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Message: [QUOTE="starting_at_the_bottom, post: 2023821, member: 93042"] If I have understood what you are asking correctly, in that how long (in the long run) does it take for getting it in ahead, to become profitable. Then perhaps this is explained via the old coin flip example. I have copied this from another site, and will then move on to explaining how it can relate to poker "[COLOR=Navy]If a coin is balanced (by shape and weight), we reason that it should have equal chance of falling heads or tails. There is only two possible outcomes and they have equal chance ie 50% - 50%. All we can then say with certainty is that if we toss the coin, it will fall either heads or tails for each throw. We cannot be sure whether it will fall heads or whether it will fall tails. All we can say is that there is a 50% chance it will fall heads and a 50% chance it will fall tails. We have assigned a probability of outcome to the toss of the coin. When we toss the coin a second time, the probability is again 50% - 50% . It does not matter what happened in the last throw. Each throw is independent. So there is no reason why we can't have heads, heads, heads, tails, heads in consecutive throws because each throw is not effected by the previous outcome. Also, it is quite reasonable to get h,t,t.h,h,t or even h,h,h,h,h,h,h,t. Fortunately before we go mad, what probability theory does tell us is that the more tosses we make the closer the number of heads and tails will tend to 50% each. So for instance if we toss the coin 100 times the count could be 47 heads and 53 tails. If you had tossed the coin only twice you could have land up with 2 heads only. Hence to check if the coin was balanced you might want to toss it 100 times and not two or three times." ---------------------------------- [COLOR=Black]Now for example[/COLOR][/COLOR], lets assume we are talking about specifically when we get in KK vs AJoff pre flop. [COLOR=Navy] If a coin is balanced (by shape and weight), we reason that it should have equal chance of falling heads or tails. There is only two possible outcomes and they have equal chance ie 50% - 50%. [COLOR=Black]Well, we actually have 3 possible outcomes, they are:[/COLOR] [COLOR=Black]The odds are KK 71.06% AJ 28.61% tie 0.33% [/COLOR] All we can then say with certainty is that if we toss the coin, it will fall either heads or tails for each throw. We cannot be sure whether it will fall heads or whether it will fall tails. All we can say is that there is a 50% chance it will fall heads and a 50% chance it will fall tails. We have assigned a probability of outcome to the toss of the coin. When we toss the coin a second time, the probability is again 50% - 50% . It does not matter what happened in the last throw. Each throw is independent. So there is no reason why we can't have heads, heads, heads, tails, heads in consecutive throws because each throw is not effected by the previous outcome. Also, it is quite reasonable to get h,t,t.h,h,t or even h,h,h,h,h,h,h,t. [COLOR=Black]We can relate this to the above odds, and understand that the result of the previous KK vs AJ has no bearing on the current KK vs AJ Although as this is not 50/50, (the odds are in our favour) there is a lower chance of getting x number of losses in a row, and a higher chance of getting x number of wins in a row. [/COLOR] Fortunately before we go mad, what probability theory does tell us is that the more tosses we make the closer the number of heads and tails will tend to 50% each. So for instance if we toss the coin 100 times the count could be 47 heads and 53 tails. If you had tossed the coin only twice you could have land up with 2 heads only. Hence to check if the coin was balanced you might want to toss it 100 times and not two or three times. [COLOR=Black]This is the crux of the matter, [B]on the whole[/B], the more times you get into this situation, the closer the % outcome gets to 71.06% wins, 28.61% losses and 0.33% draws. As you play more and more hands the % values will get closer and closer to this. This might not seem aparrant early on, I mean with a microscopical sample size of say 4 hands you might lose 100%. But over 400 hands the percentages will be closer to the above, with 4,000 hands it will be closer still and so forth.[/COLOR] [COLOR=Black]If you were talking about specific "plays". Then that is a whole new ball game, as first you would need to quantify the optimum play. And trying to explain that is way way above my understanding.[/COLOR] [/COLOR] [/QUOTE]

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