goat_beard
06-25-2007, 04:04 PM
Hi I hope this hasnt been covered already but in case it hasnt here is a little something I wrote up in my freetime.
Goat's Theorem.
Can you make a -eV move but it end up being +eV over the longrun? My quick response would be yes, thats how you become a great player. Good players can calculate the math in their head and make correct decisions every time which yields them great profits over time, but the best players in the world can make higher level mathematic decisions by placing their opponents on a range of hands. I haven't thought too much about what I am about to right but I have a lot of ideas swirling throughout my head and just wanted to try and get them out. Any math in this post is probably wrong but if I could get a good mathematician to verify/correct it we can work out a new theorem name :-D.
I want to first bring up a hand to illustrate what point I am trying make. The scenario is as follows: You are playing a 6max game .10/.25 blinds and the table is full. Everyone at the table has 150BBs and you are on the button(OTB) with KJss. Middle position(MP) limps, Cut off(CO) folds, and you raise to 1.25, the small blind folds and the big blind re raises to 3.75, MP who limps cold calls this and you with decent odds complete the call as well. So we are three way to the flop and it comes out Qs2s7c. A pretty dry flop but you picked up the flush draw with an over pair and a backdoor straight draw. The BB leads out for 8$ into the 11.5$ pot. You have played one million hands with the BB and know that when he leads he has TP or better, we also know that he doesnt like to lead overpairs and that he would rather c/r them, overall he likes to lead overpairs about 33% of the time. MP folds, and it gets to you. The pot is now 19.5$ and its 8$ to you. The BB has committed 11.75 of his 37.50$ stack. You still have 33.75 behind you and you are faced with a dilemna. You are 100% sure that BB has TP or better here and therefor you are statistically behind no matter what. You also know that the BB is afraid to get AI with just TPTK and will often fold that to a lot of resistance. The way this certain pot has played out Hero can easily represent a low pocker pair such as 22 or 77, but he may also represent big ones such as AA,KK, and even TPTP AQ. If the BB holds AQ here we are 45% to win and if we shove and get called the pot will be 78.75 and we will have 45.455% equity against AQ. So therefor our EV would be 45.455%x78.75=35.80$. Yet if the BB has KK/AA we know he is calling for sure and against those hands we have an EV of 30.07$ and 27.72$ respectivly. Obvisouly these are very bad hands to run into but if AQ is 33% of his range and he will fold it 100% of the time would this make a shove +EV?
Now into math that I am sure to screwup.
If villian folds to us 67%(representing he only leads overpairs 33% of the time and leads TPTK the other times, but then folds to a reraise 100% of the time)of the time than we for sure win a pot of net profit worth 15.5$. So our EV from our shove would then increase 15.5x.67=+10.39 everytime we shove.
So the other 33% of the time that we run into AA or KK do we have enough EV to validate our shove? As stated before if villian has KK we would have 30.07$ EV. That in itself is not profitable enough to validate a shove it would be -6.43$ EV. But if we now add on our extra 10.39$ EV from above we find that it would be +3.96$ EV. This would warrant a shove everytime we run into this situation.
What about AA? As stated above we would have EV of 27.72$ against AA which would be -9.78$ EV. But again we add our extra 10.39$ and find that we actually have an EV of +0.61$.
So each time we have a positive EV in this situation according to my (hopefully correct) calculations. The play was very read dependent and certainly only makes sense to villians that we have history with. I hope what I wrote makes sense and I hope even more that it checks out even though I could be calculating the EV wrong etc. I do hope that what was swirling through my brain makes sense now that its typed up somewhat comprehensibly. If I could get someone to go over the math again that would be nice.
Thanks,
Goat
Goat's Theorem.
Can you make a -eV move but it end up being +eV over the longrun? My quick response would be yes, thats how you become a great player. Good players can calculate the math in their head and make correct decisions every time which yields them great profits over time, but the best players in the world can make higher level mathematic decisions by placing their opponents on a range of hands. I haven't thought too much about what I am about to right but I have a lot of ideas swirling throughout my head and just wanted to try and get them out. Any math in this post is probably wrong but if I could get a good mathematician to verify/correct it we can work out a new theorem name :-D.
I want to first bring up a hand to illustrate what point I am trying make. The scenario is as follows: You are playing a 6max game .10/.25 blinds and the table is full. Everyone at the table has 150BBs and you are on the button(OTB) with KJss. Middle position(MP) limps, Cut off(CO) folds, and you raise to 1.25, the small blind folds and the big blind re raises to 3.75, MP who limps cold calls this and you with decent odds complete the call as well. So we are three way to the flop and it comes out Qs2s7c. A pretty dry flop but you picked up the flush draw with an over pair and a backdoor straight draw. The BB leads out for 8$ into the 11.5$ pot. You have played one million hands with the BB and know that when he leads he has TP or better, we also know that he doesnt like to lead overpairs and that he would rather c/r them, overall he likes to lead overpairs about 33% of the time. MP folds, and it gets to you. The pot is now 19.5$ and its 8$ to you. The BB has committed 11.75 of his 37.50$ stack. You still have 33.75 behind you and you are faced with a dilemna. You are 100% sure that BB has TP or better here and therefor you are statistically behind no matter what. You also know that the BB is afraid to get AI with just TPTK and will often fold that to a lot of resistance. The way this certain pot has played out Hero can easily represent a low pocker pair such as 22 or 77, but he may also represent big ones such as AA,KK, and even TPTP AQ. If the BB holds AQ here we are 45% to win and if we shove and get called the pot will be 78.75 and we will have 45.455% equity against AQ. So therefor our EV would be 45.455%x78.75=35.80$. Yet if the BB has KK/AA we know he is calling for sure and against those hands we have an EV of 30.07$ and 27.72$ respectivly. Obvisouly these are very bad hands to run into but if AQ is 33% of his range and he will fold it 100% of the time would this make a shove +EV?
Now into math that I am sure to screwup.
If villian folds to us 67%(representing he only leads overpairs 33% of the time and leads TPTK the other times, but then folds to a reraise 100% of the time)of the time than we for sure win a pot of net profit worth 15.5$. So our EV from our shove would then increase 15.5x.67=+10.39 everytime we shove.
So the other 33% of the time that we run into AA or KK do we have enough EV to validate our shove? As stated before if villian has KK we would have 30.07$ EV. That in itself is not profitable enough to validate a shove it would be -6.43$ EV. But if we now add on our extra 10.39$ EV from above we find that it would be +3.96$ EV. This would warrant a shove everytime we run into this situation.
What about AA? As stated above we would have EV of 27.72$ against AA which would be -9.78$ EV. But again we add our extra 10.39$ and find that we actually have an EV of +0.61$.
So each time we have a positive EV in this situation according to my (hopefully correct) calculations. The play was very read dependent and certainly only makes sense to villians that we have history with. I hope what I wrote makes sense and I hope even more that it checks out even though I could be calculating the EV wrong etc. I do hope that what was swirling through my brain makes sense now that its typed up somewhat comprehensibly. If I could get someone to go over the math again that would be nice.
Thanks,
Goat