.36%-> one card that is NOT an ace on the turn, and a jack on the river (Situation B)(3/45)*(2/44) = 0.3%-> hit runner runner Jacks (situation C)all toghether the estimated probability that KJ will draw out on AK is: 12.56% (might be a different from the simulation results, this is just an estimate anyway)So the probability of NOT drawn out is about 100% - 12.56% = 87.44% (Situation D)Now what if we run it twice? The first run obviously is identical to the abovenow the second run:provide that it is situation (D)we had a new set of probabilities, similar to the above caculation only now there are only 43 cards left: (3/43)*(37/42) + (40/43)*(3/42) + (3/43)*(2/42) = 13.12% (E)Notice 13.12% > 12.56%This is the probability that KJ drawn out on AK PROVIDE THAT it didnt drawn out in the first run, the overall probability for this to happen is: P(D) * P(E) = 87.44%*13.12% = 11.47%THIS IS A SPLIT POT, but this is only one situation.IN total we have the following situations: 1) when we draw out on AK at the one time, but didn't draw out at the other time (this has eight combinations, 1st turn, 1st river, 2nd turn, 2nd river, 1st turn and river and NO JACKS in 2nd, 1st turn and river and one ace one jack, 2nd turn and river and no jacks in 1st run, 2nd turn and river with one ace and one jack in 1st run) 2) when we draw out on AK at the first time AND we draw out on AK at the second time (this has eight combinations, 1st turn+2nd turn, 1st turn+2nd river, 1st river+ 2nd turn, 1st river + 2nd river, 1st turn and river + 2nd turn and no ace on the river, 1st turn and river + 2nd river and no ace on the turn, 1st turn and no ace on the river + 2nd turn and river, 1st river and no ace on the turn + 2nd turn and river) 3) we didnt draw out on neither runs: this is rather easy to calculate: 87.44%*(1-13.12%) = 75.98%Notice the drop in probability compare to situation Dwhich means what? your AK is that 87.44% - 75.98% = 11.46% less likely to hold for the whole pot!Since no one is paying me for doing this, Im not gonna bother about the details. But HOPEFULLY you can see why it is NOT GOOD to run more than once as a favourite.

[Shaffer 0]

I don't understand what all the math is supposed to be about here. The EV of running it twice is the same whether you run it once, twice, or eight times. The only thing you affect is the variance. In effect, you are putting yourself in an identical situation twice for half the stakes each time. Yes, if you are the favorite, you gain the additional chance of your opponent getting half the pot, but you also essentially kill your opponent's chance of scooping it with a bad beat. The only variable that is affected is your variance.

[Mriya 0]

READ my post carefully, your assumption is WRONGTHERE ARE ONLY 52 CARDS IN A DECK and it matters GREATLYthat is, if you didnt get the card you want from the 1st run, you have a HIGHER probability of hitting it at the 2nd run. If you run it a 3rd time, the probability is going to be even higher. Understood?if you cant understand the math, at least try to understand the logic

[dingas 0]

As I mentioned in the other thread, your logic is flawed. If you don't hit on the first run, you have a greater chance to hit on the second, but if you do hit on the first you have a lesser chance on the second. These two effects cancel each other out.The chance of only getting half is mitigated by the reduced chance of leaving with nothing, both for the favourite and for the underdog.

[Shaffer 0]

Ah, I love being talked down to by someone that I (hope and pray) has never taken a statistics course. Mriya, you are simply wrong. Not "I disagree" wrong, but "2+2=5" wrong.Let's boil it down to the basics. Let's say you have your opponent drawing to 1 out with 1 card to come (under-set vs overset, for example). There's an even $1000 in the pot. With 4 cards on the board and 2 in each of your hands, that leaves 44 cards unaccounted for. You are a 43:1 favorite; your opponent has a 1 in 44 chance of sucking out.Therefore, running it once, your expected value is (43/44) * 1000 = $977.27.Running it twice isn't much more complicated. On the first card, your EV is calculated in exactly the same way: your chance of winning the first half of the pot is 43/44, just as it was running it once. Therefore, on the first run, your EV is (43/44) * 500 = $488.64On the second run, 1 out of every 44 times your opponent will have sucked out on the first run. When this happens, your opponent will have no outs left and be drawing dead, so your EV for this happening is (1/44)*(1/1)*500 = $11.36.The other 43/44 times, your opponent will not have sucked out on you and will be drawing live, with 1 out out of 43 cards. Therefore your EV in this instance is (43/44) * (42/43)*500 = $477.27.To get your total EV for running it twice you just add your three EV's together: $488.64 + $11.36 + $477.27 = (gasp!) $977.27, the exact EV of running it once.I've expanded this way more than it needs to be, with the hopes that you'll be able to follow and see why running it twice does not raise or lower your EV in any way at all. Your variance is reduced, but that's a complication more complex than you're probably ready for at this point.

[Vman96 0]

I've expanded this way more than it needs to be, with the hopes that you'll be able to follow and see why running it twice does not raise or lower your EV in any way at all. Your variance is reduced, but that's a complication more complex than you're probably ready for at this point.

Burnnnnnnnnned! You're the insult master! (Aqua Teen Hunger Force quote)And you're right...nice example too.