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Server Time: 9/5/2008 1:11:41 AM PACIFIC |
 Back to back pocket aces, stdioh, 3. Apr 2003 09:44 | ||
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| I remember something posted here about a month ago as to how often back to back pocket aces happen. We agreed that on any given hand, you chance of having aces the following hand is about 1:50,000, but my contention was that they happen all the time in a busy cardroom. I hit them last night. I had a great session - everything was wonderful. Just playing a short 3.5 hour before bed poker snack at Brantford and hit the perfect game. For starters, there was one giant maniac and I was sitting two seats to his left. There was another big fish in the game (who scared the sock off me when he limp reraised with TJo against my AKs). There were a couple of calling-stationy players and a couple of rocks and a couple of people to avoid. All in all, it was exactly the table I look for. One fish pays everybody's session fees, another one donates proffit, and they are easy to isolate. Then I sat down and was run over squarely by the deck. In my 3 hours I managed to make 30 big bets and that included taking some beats. I had pocket aces three times. The first I was heads up with the maniac preflop and he managed to flop the nut straight and I payed him off very well. On the next dealer's rotation, the solid player to my right hit pocket queens two hands in a row and made a fuss over it. Shortly thereafter I had aces and raised one from UTG. It was the only hand of the night where the blinds were stolen. For no good reason I violated personal policy and flipped my aces onto the table face up - still don't know why. Next hand I get aces again (one 50K to one shot made - ka-ching). I raise UTG and get 4 opponents including both fish, the maniacal one of course raising and I cap it. I knock them all out on the flop except for the maniac who raises and says, "What, you have pocket aces again?" I figured that it was time for the anti-bluff - something I use very sparingly. "Yup. I have back to back pocket aces." I raise. He calls and says, "Pocket aces are good." I know that he is telling the truth. He bets out on the turn and I raise him. Again he calls and says, "Pocket aces are good." I still believe him. He calls my river bet and I got such a reaction out of the table when I exposed my aces and dragged the pot. Life is good. Sometimes good things happen to good people. I'm officially out of my slump and my 2003 figures are steadying out a bit and are thankfully ahead of the 1 BB/hour curve. Incidentally, if my quick calulations are correct, the chance of two players at a table hitting back to back same pocket pairs (ie back to back queens for Ken and back to back aces for me) within an arbitrary 1 hour shift of the dealer are around 1:400,000 ... that both back to back pocket hands were premium pocket pairs (queens or better) is about a 1:6,000,000 shot. Just proving that it is very statistically likely that very statistically unlikely things happen all the time :) | ||
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| Incorrect, Easy E, 3. Apr 2003 09:57 | ||
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| Independent events. It's 220:1 to have ANY pair on ANY hand. Having aces the hand before meant nothing... Now, the odds against getting Aces on TWO consecutive hands are about 48K:1.. | ||
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| Re: Incorrect, stdioh, 3. Apr 2003 13:48 | ||
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| on 3. Apr 2003 09:57 Easy E wrote: > Independent events. It's 220:1 to have ANY pair on ANY hand. Having aces the hand > before meant nothing... > > Now, the odds against getting Aces on TWO consecutive hands are about 48K:1.. Indeed. So you should get back to back pocket aces about once every 50K hands or so...which is what happened. No kidding they are independant events. | ||
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| Re: Incorrect, Paul Stine, 3. Apr 2003 14:43 | ||
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| on 3. Apr 2003 13:48 stdioh wrote: > on 3. Apr 2003 09:57 Easy E wrote: > > Independent events. It's 220:1 to have ANY pair on ANY hand. Having aces the hand > > before meant nothing... > > > > Now, the odds against getting Aces on TWO consecutive hands are about 48K:1.. Actually, the odds of being dealt *any* pair on any hand are 16:1 against. The odds of beng dealt a specific rank pair on any hand are 220:1 against. Semantics. > > Indeed. So you should get back to back pocket aces about once every 50K hands or > so...which is what happened. No kidding they are independant events. The 220*220 = 48,400 number is the odds against being dealt any two specific rank poket pairs (in a given order) on back to back hands. The odds against being dealt any two specific rank pocket pairs without regard to order on back to back hands is 24,200:1 (48,400 divided by the number of ways (2) that they can be ordered.) Note these are the odds of it happening *before* the first hand is dealt. The odds of it happening after the first hand is dealt is greatly influenced by the first dealt hand. So, when someone is dealt pocket aces on back to back hands and someone else makes some remark about the odds of what just happened you can be smug in the knowledge that they will probably get it wrong. This is because they will only make this statement after it has happened and at that point the odds of it happening are, of course, 1. Semantics. Paul Stine College Station, TX | ||
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| Touche, Paul! and stdioh.., Easy E, 3. Apr 2003 14:55 | ||
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| If I'm going to be picky on wording, I guess I should be held to the same standard.... my response should have said "ANY particular pair..." One point for Paul stdioh- "We agreed that on any given hand, you chance of having aces the following hand is about 1:50,000" This is the statement that was incorrect. I was nitpicking. | ||
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| Re: Touche, Paul! and stdioh.., stdioh, 3. Apr 2003 14:58 | ||
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| on 3. Apr 2003 14:55 Easy E wrote: > If I'm going to be picky on wording, I guess I should be held to the same standard.... my response > should have said "ANY particular pair..." One point for Paul > > stdioh- "We agreed that on any given hand, you chance of having aces the following hand is about > 1:50,000" > This is the statement that was incorrect. I was nitpicking. My appologies for the poor wording...I could stand to be more eloquent. Still, I think we all know what I meant. | ||
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| Re: Touche, Paul! and stdioh.., Easy E, 3. Apr 2003 16:26 | ||
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| thus my backhanded apology for being a schmuck | ||
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| Re: Incorrect, NiceFella, 3. Apr 2003 23:11 | ||
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| OK, I can see this odds calculation going back and forth, and I'm not sure I want to get dragged into it, but here's my stab at it. The probability of getting pocket rockets on any given hand is 1/[(4/52) * (3/51)], or 220:1 against. I think we are all in agreement on this much at least. However, the odds of getting AA twice in a row is then 1/(221*221), or 48,840 to 1 against. I don't believe it is correct to then double these odds based on the reasoning that "there are two ways they can be ordered". These are independent, identical events which both must occur, so their probabilities simply multiply. It's not as if there are two different events A and B which can occur in the order A then B or in the order B then A. Getting aces is getting aces -- there's only event A, and it must occur in the order AA. This is similar to flipping a coin twice and having it come up heads both times. The odds of this are 1/2 times 1/2, or 3:1 against. You don't then double the odds "because there are two ways to order the heads flips". As you said, the person is "likely to get it wrong." I decline your kind offer to be smug, though, because I'm sure I'll make a mistake real soon now. NiceFella | ||
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| Re: Incorrect, stdioh, 4. Apr 2003 08:46 | ||
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| on 3. Apr 2003 23:11 NiceFella wrote: > OK, I can see this odds calculation going back and forth, and I'm not sure I want to get dragged > into it, but here's my stab at it. > > The probability of getting pocket rockets on any given hand is 1/[(4/52) * (3/51)], or 220:1 > against. I think we are all in agreement on this much at least. > > However, the odds of getting AA twice in a row is then 1/(221*221), or 48,840 to 1 against. > > I don't believe it is correct to then double these odds based on the reasoning that "there are two > ways they can be ordered". These are independent, identical events which both must occur, so their > probabilities simply multiply. > > It's not as if there are two different events A and B which can occur in the order A then B or in > the order B then A. Getting aces is getting aces -- there's only event A, and it must occur in the > order AA. > > This is similar to flipping a coin twice and having it come up heads both times. The odds of this > are 1/2 times 1/2, or 3:1 against. You don't then double the odds "because there are two ways to > order the heads flips". > > As you said, the person is "likely to get it wrong." I decline your kind offer to be smug, though, > because I'm sure I'll make a mistake real soon now. > > NiceFella Your assessment is correct. Now calculate the odds of getting AA, AA or KK, KK or QQ, QQ at one table in one hour twice...in the case where the player to my right had QQ, QQ, and then I had AA, AA. This is what is so intriguing...that they happened together like that in the same dealer shift. | ||
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| Re: Incorrect, NiceFella, 4. Apr 2003 12:49 | ||
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| stdioh, I've taken up the challenge of the probability problem you pose. To make sure we're all on the same page, I carefully reread your original post, and I'll restate the problem as I understand it: "An opponent gets dealt the same premium pair twice in a row. What are the odds of this? Given this, what are the odds that I will also get some premium pair twice in a row during the same dealer shift?" Given that an opponent just had a pocket pair, the odds that he'll get that same pair again on his very next hand are 220:1 against. Now what are the odds that you will also get a back-to-back premium pair? The chance of getting any pair JJ through AA on any particular hand is (16/52)*(3/51), or about 54:1 against. The odds of repeating that feat on your next hand are 220:1 against. So the overall chance of getting a back-to-back premium pair beginning with your next hand is (16/52)*(3/51)*(4/52)*(3/51), or 12,208:1 against. But you don't have to get it in your next hand -- you've got the whole dealer shift to wait. The chance of NOT getting back-to-back premium pairs beginning with your next hand is 1-(1/12209). The odds of NOT getting back-to-back premium hands at least once in, say, 20 hands reduces substantially -- [1-(1/12209)]^20, which is about 610:1 against. If we let the dealer shift stretch out to 50 hands, then the odds against getting back-to-back premium pairs fall to just 244:1 against. So overall, I put the chance of an opponent and then sometime later yourself getting back-to-back premium pairs at least once during a dealer shift at (1/221)*(1/611), or 135,000:1 against for a short 20-hand dealer shift, or (1/221)*(1/245), or 54,000:1 against for a longer 50-hand dealer shift. I think an interesting result of this calculation is the realization that about once in every 245 dealer shifts you'll get back-to-back premium pairs. I welcome corrections and comments (and outright invitations to shut up and get a life), NiceFella P.S., Now, about this time I entered a tournament and got AA, KK, QQ, and JJ within my first ten hands, and lost them all.... | ||
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| Re: Back to back pocket aces, The Fish, 3. Apr 2003 11:09 | ||
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| You say you play in Brantford ..........who are you? ...... I haven't been in a while ........just curious ....i used to go there quite a bit ....... | ||
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| Re: Back to back pocket aces, stdioh, 3. Apr 2003 13:49 | ||
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| on 3. Apr 2003 11:09 The Fish wrote: > You say you play in Brantford ..........who are you? ...... I haven't been in a while > ........just curious ....i used to go there quite a bit ....... You'll often see me there wearing a big brown suede hat (think Neil Young on the cover of Back from the Gold Rush), a *VERY* loud hawaiian shirt, and chillaxin' at the 10-20. I play about 2-3 sessions a week...usually weekends or early weekday mornings. Sometimes weekday nights. | ||
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| Re: Back to back pocket aces, The Fish, 5. Apr 2003 13:30 | ||
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| Thx ......I will keep this in mind next time i go .......I am a small timer.....only play the 5-10 .....not enough cash or skill to play at the higher limits! .... | ||
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| Re: Back to back pocket aces, Andrew Wells, 3. Apr 2003 15:52 | ||
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| Last Saturday I had pocket aces vs. pocket aces back to back same opponent both hands. I actually won one outright with running diamonds. I've been on a 10 BB/hr. heater for the last two weeks, so these things don't seem so outrageous. When you keep making straights instead of overcards with your AK and no one ever calls a river bluff, it tends to reinforce the illusion that poker is easy. | ||
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| Re: Back to back pocket aces, dmn, 3. Apr 2003 20:35 | ||
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| Not too long ago (recently that I still have the scars) in a 3-6 game, I held pocket As, bet 'em hard and lost to Seat 4 who had flopped a set, with rolled up 2s. I got up, took a steam break, and tried to shake it off. About 15 minutes later, I sat down again and picked up--pocket As. Again. Bet em hard to the river, and lost to the SAME GUY who had flopped a set AGAIN, with rolled up 7s (or 9s or some d--n thing). Figure the odds. Two hands back to back, pocket aces losing to a flopped set. | ||
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| Re: Back to back pocket aces, stdioh, 4. Apr 2003 09:05 | ||
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| What the damn hell? Two hands in a row you had AA and the same opponent had the case AA?!? The odds of that are just about incalculable...let me see. I make that at a 1: 32,574,233,611 chance that you get AA on a given hand and some opponent at the table gets AA as well and then on the next hand the two of you get AA and AA. Zoinks. | ||
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| Re: Back to back pocket aces, timmer, 4. Apr 2003 10:43 | ||
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| 220*220/1*2 = 1 in 24200.00 times isnt this correct? | ||
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| Re: Back to back pocket aces, Andrew Wells, 4. Apr 2003 15:21 | ||
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| How much of this sort of thing happening must occur before you become reasonably certain there's something paranormal going on? That seems to me a more interesting question than what are the astronomical odds. This whole infusion of good fortune began two weeks ago when a good friend and poker player died. He had been fighting a serious illness and knew he wasn't going to be with us much longer. In the past we would always support each other financially if one of us ran badly. One of the other half dozen or so times I held pocket aces vs. pocket aces, he was the other player. I've had other curious hands as well. My third ever royal in hold'em happened that same Saturday. For the first five sessions of this run, I did not lose a showdown. There were maybe two dozen. I've had longer streaks and bigger wins, but never anything close to this hourly rate over multiple sits. I choose to believe. | ||
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| Re: Back to back pocket aces, dmn, 4. Apr 2003 15:36 | ||
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| I didn't think I was that unclear. I held pocket aces twice in a row, and on both those hands, the same opponent held a smaller pair which paired (tripled?) the board on the flop. I had AA, he had 222. I lost. Next hand I had AA, he had 777. I lost. The odds of me having my two hands are 220:1*220:1 or 48400:1. The same odds are true of his having his two pairs. I don't know what the odds of him flopping a set twice in a row are. Btw, this was a brick and mortar card room, not online. | ||
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| Re: Back to back pocket aces, stdioh, 4. Apr 2003 16:05 | ||
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| on 4. Apr 2003 15:36 dmn wrote: > I didn't think I was that unclear. I held pocket aces twice in a row, and on both those hands, > the same opponent held a smaller pair which paired (tripled?) the board on the flop. I had AA, > he had 222. I lost. Next hand I had AA, he had 777. I lost. > > The odds of me having my two hands are 220:1*220:1 or 48400:1. The same odds are true of his > having his two pairs. I don't know what the odds of him flopping a set twice in a row are. > > Btw, this was a brick and mortar card room, not online. That sort of thing is not at all uncommon, compared to AA vs AA twice in a row. Having AA in two consecutive hands, as has been talked about incessantly, is about a one to 50 thousand shot. Once that has happened, there are lots of ways to lose and of course of all the ways that aces can lose, losing to a set is a very common way. | ||
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| Re: Back to back pocket aces, NiceFella, 5. Apr 2003 11:51 | ||
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| What happened to dmn I would definitely consider "uncommon". First of all I want to point out that it's not really at 50,000:1 shot to get AA twice in a row. Sure it is, if you say "OK, what are the odds that my NEXT TWO HANDS will be AA?" But in retrospect what we're really asking is, "I just had AA, what are the odds that my next hand will also be AA?" which is a much, much more likely event. Once out of every 220 times you get dealt AA, you'll get it again right away. Given that you have AA, it's not uncommon for another player to also have a pair. I don't know the exact odds of this, but I think it's around 40% chance for another player at a full table to have a pair (and individual opponent has a 3/49 chance, and there's 9 opponents). Now if you raised your AA and they called with 22, well, now you have to factor in the probability that the opponent was stupid enough to do this. Now we get to the part about flopping a set. If you both have pocket pairs, it's 7.2:1 against your opponent flopping a set or better. You've got the same chance to flop your own set. Overall, AA against 22 wins 81% of the time heads-up according to the twodimes.net poker calculator. So dmn had AA, another player had a smaller pair (P=.4), then beat him (p=.2). That's about .08, or 12:1 against. It's a little touchy here, because AA you're going to lose more often than 12:1, but that's the odds of losing in this particular way. That's not so unusual, but now we get to the interesting part: dmn gets AA on his next hand (220:1 against this), the very same opponent gets another pocket pair (3/49 chance of this), then flops a set again (7.2:1 against this). This totals up to 29,600:1 against. Coupled with the 12:1 setup of the previous hand, it's about 385,000:1 against get AA snapped twice in a row by the same player with a flopped set. I know that this calculation is crude and inaccurate, but I think it's in the right ballpark and it's definitely "uncommon". And I just want to reiterate that getting a premium pocket pair twice in a row is not the astronomical oddity that some people seem think. Look at this way: for every 55 times you get AA, KK, QQ, or JJ, you'll get the same or another premium pair on your very next hand. NiceFella | ||
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| Re: Back to back pocket aces, dmn, 5. Apr 2003 16:29 | ||
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| Nice Fella- Thank you for your analysis. Sounds about right to me. It's not that I expect AA to win every time, but surely the Poker Fates were sitting over on Seat 4's side of the table that night. But at least now, having had that happen to me once, I shouldn't expect it again for oh, maybe another 100,000 hand or so. :) That's good to know. dmn | ||
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| Re: Back to back pocket aces, stdioh, 7. Apr 2003 10:01 | ||
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| We've discussed this ad nauseum, so I'm going to sum up. You should expect back to back pocket aces to come around roughly once every 50,000 hands. So if you play around the clock and get in 35 hands per hour, then roughly every 2 months, it should happen to you. That is rare. | ||
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