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Server Time: 10/6/2008 4:46:38 PM PACIFIC |
 Attn Mark: Flush Thread, cont'd., Harold Pierce, Jr., 16. Dec 2003 03:36 | ||
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| Computer says message limit reached for flush thread and I should start a new one. In your last post, please edit it and provide additional info. Does the hand start with 8 players? You mention there are 6 opponents. Does this mean there are 7 players on 6th street? Or does this mean there 6 players on 6th street and the hand started with 6 players? Please clarify. Then redo you math, and you should use paper and pencil to avoid math errors. -=-MousEars | ||
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| Re: Attn Mark: Flush Thread, cont'd., Mark, 16. Dec 2003 10:15 | ||
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| >In your last post, please edit it and provide additional info. What other info are you looking for? I just picked a random situation and used #s that, while realistic, make for very easy calculations. > Does the > hand start with 8 players? Does it matter? Yes or No, you pick. >You mention there are 6 opponents. Does this mean > there are 7 players on 6th street? Or does this mean there 6 players on 6th > street and the hand started with 6 players? Please clarify. The situation i picked had 6 opponents (7players) on 6th. I just picked that # randomly. The actual # of remaining cards and outs obviously wouldn't be as high as i picked, but the math will still hold true with smaller ratios (e.g. 8:4 and 6:3 both = 2:1) > Then redo you math, and you should use paper and pencil to avoid math errors. I just came up with common situation and used variables that were very easy to calculate. If you replace the unkown cards with 12 and the outs with 4 (which would be closer to realistic #), the math still holds true (8:4 = 2:1) Against 6 opponents, when you figure that they will all recieve 1 card, your odds go to 4:2 (= 2:1) If you got rid of 3 opponents 6:3 = 2:1. This is why no one ever talks about odds with regards to the # of players in a hand. The odds of catching a card (regardless of the # of opponents) and pot odds are what every one focuses on, for good reason. Now, it doesn't matter what #s you pick for unknown cards and outs, there will always be a ratio that is independant of the # of players. If you pick the # of opponents to be other than a multiple of 3 (for my example the math still holds true. the first 3 opponents will take 1 flush card and 2 non-flush cards. The 4th opponent will take a flush card 1 in 3 times. While this specific example "appears" to affect your odds it actually doesn't because in multiple trials (say 3) of the same situation, the net effect of the 4th opponent is 0. ( 1 time he gets a flush card, 2 times he doesn't) Hope this makes sense. If you have a problem with any of it, pick something specific to talk about, its easier than trying to rewrite the whole thing. Mark | ||
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| Re: Attn Mark: Flush Thread, cont'd., Harold Pierce, Jr., 16. Dec 2003 14:15 | ||
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| Thanks for the new info. If there are 7 active players on 6th street, there are 42 (6 x 7) cards on the board and 10 (52-42) left in the stub. Of the cards on the board, 6 are unknown hole cards. Thus, the number of unknown cads is 16 not 27. If 9 hearts are out, the odds against catching a heart on 7th street is 16-9/9 =0.78 or you have a 78% chance of catching the heart. You calculated the odds as 2 to 1, and this is clearly incorrect. Interestly, I note that 16+9=27. Now lets re-do this example except there are only 4 players on 6th street: you and three opponents. In this game there are only 4 players. Thus, there are 24 (6 x 4) cards on the board and 28 (52-24) in the stub at 6th street. The number of unknown cards is 31 (28 + 3). The odds against of receiving a heart on 7th street is 31-9/9 = 2.4. Thus, in this paired example, the odds are indeed dependent on the number of players on 6th street. Would you like me to work out and post examples that show how knocking out opponents on various streets effects drawing odds on subsequent streets? -=-MouseEars | ||
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| Re: Attn Mark: Flush Thread, cont'd., Mark, 16. Dec 2003 15:18 | ||
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| Like i said in my original example, i was just picking # s that are easy to use, but the concept doesn't change. > Would you like me to work out and post examples that show how knocking out opponents on > various streets effects drawing odds on subsequent streets? > > > -=-MouseEars Go for it. The problem is, since you don't know what cards will be distributed, you can't correctly guess what your odds to catch a flush on the next street are. But i would really like to see what you come up with. Mark | ||
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| Re: Attn Mark: Flush Thread, cont'd., Harold Pierce, Jr., 16. Dec 2003 16:13 | ||
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| I'll work an example or two and post them in a day or so. -=-MouseEars | ||
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| Re: Attn Mark: Flush Thread, cont'd., Brian Starr, 16. Dec 2003 16:50 | ||
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| lol, i think this is why Roy doesnt start stud threads. Harold- what you are saying makes absolutley no sense and defies all mathematical laws. Kill this thread! | ||
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| Re: Attn Mark: Flush Thread, cont'd., Harold Pierce, Jr., 16. Dec 2003 23:29 | ||
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| Here is info on hypothesis formation. A hypothesis can be formulated on one observation, any number of observations, anecdotal information or imagination. The Pierce Poker Hypothesis (PPH) has been formulated on the basis of hand simulations using paper and pencil. Formulation of PPH would require just two hand simulations. The math that shows that drawing odds depend on the number of players in a hand has been given above. I'm working a set of hand simulation that shows the effect of knocking out players with bets or reaises on the value of drawing odds. This set will have only two hands. You might ask: How do you know that if you only use two hands for this simulation, the results represents a very special case and are not generaly applicalble? The answer is you don't know for sure. However, generality is not required for formulation of a hypothesis. Since the Pierce Poker Hypothesis has been formulated, it provides a framework for designing experiments to test it. The standard statisical method that is most used is a test of the null hypothesis which is essentially a test of whether the control experiment and treatment experiment are the same or different. The null hypothesis formulation would be: Does or does raising to knock out players on a street effect the drawing odds on the next and susequent streets? One of the most important aspect of the experimental design is replication. How many replications must be run so that when a statistical test is applied to the data a statistially significant result is obtained? It depends on the nature of the things being tested. For biolagical systems N must be at least 10 and more preferably 20 or more. I shall present some examples as test of this hypothesis. If all or a great many of these simulation support the hypothesis in a general way and no exceptions can be found, the PIerce Poker Hypothesis becomes the Pierce Law of Poker. And most importantly, I become absolutely immortal! -=-MousEars | ||
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