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Server Time: 11/23/2008 5:05:21 AM PACIFIC |
 Coin Toss Early in SNG, PairTheBoard, 5. Nov 2003 23:22 | ||
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| It seems the common wisdom among winning SNG players is to avoid coin toss situations for your entire stack early in the SNG. I've been wondering about this. Consider this proposition. Would you be willing to pay $60+6 for a seat in a $30+3 SNG if you were to be given 1600 in chips instead of the normal 800? I'm thinking it would be a good deal to take. If you play your 1600 chips right you should almost be guaranteed a spot in the money, the way $30 SNG's that I've seen go. If the 1600 chips give you about a 1/3 chance at each of the top three spots, your expected return on your $66 would be $100, ie. better than a 50% average return on every $66 invested. I suspect most SNG players would be happy with that. So, if you are very certain you are being offered an actual coin toss for all your chips early in a SNG, doesn't the result amount to exactly the above proposition? In other words, isn't it a pretty good deal? Of course you never know for sure if the situation is a coin toss, but if my best estimate of all the possibilities adds up to what amounts to a coin toss I don't think I'm going to give up valuable chips I've already invested in the pot to avoid it. Naturally, if I have a bad estimator I'm in trouble. But in that case I'm going to have lots of troubles anyway. Opinions? | ||
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| Re: Coin Toss Early in SNG, Dr_Monkey, 6. Nov 2003 04:51 | ||
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| I don't see the advantage of getting 1600 in chips for a $33 SnG. Since you paid $66 for the extra chips you eliminate one of the money spots. If you come in 3rd, you break even, actually you are down $6. And second only brings you a profit of $24, which is less than what you would get in the original 3rd place, $27 ($60-33). | ||
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| Re: Coin Toss Early in SNG, Grateful Rooster, 6. Nov 2003 07:28 | ||
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| I don't see the scenario of a double buy-in as analogous to the coin flip all-in. One is a double or nothing proposition and the other is a double investment for increased leverage. there does not exist the immediate downside in the double buy-in scenario. Without rebuys, tournament play is all about survival. Also, your premise assumes that you are a better player than the rest of the 30+3 crowd. Otherwise, you are certainly not assured a finish in the money, even with the double chip advantage. Additionally, a good player can find much greater post-flop advantages to get their chips in on than coin flips, if they are looking to double up. Otherwise, why play poker at all? Just go find someone to bet on an actual coin flip. But mostly, the advice against an all-in on a coin flip is about survival. --GR | ||
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| Re: Coin Toss Early in SNG, PairTheBoard, 6. Nov 2003 08:21 | ||
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| In reply to both posts by Dr_Monkey and Grateful Roost... : Actually, the coin toss is a better deal than paying an extra $33 for the extra 800 chips. In both cases you will find yourself on average holding a seat in a 30SNG that cost you $60+6. But in the coin toss case you will only be up against 8 opponents holding a total of 6400 in chips while in the $66 Buy In Case you will be holding the seat against 9 opponents with 7200 in chips. imo, there is a BIG advantage to starting out with a double chip stack. Obviously there is SOME advantage. Surely you would not disagree with that? The only question is, how much is it worth? How much extra WOULD you pay for the double chip stack? Now I understand there is Tournament theory that says that the marginal increase in chips goes down in value as your chip stack rises. But I'm not so sure about this going from 800 to 1600. It seems to me that with 1600 in chips you are in MUCH better position to take advantage of weak stacks that are desperately going all in. Also, an extra tight strategy is MUCH more viable. In fact, in the $30 SNG's I've been playing, once you get about 1600 chips you will place in the money a good deal of the time by never playing another hand. You can almost do this with 800 in chips for that matter. With 1600 your survival odds go WAY up, and as was pointed out, survival is the name of the game. Yes, the assumption IS that you are a better player than your opponents. Indeed, why else play? The assumption is that you will play your 1600 chips correctly, which many players do not. Many players get 1600 in chips and then continue to gamble, which is a big mistake. Once at 1600 or so you should really tighten up. The really arguable assumption is that correct play with the 1600 chips could give you a 1/3 chance of placing in each of the top 3 spots. If it does, then the conclusion about the 50% return is correct. But maybe it doesn't. I'm not sure. That's why I'm asking for opinions. | ||
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| Re: Coin Toss Early in SNG, Grateful Rooster, 6. Nov 2003 11:14 | ||
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| I still don't think this is a good play. In the coin-flip scenario, you've invested 33 to get 800 in chips with an even chance to go bust or continue with 1600 (Where do you get the larger figures? 5400? 7200?). So, yes played over many SNGs, you would expect to hit T1600 once for every $66 invested, and if you shut down tight, you could make the money most (but not all) of the time. You will get taken out by some bad beats occasionally, and against smart players, you will blind out on other occassions. Also, playing overly tight, you will rarely win the SNG, so your 50% LT return is overly optimistic, I think. The larger question still stands, though: why put it all on a 50% chance when you could get it in on a 60% chance or better? Or better yet, spread the downside risk by playing multiple smaller bets with the larger advantages? Besides, that's a more enjoyable way to play, especially if you are better than the table average. I have read though (and it logically follows), that if you feel you are weaker than other players, your best strategy is to get your money in pre-flop much more often to negate the skill elements of the game. --GR | ||
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| Re: Coin Toss Early in SNG, Grateful Rooster, 6. Nov 2003 11:24 | ||
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| Oh, and with a 9-player SNG, your return goes way down. Even assuming placing 1/3 in each of the money spots, with a 50-30-20 payout, you would expect $90 ($270/3) for every $66 invested for a 36% ROI. --GR | ||
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| Re: Coin Toss Early in SNG, PairTheBoard, 6. Nov 2003 15:30 | ||
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| Think about it a little and understand the scenario. In the coin toss, those times you win will give you 1600 in chips. One of your opponents has been eliminated leaving 8 remaining opponents. Each of those opponents still has 800 chips for a total of 6400 against you at the table. The payout remains that of a 10 player game. In the proposition you would just start out with 1600 chips but there would still be 9 opponents, each holding 800 chips for a total of 7200 chips against you. Clearly the coin toss is a better deal than the proposition. My experience with 30+3 SNG's is that I usually don't get a lot of action in with Far superior odds. Sometimes I do, but very often I place in the money with skillful survival tactics on what becomes a short stack - and usually involves some coin flip situations somewhere down the line anyway. You really beg the meat of the question. How much would it be worth to you to be able to start out with 1600 chips. If not double the entry fee, then how much is it worth? I'm not sure it's such a clear cut answer - common wisdom aside. It's worth serious thought. | ||
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| Re: Coin Toss Early in SNG, PairTheBoard, 7. Nov 2003 00:33 | ||
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| seems I may be talking to myself now. oh well. btw, I'm pretty sure Sklansky discusses this in his writings on tournament poker. And I think he essentially declares that the utility of funds curve for tournament chips has slope that declines monotonically. That means, twice the chips is never worth twice the buy-in. But could David be wrong? Could the well known shape for utility of funds commonly used by actuaries possibly be wrong for tournament poker chips? Could the curve possibly be somewhat S shaped with an inflection point around 800 in this case? I think it's a somewhat important question because, although you don't have the option of buying in for twice the chips, you do make judgement calls for all in type wagers according to your estimate of your chances of winning, AND your estimate for the value of chips you may win or lose. | ||
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| Re: Coin Toss Early in SNG, Grateful Rooster, 7. Nov 2003 12:45 | ||
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| No, I'm still here. I realized after my last post that I misunderstood your use of the 6400 and 7200 figures. Didn't realize you were stating those as opposing figures. Yes, your analysis seems correct to me at first glance. Coin flip would give you better odds of making the money (all else equal). But, read on.... You're also right that I haven't answered the WTP for the double stack. It is an interesting question that gets to the theoretical value of chips, with different stacks at different stages of a tournament. I haven't yet read Sklansky's take on this, but my understanding is that he simply correlates the prize expectation with chip holding. Is this correct? If so, you may be on to something, because he's missing some factor that would reflect how the extra chips give you a higher expectation for the ultimate tourney outcome. Here's a simple theoretical example: Head's up match w/ $50 entry and T1000 chips each where winner gets 75% and loser gets 25%. At beginning, each chip would be worth $0.05 or (0.5*75+0.5*25)/1000. Some point later, player A has T1500 and B has T500. I think Sklansky would calculate that A's chips are worth $0.03 each -- ($50 EV)/1500 -- and B's are worth 50/500 or $0.10. But, those extra chips makes it more likely that A will win. Let's say it make's him a 3 to 1 favorite (equal to the chip advantage). A's chips are now worth (.75*75+.25*25)/1500= $0.04 each and B's are worth $0.075 each. This would still result in a monotonic decline in marginal chip value. Only way it would be otherwise is if the advantage of the extra chips is greater than the total chip advantage (i.e. a 3:1 chip advantage would make you a 4:1 favorite). Based on this, I calculated that a double buy would yield a EV of $60, but you now have to overcome the $6 in entry fees. The coin flip doubling would also yield a $60 EV, because the added chip advantage (20% in coin flip, 18% in double buy) is checked by the lower prize pool (300 vs. 330). So the WTP either way should be $60 rather than $66. For that matter, if you have an even chance of winning, the WTP for any event should be the entry minus the house take. A coin flip is an even proposition no matter how you slice it. If you want the spreadsheet I worked this out on, let me know. Thanks for the interesting problem. --GR | ||
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| Re: Coin Toss Early in SNG, PairTheBoard, 7. Nov 2003 15:43 | ||
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| Great example GR. Simplify and analyze. I had thought that Sklansky's principle was that extra chips gained at the 1500 level are worth LESS than extra chips gained at the 500 level. In other words, the marginal value of chips decrease as your chip stack rises. I may be misremembering or misunderstanding what I read of Sklansky years ago. If it's correct it would mean the 1500 stack is LESS than a 3-1 favorite over the 500 stack. But now that I think some more about it, I'm not sure that's what Sklansky was getting at. It may be the 1500 stack is a 3-1 favorite but the 1500 chips may not be worth 3 times the 500 chips. It depends on the payout schedule doesn't it? In fact, isn't the ONLY case that the 1500 chips are worth 3 times the 500 chips - assuming they make you a 3-1 favorite to win - is when it's a winner take all payout? THAT'S what Skansky observed. If it's winner take all 1500 chips have expected value of 75% of the pool, 3 times expected value for the 500 chips. But suppose the payout is 60-40. Then the 1500 chips have expected value of: 1500 chips : 75%(60) + 25%(40) = 55 percent of the pool 500 chips : 25%(60) + 75&(40) = 45 percent of the pool With that payout schedule the 1500 chips are worth FAR less than 3 times the 500 chips. Clearly you would not want to pay 3 times as much for them to enter the tourny on a 1500 vs 500 starting basis would you? AND if you bought in normally for 1000 chips you would certainly NOT want to enter a pure gamble situation that would effect something similar to buying in for 3 times as much to get a 3-1 chip lead. AHA! In anything but a winner take all payout schedule it looks like he who gambles loses. The best strategy is to gamble as little as possible and minimize risk. Let the others gamble between themselves. Those who gamble lose. This has exhasted me. I will continue with an analysis of the 30+3 SNG scenario next time. | ||
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| Re: Coin Toss Early in SNG, ADAM THE EXPERT, 9. Nov 2003 06:48 | ||
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| THE MAIN PROBLME HERE, AS YOU NOTED, IS THAT YOU CAN NEVER BE SURE, THAT IT IS INDEED, A SO-CALLED ;' COIN TOSS" ADAM THE EXPERT, DOES NOT LIKE THIS TERM, AS IT IS NOT ACCURATE AT ALL. A SIX TO FIVE FAVORITE, IS HARDLY A "COIN TOSS" THEY BUILD BILLION DOLLAR CASINOS ON FAR LESS ODDS, SO IF YOU COULD SOMEHOW SEE, THAT YOU WERE ON THE WINNING SIDE OF THAT COIN ( JJ VRS. AK) YOU WOULD TAKE IT, EVERY DAY, ALL DAY LONG. THIS IS NOT SOME GIANT TOURNAMENT, WITH TWO HOUR ROUNDS, THAT YOU FLEW THREE THOUSAND MILES TO GET TO. IT IS AN EVENT, THAT IS SPREAD ALL DAY, ALL NIGHT, EVERY DAY. AND, IF YOU ARE DESTINED NOT TO PLACE, WHICH WOULD YOU RATHER SPEND, ONE MINUTE, OR THIRTY MINUTES. ADAM THE EXPERT IS NOT PHAZED IN THE SLIGHTEST, WHEN HE BUSTS OUT EARLY, AS LONG AS I PUT IN MY CHIPS, WITH THE BEST OF IT. EVEN IF THE "IT" WAS ONLY SIX TO FIVE, BECAUSE I JUST MOVE ON TO THE NEXT GAME OR TOURNAMENT, AND THE NEXT AND THE NEXT AND THE NEXT OPPS OVER TO THE TRIPLE DRAW, NOW I'LL PLAY A MULTI TIME FOR A LITTLE TEN TWENTY OMAHA, A HA, THE WORSE PLAYER, IN THE HISTORY OF FIFTEEN THIRTY HOLD EM, DEAL ME IN HEY, THERES' A THIRTY SIXTY HIGH LOW STUD GOING AND SO ON AND SO ON, UNTIL I'VE FINISHED MY WORK DAY. GET THE POINT. IT'S ALL ABOUT DOLLARS PER HOUR. DOUBLE UP, OR BUST OUT SOON ADAM | ||
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| Re: Coin Toss Early in SNG, PairTheBoard, 9. Nov 2003 13:53 | ||
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| I'm inclined to agree with you Adam. And of course you are right in pointing out that you never know what your opponent is holding so you never know exactly what your chances are in the all-in match up. All you have to rely on is your ESTIMATOR of the probablity given all the information available. Besides the cards you hold and the betting in relation to previous betting patterns of your opponent, you also have the factor of experience of the type of players in these SNG's - especially ones eager to gamble early. Putting all these factors together your personal ESTIMATOR comes up with an estimate of your chances for the hand. If you have a Bad ESTIMATOR you had better get a better one because you won't do well on many of your other decisions. You have to assume you have a Good Estimator and make your decision based on it. Now, given that your ESTIMATOR says you are a 6-5 favorite for the all-in gamble, you claim you should take it. I tend to agree. But would you take it if you estimated you were a 7-6 favorite, or 10-9? What is your cuttoff criteria? And is it possible that even 50-50 is ok? In my discussion above I showed how in a Non Winner Take all heads up tourny, you would not want to pay three times your opponent's entry fee to start with a 3-1 chip advantage in the tourny. But as I think some more, this does not equate to making a 50-50 gamble for a chunk of your stack when starting even. After all, heads up 50-50 gambles are zero sum propositions - less the entry fee. Suppose it's a 3 player tourny with a 60-40 split for 1st and 2nd place. $20 to enter and 1000 in chips. Assume as Skansky does that your chances to win are proportional to relative chip stack sizes. Starting out, your exectation on the payout schedule is: 1/3($0) + 1/3($24) + (1/3)($36) = $8+$12 = $20. Fair enough. Now suppose you gamble heads up for all your chips on a 50-50 situation. Half the time you will lose and have Zero expectation for the payout. The other Half of the time you will end up with 2000 chips against one opponent with 1000 in chips, making you a 2-1 favorite to win. Thus your expectation on the payout when you win the coin flip is: 1/3($24) + 2/3(36) = $8 + $24 = $32. But that only happens half the time. Your overall expectation for the coin flip is then 50%($32) = $16!! Because of the Non-WinnerTakeAll payout schedule, both players in the early heads up coin flip have reduced their original $20 expectation to $16. The Expectation Winner is the player who sits out! Do the algebra for this example and you can compute EXACTLY how much of a favorite you need to be in the Heads up All-In gamble in order for the Gamble to be a Break Even propositon, Expectation-Wise. I suspect the greatest skill factor in SNG's is your chip management. As aspiring SNG pros we should know these kinds of analysis like the back of our hands. Although I suspect most successful SNG pros come to terms with these ideas by way of feel and experience. Also, is Sklansky's assumption that your chances of winning the tourny being proportional to your relative chip stack sizes Correct or possibly Incorrect? | ||
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| Re: Coin Toss Early in SNG, Grateful Rooster, 10. Nov 2003 07:04 | ||
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| I see two interesting points in this discussion. First, I think Adam makes the point that SNGs, or even other regular tourneys shouldn't be viewed individually, but as a part of a greater whole of long term poker play. In other words, if you have two strategies -- one the recommended "survive to the money" and another "all or nothing" -- the riskier strategy might still be valid because of time cost. With the survival strategy you make the money more often, and rarely bust out early. With all or nothing, you bust out early a lot, but also win more often. If you move on to another opportunity when you bust out, then the riskier strategy might pay off better over time (as long as you are getting your money in with favorable odds -- i.e. pot odds better than draw odds, etc.). Does this mean that the conventional wisdom against betting draws in NL tourneys is wrong? Second, Pair's last question, "Is Sklansky's assumption that your chances of winning the tourny being proportional to your relative chip stack sizes Correct or possibly Incorrect?" is a good one. I feel like, when I get a large stack, I can open up my game more and bully a lot of money over to my side and bet some favorable draws. All of which makes it more likely that I am going to increase my lead. Do my odds of winning increase above my stack advantage though? I think they do, but not at any quantifiable rate, because it's more subjective. Finally, nice analysis of the 3-way, Pair. You've hit it right on. I see how this calculus works for "odds to win", but earlier in the tourney, how does this figure into odds for 2nd or even just to reach the money? How do you figure expectation if you have T2000 against a T1000 average and 8 surviving opponents with the standard 3 payouts? Not something you really want to calculate while playing, but it is helpful in really thinking about the best strategy for SNGs or multi tourneys. --GR | ||
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| Re: Coin Toss Early in SNG, PairTheBoard, 10. Nov 2003 08:38 | ||
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| Thanks GR. I've rechecked the math on 3-way and cant find anything wrong with it. I might do another example just to make sure. But unless someone comes up with a counterexample it looks conclusive that coin flip situations do not effect your expected value regardless of payout schedule AND regrardless of relative chip stack sizes in a Three-Way.. I think that's a BIG suprise to a lot of people. This is assuming the Sklansky axiom that chances of winning are strictly proportional to stack sizes. At least to the extent that Sklansky's axiom is applicable I think the math is conclusive. I'm glad you brought up the argument about why Sklansky's axiom may not be true though. I've been thinking the same thing. It seems to me that tourny poker is not a homogeneous game. By this I mean: There are chip stack THRESHHOLD LEVELS at which certain plays become enabled or disabled. For example, you have 200 in chips left which you must put in the small blind. The Big Blind is 400. You are dealt 55. With more chips you could raise the BB and win it without a fight a good deal of the time. But this Play is Disabled because of your small chip stack. Instead you go up against a 69o which most certainly would have folded to a raise and you end up losing the virtual coin toss when all the other players fold. I'll bet if we thought about it we could come up with an abundance of such plays whose Viability depends on your #chips. While I think there are cases where it's actually an advantage to have fewer chips, I'm confident the vast majority of plays become More viable as your chip stack rises. I also suspect there is a Motherlode of such plays that beome enbabled somewhere between 75% of your initial stack and 200% of your initial stack. Each of these plays adds a certain Value to your position in the tourny. In fact, one of the reasons you are a Winning player is that you already have the First Criteria for making these plays - which others don't - Knowledge. It would be worth having an idea of how the Value for these plays is distributed according to Chip Stack Levels. I don't think the math is too hard to do something similar to my 3-Player example for the 10 player case, early in the tourny. There is a simplification that helps. Suppose each player has 1000 chips with a 50-30-20 payout schedule. And suppose each player buys in for $100. Clearly, by Sklansky's axiom your initial expected value for the tourny is $100. Now suppose you go all-in against another 1000 stack in a coin toss early in the tourny. Half the time you win and end up with 2000 chips against 8 other players each having 1000 chips. What is your expected value in this case according to Sklansky's axiom? Well, you should win the tourny 20% of the time. The remaining 80% of the time the tourny will be won by one of the other 8, EACH OF WHICH IS EQUALY LIKELY - this is the simplification. That means you will be competing for 2nd against the remaining 7 AND you will Place 2nd against those seven 2/9ths of the time. So you will Place 2nd in the tourny 80%(2/9) = 17.8%. Finally, you will be competing for 3rd the remaining 62.2% of the time, against the remaining 6 players who you will beat out in the proportion (2/8). ie. You will capture Third Place 62.2%(2/8)=15.6% of the time. Recapping: When you win the coin toss you place 1st,2nd,3rd 20%,17.8%,15.6% respectively. Your expected value in this case then becomes: 20%($500) + 17.8%($300) + 15.6%($200) = $185 !!!! OMG! Another Suprise. It DOES make a difference. Since you only win the coin toss Half the time, the Coin toss reduces your expected value for the tourny from $100 to 1/2($185) = $92. WOW! Getting in an all-in coin toss early amounts to giving up an 8% edge on your money. Evidently there's something to this Survival Strategy. I think I'd better look at some more examples in the Three Way too. Feel free to check and correct my Phd Candidate's Math above. Markov Chains are easy. Arithmetic is HARD. lol | ||
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| Re: Coin Toss Early in SNG, PairTheBoard, 10. Nov 2003 09:06 | ||
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| Ok, there's definitely something wrong with my 3-Way analysis. This Survival Principle has to hold there too. Consider this example. Each player in a 3-Way has 1000 chips. The payout schedule is $75-$25. Each player starts out with expected value of $33.33. Suppose two players get in an all-in coin toss. The winner then has 2000 chips to his opponent's 1000. His expected value in that case becomes (2/3)$75 + (1/3)$25 = $58. Overall, the Coin Toss Reduces his expected value from $33 to (1/2)$58 = $29. He gives up a huge 12.5% Edge on his money to make the gamble. I've got to look a lot closer at my calculation in the 3-Way Thread, and do some more examples. It may be relative chip stack size matters there as well. | ||
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| Re: Coin Toss Early in SNG, Grateful Rooster, 10. Nov 2003 09:24 | ||
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| I think all your math is correct. At least that's my Master's opinion. :^) See my re to your other post on the 3-way. The EV of all 3 players is affected, and it seems counterintuitive until you back out the math. It is not an even money situation for all 3. You've hit on something important. The coin toss situations are -EV until you reach a significant advantage over someone stackwise. This fits with the rest of what we're talking about. More plays become +EV the larger your stack becomes relative to others. This seems to argue for a strategy of playing quite tight early and loosening up as you gain stack leverage -- the strategy I've employed to success at least in SNGs. --GR | ||
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