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Server Time: 11/23/2008 5:18:52 AM PACIFIC |
 Morton's Theorem - Ram, Mark, 8. Nov 2003 11:31 | ||
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| Ram wrote: >A number of theorists has taken this theorem a step further. I was actually quoting Gary Carson where he has looked at it from the drawing hand's perspective. In his book he states "When many hands with draws are competing on the flop against a semi-strong made hand, the primary beneficiary of the flop bets is the best draw, not the best hand". >In our case, the best draw against a made straight is most likely the set. When you have several other people calling incorrectly , the set benefits. Ram, Interesting stuff. I can easily see how the best draw hand is benefiting, but i think there is a difference between benefiting and +EV. The best draw (set or not) definately does benefit when the pot grows in volume, because their odds increase. However, the draws odds may increase from very -EV to slightly - EV. This may make calling or raising LESS wrong, but not right. Being less wrong does make it a good play. An example (as I see it) you have top pair vs 2 opponents on the turn. One opponent has a str8 draw and the other has a flush draw. Flush draw = 9 outs Str8 draw = 6 outs Pot is $100, you bet $100. The flush draw does not have sufficient odds to draw. However, if the flush draw called and the Str8 draw also called (without odds) the flush draw would benefit because his call became LESS wrong, meaning he would lose less over multiple trials. Flush draw calls but Str8 draw does not 2:1 for flush draw Flush draw calls and so does Str8 draw 3:1 for flush draw Obviously the flush draw gains, but is still not correct to call. In this case, the top pair hand is does lose equity in the pot when called by both, but is still a 3:2 favorite. So Morton's Theorem is right, the only one to gain by the Str8 draw's call is the flush draw, but he is still not correct to call (or raise to get more money in the pot). Mark Mark | ||
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| Re: Morton's Theorem - Ram, PairTheBoard, 8. Nov 2003 14:14 | ||
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| Another perspective is that the Top Pair made hand is also on a draw. It's drawing for blanks and in fact has the best draw of all, especially if a blank comes on the turn. | ||
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| Re: Morton's Theorem - Ram, RamDannyboy, 10. Nov 2003 20:36 | ||
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| Mark, I've been offline for a few days and only just noticed this thread. I think there are several aspects to your example, but the main question being ... should you be calling (or even raising) on the flop with a flush draw when you are behind? Correct me if I'm wrong, you seem to be saying, when the flush calls, the odds against making the flush is 2:1. When the str8 draw calls as well, the odds against making the flush is 3:1. That's not right. The odds against still is 2:1. Certainly, with more callers, you are less likely to have clean outs, but you don't know that. In any event, your outs would counterfeit other draws so, all things being equal, the odds remain the same. In this case, the flush draw is the best draw. Give that, the EV is as follows.... Scenario 1. $100 pot, TP (top pair) bets and FD calls. FD gains $200 if he wins, loses $100 if he doesn't. $200 * .33 = +$66 $100 * .67 = -$67 EV = -$1 FD doesn't have odds to call. Scenario 2. $100 pot, TP bets, SD (str8 draw) and FD calls. FD gains $300 if he wins, loses $100 if he doesn't. $300 * .33 = +$100 $100 * .67 = -$ 67 EV = +$33 Scenario 3. $100 pot, TP bets, 2 other callers in addition to SD and FD. FD gains $500 if he wins, loses $100 if he doesn't. FD still has the best draw. $500 * .33 = +$166 $100 * .67 = -$ 67 EV = +$ 99 Scenario 4: $100 pot, TP bets, 2 other and SD calls. FD raises. All call. FD gains $900 if he wins, loses $200 if he doesn't. $900 * .33 = +$300 $200 * .67 = -$133 EV = +$167 Scenario 5: As in scenario 4 but the flop gets capped. You do the maths but EV = +$300!! I know this model is simplistic, but what I'm trying to demonstrate is that despite being behind on the flop, the flush draw (best draw) should be jamming where there are more than 2 callers. In fact, the straight draw (with only 6 outs) should be doing the same! If this doesn't make sense, have a look at posts by Izmet Fekali on R.G.P. Ram PS. Suppose you adopt this strategy, imagine what it does to your variance!!! | ||
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| Re: Morton's Theorem - Ram, Mark, 11. Nov 2003 10:54 | ||
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| on 10. Nov 2003 20:36 RamDannyboy wrote: > Mark, > I've been offline for a few days and only just noticed this thread. > > I think there are several aspects to your example, but the main question being ... > should you be calling (or even raising) on the flop with a flush draw when you are > behind? > > Correct me if I'm wrong, you seem to be saying, when the flush calls, the odds > against making the flush is 2:1. When the str8 draw calls as well, the odds against > making the flush is 3:1. That's not right. The odds against still is 2:1. Ram I must correct you as you were wrong. I was talking about the pot odds for the FD on the turn, not the odds of making the hand (with 1 card to come the odds are always 4.1:1). So althought the FD doesn't have sufficient drawing odds (in my example), he is less wrong when the str8 draw calls. (2:1 pot odds vs 3:1 pot odds when SD calls) > > I know this model is simplistic, but what I'm trying to demonstrate is that despite > being behind on the flop, the flush draw (best draw) should be jamming where there > are more than 2 callers. In fact, the straight draw (with only 6 outs) should be > doing the same! > > If this doesn't make sense, have a look at posts by Izmet Fekali on R.G.P. > > Ram You have to be careful with how far you take the ramming and jamming. It does hold true, as you show, that the best draw gains as more bets get into pot, whether or not he starts out with correct odds. ( he always gains) However, if you are ramming and jamming the pot, you may come to a point where you start to decrease the EV. 1. If you bet or raise and only get one caller. (you now have a negitive value on that bet) 2. In NL and PL, you can easily get re-raised and have your odds and +EV destroyed. I do agree with you on how the theory works. My last post was just trying to show that although the best draw gains by the extra bets, it does not mean he should always bet or raise. Although he gains, he the bet or raise may still NOT be +EV. As this relates to the original post we started on, if the set of 9s is the best draw, his 3-betting may not have a + EV. It may well be very close to neutral EV or slighlty ( - ). If this is the case (- EV), although he does gain by 3-betting and pulling more bets into the pot, he gains by making the EV less negative. This is not the same as a +EV. The worst possible scenario of 3-betting the flop is that a made str8 raises and the other two players fold. This obviously has a negative value for the set. Although the above example is extreme, there are other scenarios of 3-betting the flop that have a negative value. Mark | ||
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| Re: Morton's Theorem - Ram, Snorbolus, 11. Nov 2003 06:52 | ||
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| Here is a link to Morton's original post: http://groups.google.com/groups?hl=en&lr=&ie=UTF-8&selm=33442BD0.6ABE%40ix.netcom.com&rnum=1 Snorbolus | ||
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