fimbulwinter
07-29-2005, 06:33 AM
A lot of you are posting hands where you are facing turn and river decisions where it is very likely you are beaten but still must call. Hopefully this will help you all analyze such situations in the future and make sense of some of your easier decisions.
CAVEAT: First off, there is only one poker book that every poker player must read: Theory of Poker. From that book one can teach oneself to beat any game with enough thought and introspection.
If you dont have it yet buy it and read it (http://www.amazon.com/exec/obidos/tg/detail/-/1880685000/qid=1122628681/sr=8-1/ref=pd_bbs_1/102-0971857-4680964?v=glance&s=books&n=507846)
That said, by DS's own admission, the math parts of poker are hard. moreover, it can be hard to glean an easily-applicable way of doing them so that you can honestly evaluate the value of such decisions.
Part I will be this post giving an overview of the simple analysis of calling all-in bets. there will be three examples, increasing in difficulty at the end and then one for you to try on your own.
Part II will deal with the ultimately way more interesting concept of making all-in bluffs and semibluffs. The same examples and final question format will be used.
Part I: How to analyze the EV of calling an all-in bet.
When faced with a bet that is all-in you have two options: call or fold. by definition, we set the EV (expected value) of folding as zero. this is just like standard reduction potentials, physical origins and the like in that we simply do this to set a reference by which to evaluate other options.
Another way to think of it is this: if you muck, your chipstack does not change at all. what was in it at the time stays in it and no extra money will ever come to it from folding.
The interesting thing is analyzing the "call". as i went over in the "raising middle pairs" post in MHPLNL, EV is simply the probability of each possibility times the profitability of each possibility. the probabilities portion is what you, the poker player, should (and are) constantly calculating and handicapping subconsicously.
for example:
a player raises preflop, three callers, then an uncreative, timid, tight, passive player comes over the top for a very large amount of cash, vastly overbetting the pot. Mentally you know some probabilities right off: it is highly likely he has aces, it is somewhat likely he has kings, it is very unlikely he has 94o.
So all we do is take these probabilities (in number form) and multiply them by the expected value of the play. on the river, the hand is already won or lost, so the math is much easier. the profitability of calling is the amount in the pot that your stack will increase should you call and win times the chance of that happening, minus the cost of calling and losing times the probability of that. this is extrememly simple math and so we'll start the examples with earlier street bets.
on the turn and flop, however, we need to take into account the times we have the best hand and will lose and the times we have the worst hand and will win. we can do that by taking the villains hand and estimating outs (outs*2% for turn action and outs*4% for flop actions is a good guesstimate).
onto the examples:
Ex1: Simple
I raise UTG with KK to 5xBB and are called in MP and BB.
K72 all /images/graemlins/spade.gif (15BB)
SB checks, I bet 15BB, MP folds and SB moves all-in for 30BB total. I know he will only do this with a made flush.
So now, should I fold or call?
EV folding = 0
EV calling = (probability)(profitability)
Since we know he has a flush, the probability is 1 for him having a flush and 0 for all other hands
EV calling = 1(profitability him having flush)
EV calling = (profitability him having flush)
When he has a flush, we are behind, but we have outs to improve to quads or a full house, namely we have 1 K, 3 7's and 3 2's to improve on the turn and 3 more outs if we don't make it on the river. quick head math gives 4(turn outs)+2(river outs) = 4*7+2*3 (so we don't double count) = 35% to improve to the full house and win.
www.twodimes.net (http://www.twodimes.net) can do this precisely for you if you desire (http://www.twodimes.net/poker/?g=h&b=Ks+7s+2s&d=&h=Kd+Kh%0D%0AAs+Qs)
note how close our head math gets to the real answer of 34.4%.
so we will win 34.4% of the time and lose the rest. we are paying 15BB to win a final pot of 75BB in which we will have 35% equity. we're paying 1/5 on a 1/3 shot, so even intuitively we can see we're making money here.
the real EV is:
EV = -15BB(.65) + 60BB(.35) = 11.25BB profit from making this call. therefore the call has a positive (as 11.25 is a positive number) expectation (is "+EV") and should be made.
now substitute in variables for how big his raise is and we can see how big of a raise he must make until we must fold, assuming he has the flush every time:
Note: this part is extra, you can skip it if you want
EV = (-xBB)(.65) + (45BB+x)(.35) = 0 (equivalent to folding, this is the breakoff point)
-15.75BB = -.3x
x = 52.5BB or a raise to 67.5BB or more total until we must fold, if he has the flush every time.
Ex2: Intermediate
If we have a hand range for the opponent, we can calculate how often we must not be beat in order to make a call. I'll steal a recently posted hand and simplify it a little.
It's the turn, we have AA and the board is KQ84 with no flush draws. we've bet 15BB's into a 25BB pot and have been raised 15 more all-in by a tight player (call 15 to win 70). we know he most often has KK or QQ here but can also have KQ or AK. he's not creative enough to do this with any other hands.
First we lump these into "we're ahead and "we're behind"
when ahead, he has two outs (two K's) to improve to beat our AA, so we will win 96% of the time.
when behind to KQ we have 8 outs to beat him and when it's KK or QQ we have two. lets say we then have 4 outs on average (1/3 the time he has KQ, the other times he has KK/QQ when we're behind so .33*8+2*.66 = ~4).
so now we sum the ranges and probabilities and add in x for how often we must be ahead to make the call:
EV = EV call and are ahead + EV call and are behind = 0
EV = x((.96)(70BB) + (.04)(-15BB)) + (1-x)((.08)(70BB) + (.92)(-15BB)) = 0
EV = x(67.2 + -.6) + (1-x)(5.6 + -13.8) = 0
EV = x(66.6) + (1-x)(-8.2) = 0
8.2 = 74.8x
x = ~11%
So we need to be ahead here farily rarely to make the call, so we will most likely call.
Ex3: Advanced
We're at the turn with AA and are facing an all-in PSR (pot sized raises, by definition, offer the caller 2:1 to call) on a board of J872 with a flush draw present. we know there are three possible holdings for our opponent:
a set
a straight
a straight and flush draw
moreover, we've forgotten the suits of our cards and can't break our cool table image by re-looking so his draw has either 15 or 14 outs, but on average will have 14.5 outs.
when ahead we have 0 outs over the straight, 2 outs over the set, so on average we'll say 1 out.
how often must he be bluffing for us to call?
now i will do this in an offhand fashion that is easier to do in the head/while at the table:
I'm getting 2:1 so i need 1/3 pot equity. when i'm ahead i have a little better than 2/3 pot equity (he has 15ish outs), when i'm behind i have roughly zero pot equity.
1/3 = x(2/3) 1-x(0)
.333 = .667x
x = 1/2
So he must be making a move on me a little less than (remember our simplifications from before) 50% of the time for me to call here. that means that even if i know i have the best hand here 1/3 of the timer, i do not have odds to call a 2:1 bet. interesting, right?
Problem:
I've raised 5xBB UTG with KK and get two callers, one in the blinds who is good and aggressive.
J/images/graemlins/heart.gif8/images/graemlins/club.gif5/images/graemlins/heart.gif (15)
I bet 15 and the blind checkraises me all-in for a full buyin (80BB more, 95BB total). he will only do this with a straightflush draw or a nutflush draw or a set.
how often does this have to be a draw to make the call?
hope you all enjoyed this, next part is much more fun and will hopefully get you guys to start getting much more aggro with your draws.
fim
CAVEAT: First off, there is only one poker book that every poker player must read: Theory of Poker. From that book one can teach oneself to beat any game with enough thought and introspection.
If you dont have it yet buy it and read it (http://www.amazon.com/exec/obidos/tg/detail/-/1880685000/qid=1122628681/sr=8-1/ref=pd_bbs_1/102-0971857-4680964?v=glance&s=books&n=507846)
That said, by DS's own admission, the math parts of poker are hard. moreover, it can be hard to glean an easily-applicable way of doing them so that you can honestly evaluate the value of such decisions.
Part I will be this post giving an overview of the simple analysis of calling all-in bets. there will be three examples, increasing in difficulty at the end and then one for you to try on your own.
Part II will deal with the ultimately way more interesting concept of making all-in bluffs and semibluffs. The same examples and final question format will be used.
Part I: How to analyze the EV of calling an all-in bet.
When faced with a bet that is all-in you have two options: call or fold. by definition, we set the EV (expected value) of folding as zero. this is just like standard reduction potentials, physical origins and the like in that we simply do this to set a reference by which to evaluate other options.
Another way to think of it is this: if you muck, your chipstack does not change at all. what was in it at the time stays in it and no extra money will ever come to it from folding.
The interesting thing is analyzing the "call". as i went over in the "raising middle pairs" post in MHPLNL, EV is simply the probability of each possibility times the profitability of each possibility. the probabilities portion is what you, the poker player, should (and are) constantly calculating and handicapping subconsicously.
for example:
a player raises preflop, three callers, then an uncreative, timid, tight, passive player comes over the top for a very large amount of cash, vastly overbetting the pot. Mentally you know some probabilities right off: it is highly likely he has aces, it is somewhat likely he has kings, it is very unlikely he has 94o.
So all we do is take these probabilities (in number form) and multiply them by the expected value of the play. on the river, the hand is already won or lost, so the math is much easier. the profitability of calling is the amount in the pot that your stack will increase should you call and win times the chance of that happening, minus the cost of calling and losing times the probability of that. this is extrememly simple math and so we'll start the examples with earlier street bets.
on the turn and flop, however, we need to take into account the times we have the best hand and will lose and the times we have the worst hand and will win. we can do that by taking the villains hand and estimating outs (outs*2% for turn action and outs*4% for flop actions is a good guesstimate).
onto the examples:
Ex1: Simple
I raise UTG with KK to 5xBB and are called in MP and BB.
K72 all /images/graemlins/spade.gif (15BB)
SB checks, I bet 15BB, MP folds and SB moves all-in for 30BB total. I know he will only do this with a made flush.
So now, should I fold or call?
EV folding = 0
EV calling = (probability)(profitability)
Since we know he has a flush, the probability is 1 for him having a flush and 0 for all other hands
EV calling = 1(profitability him having flush)
EV calling = (profitability him having flush)
When he has a flush, we are behind, but we have outs to improve to quads or a full house, namely we have 1 K, 3 7's and 3 2's to improve on the turn and 3 more outs if we don't make it on the river. quick head math gives 4(turn outs)+2(river outs) = 4*7+2*3 (so we don't double count) = 35% to improve to the full house and win.
www.twodimes.net (http://www.twodimes.net) can do this precisely for you if you desire (http://www.twodimes.net/poker/?g=h&b=Ks+7s+2s&d=&h=Kd+Kh%0D%0AAs+Qs)
note how close our head math gets to the real answer of 34.4%.
so we will win 34.4% of the time and lose the rest. we are paying 15BB to win a final pot of 75BB in which we will have 35% equity. we're paying 1/5 on a 1/3 shot, so even intuitively we can see we're making money here.
the real EV is:
EV = -15BB(.65) + 60BB(.35) = 11.25BB profit from making this call. therefore the call has a positive (as 11.25 is a positive number) expectation (is "+EV") and should be made.
now substitute in variables for how big his raise is and we can see how big of a raise he must make until we must fold, assuming he has the flush every time:
Note: this part is extra, you can skip it if you want
EV = (-xBB)(.65) + (45BB+x)(.35) = 0 (equivalent to folding, this is the breakoff point)
-15.75BB = -.3x
x = 52.5BB or a raise to 67.5BB or more total until we must fold, if he has the flush every time.
Ex2: Intermediate
If we have a hand range for the opponent, we can calculate how often we must not be beat in order to make a call. I'll steal a recently posted hand and simplify it a little.
It's the turn, we have AA and the board is KQ84 with no flush draws. we've bet 15BB's into a 25BB pot and have been raised 15 more all-in by a tight player (call 15 to win 70). we know he most often has KK or QQ here but can also have KQ or AK. he's not creative enough to do this with any other hands.
First we lump these into "we're ahead and "we're behind"
when ahead, he has two outs (two K's) to improve to beat our AA, so we will win 96% of the time.
when behind to KQ we have 8 outs to beat him and when it's KK or QQ we have two. lets say we then have 4 outs on average (1/3 the time he has KQ, the other times he has KK/QQ when we're behind so .33*8+2*.66 = ~4).
so now we sum the ranges and probabilities and add in x for how often we must be ahead to make the call:
EV = EV call and are ahead + EV call and are behind = 0
EV = x((.96)(70BB) + (.04)(-15BB)) + (1-x)((.08)(70BB) + (.92)(-15BB)) = 0
EV = x(67.2 + -.6) + (1-x)(5.6 + -13.8) = 0
EV = x(66.6) + (1-x)(-8.2) = 0
8.2 = 74.8x
x = ~11%
So we need to be ahead here farily rarely to make the call, so we will most likely call.
Ex3: Advanced
We're at the turn with AA and are facing an all-in PSR (pot sized raises, by definition, offer the caller 2:1 to call) on a board of J872 with a flush draw present. we know there are three possible holdings for our opponent:
a set
a straight
a straight and flush draw
moreover, we've forgotten the suits of our cards and can't break our cool table image by re-looking so his draw has either 15 or 14 outs, but on average will have 14.5 outs.
when ahead we have 0 outs over the straight, 2 outs over the set, so on average we'll say 1 out.
how often must he be bluffing for us to call?
now i will do this in an offhand fashion that is easier to do in the head/while at the table:
I'm getting 2:1 so i need 1/3 pot equity. when i'm ahead i have a little better than 2/3 pot equity (he has 15ish outs), when i'm behind i have roughly zero pot equity.
1/3 = x(2/3) 1-x(0)
.333 = .667x
x = 1/2
So he must be making a move on me a little less than (remember our simplifications from before) 50% of the time for me to call here. that means that even if i know i have the best hand here 1/3 of the timer, i do not have odds to call a 2:1 bet. interesting, right?
Problem:
I've raised 5xBB UTG with KK and get two callers, one in the blinds who is good and aggressive.
J/images/graemlins/heart.gif8/images/graemlins/club.gif5/images/graemlins/heart.gif (15)
I bet 15 and the blind checkraises me all-in for a full buyin (80BB more, 95BB total). he will only do this with a straightflush draw or a nutflush draw or a set.
how often does this have to be a draw to make the call?
hope you all enjoyed this, next part is much more fun and will hopefully get you guys to start getting much more aggro with your draws.
fim