ok, it's been a while. i've switched from sit n go's to cash, and maybe i'll do a bigger post about it at some point. right now though, i want to write up a little something about using pot odds during sit n go's. it's something that came up with a student i'm coaching, and i was going to just write something for him, but i thought i'd use this whole series of tubes i've been hearing about so much.
say hero has 900 chips in the small blind before posting, with blinds of 50/100. he raises to 300. the big blind, who has him covered, reraises all-in. what percentage of the time does hero need to win the pot in order to justify a call?
the most common way to explain this problem is to say that hero has to call 600 to win the 1200 in the pot (his original 300 plus the big blind's 900), which means he's getting 2:1, and therefore needs to win 33% of the time. i've never found this explanation very intuitive, and it's difficult to do it fast when the numbers get trickier. i prefer to talk about dead money - it's really the same idea but i find it easier.
hero is looking at a pot with 600 chips of dead money, 300 from him and 300 from the big blind. he has to call a raise of 600. when the size of the raise equals the size of the dead money, hero needs to win 33%. here's why:
if hero calls 3 times in identical situations, he will win one. on the hand he wins, he ends up with the dead money, 600, and also his own 600 and the big blind's 600, for a total of 1800. on the two hands he loses, he ends up with 0, so calling gives him an average of 600 chips. if he folds, then he has 600, so calling and folding are equally attractive. (of course a lot of times in a sit n go you would much rather have 600 chips instead of a 33% of having 1800 and 67% having 0 - we'll talk about that in a disclaimer later).
suppose now that hero is again in the small blind, this time with 1200 chips before posting the blind and raises to 200. the big blind once again reraises all-in. now there is 400 in dead money, and hero is facing a push of 800 more. when the size of the raise is double the size of the dead money, hero needs to win 40%.
it's pretty much the same idea. if hero calls in this situation 5 times, he wins twice. when he wins, he wins 800 from each player, plus 400 in dead money, for 2000 total. so the two times he wins he has 4000, and when he loses he has 0, and the average amount that he ends the hand with is 800. when he folds he has 800 as well.
i won't go through the math in detail here, but here's a useful list:
- if the push is equal to the dead money, hero needs to win 33%. one way to think about this is that hero is putting 1 unit into the pot to win a total of 3 (one from him, one from villain, one from the dead money). so he needs to win 1 time in 3.
- if the push is double the dead money, hero needs to win 40%. he's putting in 2 units to win a total of 5.
- if the push is 3 times the dead money, hero needs to win 43%. he's putting in 3 units to win a total of 7.
- if the push is one-half the dead money, hero needs to win 25%. he's putting in 1 unit to win a total of 4.
- if the push is a third of the deady money, hero needs to win 20%. he's putting in 1 unit to win a total of 5.
this is really the gist of what i'm going to tell you here. i'll do a couple of more examples and then talk very quickly about why is not perfect.
the basic idea
say hero has 900 chips in the small blind before posting, with blinds of 50/100. he raises to 300. the big blind, who has him covered, reraises all-in. what percentage of the time does hero need to win the pot in order to justify a call?
the most common way to explain this problem is to say that hero has to call 600 to win the 1200 in the pot (his original 300 plus the big blind's 900), which means he's getting 2:1, and therefore needs to win 33% of the time. i've never found this explanation very intuitive, and it's difficult to do it fast when the numbers get trickier. i prefer to talk about dead money - it's really the same idea but i find it easier.
hero is looking at a pot with 600 chips of dead money, 300 from him and 300 from the big blind. he has to call a raise of 600. when the size of the raise equals the size of the dead money, hero needs to win 33%. here's why:
if hero calls 3 times in identical situations, he will win one. on the hand he wins, he ends up with the dead money, 600, and also his own 600 and the big blind's 600, for a total of 1800. on the two hands he loses, he ends up with 0, so calling gives him an average of 600 chips. if he folds, then he has 600, so calling and folding are equally attractive. (of course a lot of times in a sit n go you would much rather have 600 chips instead of a 33% of having 1800 and 67% having 0 - we'll talk about that in a disclaimer later).
suppose now that hero is again in the small blind, this time with 1200 chips before posting the blind and raises to 200. the big blind once again reraises all-in. now there is 400 in dead money, and hero is facing a push of 800 more. when the size of the raise is double the size of the dead money, hero needs to win 40%.
it's pretty much the same idea. if hero calls in this situation 5 times, he wins twice. when he wins, he wins 800 from each player, plus 400 in dead money, for 2000 total. so the two times he wins he has 4000, and when he loses he has 0, and the average amount that he ends the hand with is 800. when he folds he has 800 as well.
i won't go through the math in detail here, but here's a useful list:
- if the push is equal to the dead money, hero needs to win 33%. one way to think about this is that hero is putting 1 unit into the pot to win a total of 3 (one from him, one from villain, one from the dead money). so he needs to win 1 time in 3.
- if the push is double the dead money, hero needs to win 40%. he's putting in 2 units to win a total of 5.
- if the push is 3 times the dead money, hero needs to win 43%. he's putting in 3 units to win a total of 7.
- if the push is one-half the dead money, hero needs to win 25%. he's putting in 1 unit to win a total of 4.
- if the push is a third of the deady money, hero needs to win 20%. he's putting in 1 unit to win a total of 5.
this is really the gist of what i'm going to tell you here. i'll do a couple of more examples and then talk very quickly about why is not perfect.
a more complicated example
obviously usually the numbers don't work out perfectly. here's a more real-world example. stacks are before posting blinds and antes.
utg (2000)
utg+1 (1300)
villain/CO (1800)
button (1300)
SB (3300)
hero/BB (3800)
blinds are 100/200 with 25 ante. first two players fold, villain pushes for 1775 (his ante is already in the middle), and it's folded to hero. what's his % needed?
first we look at the dead money. there's 150 in antes, 100 from the sb, hero's 200 for the bb, and the villain's 200 that he had to put in to match hero's 200. so there's a total of 650 of dead money. the push is for 1775 total, so it's 1575 more to the hero. now this doesn't fit neatly on our chart, so we have to fudge it a little. double 650 is 1300, and triple 650 is 1950, so the bet is somewhere between double and triple the dead money. the % needed for a double-dead-money push is 40% and for triple- it's 43%, so we can just say it's around 42%. it doesn't really matter if it's actually 41%, the key is that we know it's not 30% or 50%.
utg (1300)
villain/utg+1 (2000)
CO (1400)
button (3800)
hero/SB (3300)
BB (1700)
blinds are 200/400 with 25 ante. first player folds, villain pushes for 1975 (his ante is already in the middle), and it's folded to hero. what's his % needed?
once again, count up the dead money. to start with, we're going to assume that BB folds, then we'll go back and add a fudge factor. there's 150 in antes, 400 from the BB, 200 from hero's SB and 200 that villain has to put in to match hero's SB. the reason we only count 200 from villain's bet as dead money is because hero has to call everything above 200 in this case, not everything above the whole BB as in other hands.
so that's 950, and it's 1775 more to hero. the push is a little under double the pot (pot and dead money can be used interchangably), so hero needs a little under 40%.
but this is operating under the assumption that BB is folding everything. in fact, if the BB were sitting out, you'd already be done with your calculation. but he's not, so we have to add something. to be honest, i've never done an extensive calculation to try to figure out how much of a fudge factor we need. i think it can be done with sngwiz but i'm not sure. we have to think of a few things to get a sense of how big it should be.
- how likely is BB to call? he should be calling with a pretty wide range with only 3 bb's left after posting. on the good side, that means his hand won't be that good on average when he does call.
- how terrible is it to lose to BB? not too bad in this case. we'll still be alive with a fighting chance. on the other hand, if BB had us covered, then it would be terrible to lose to him since we're sitting in a pretty good chip position as it is.
so instead of needing about 39%, i'd bump it up to about 44% (this is still not taking into account the fact that we don't want to take a fair gamble because of tournament implications, so in reality it should be still a little higher). i hesitated to even put a number on the size of the fudge factor here b/c i really haven't done the math, but i wanted to discourage people from thinking it should be 0.5% or 15%.
SB/hero (11000)
BB/villain (2500)
blinds are 600/1200 with ante 75, and stacks are before posting anything. now, if villain has half a clue, he's calling with anything when hero pushes. we'll assume that he will call, and if you think he might fold, then open up your pushing range a little extra. (also, we'll ignore the possibility of hero just completing in the SB).
now hero knows that if he pushes, BB will call. there is 600 in dead money from each of their SB's (as discussed above, only count 600 of the BB as dead money because hero still has to match the other 600), and 150 in antes. that makes 1350 in dead money, and hero still has to put in 1825. the easiest way to figure out that it's 1825 is to add up what hero currently has to call (600) plus the amount that BB has left in his stack after posting everything (1225).
if the dead (1350) were equal to the amount SB has to put in (1825), then it'd be 33%. double the dead would be 2700, so it's between 33% and 40%, but closer to 33%. call it 36%. even a lowly 73o is 36.6% against a random hand (i searched in vain for a website that listed this kind of info so i could provide a link, but just wound up using sngpt instead). so the point here is: fold less often than you might think in the SB with micro stacks.
obviously usually the numbers don't work out perfectly. here's a more real-world example. stacks are before posting blinds and antes.
utg (2000)
utg+1 (1300)
villain/CO (1800)
button (1300)
SB (3300)
hero/BB (3800)
blinds are 100/200 with 25 ante. first two players fold, villain pushes for 1775 (his ante is already in the middle), and it's folded to hero. what's his % needed?
first we look at the dead money. there's 150 in antes, 100 from the sb, hero's 200 for the bb, and the villain's 200 that he had to put in to match hero's 200. so there's a total of 650 of dead money. the push is for 1775 total, so it's 1575 more to the hero. now this doesn't fit neatly on our chart, so we have to fudge it a little. double 650 is 1300, and triple 650 is 1950, so the bet is somewhere between double and triple the dead money. the % needed for a double-dead-money push is 40% and for triple- it's 43%, so we can just say it's around 42%. it doesn't really matter if it's actually 41%, the key is that we know it's not 30% or 50%.
SB hand #1: facing a push
utg (1300)
villain/utg+1 (2000)
CO (1400)
button (3800)
hero/SB (3300)
BB (1700)
blinds are 200/400 with 25 ante. first player folds, villain pushes for 1975 (his ante is already in the middle), and it's folded to hero. what's his % needed?
once again, count up the dead money. to start with, we're going to assume that BB folds, then we'll go back and add a fudge factor. there's 150 in antes, 400 from the BB, 200 from hero's SB and 200 that villain has to put in to match hero's SB. the reason we only count 200 from villain's bet as dead money is because hero has to call everything above 200 in this case, not everything above the whole BB as in other hands.
so that's 950, and it's 1775 more to hero. the push is a little under double the pot (pot and dead money can be used interchangably), so hero needs a little under 40%.
but this is operating under the assumption that BB is folding everything. in fact, if the BB were sitting out, you'd already be done with your calculation. but he's not, so we have to add something. to be honest, i've never done an extensive calculation to try to figure out how much of a fudge factor we need. i think it can be done with sngwiz but i'm not sure. we have to think of a few things to get a sense of how big it should be.
- how likely is BB to call? he should be calling with a pretty wide range with only 3 bb's left after posting. on the good side, that means his hand won't be that good on average when he does call.
- how terrible is it to lose to BB? not too bad in this case. we'll still be alive with a fighting chance. on the other hand, if BB had us covered, then it would be terrible to lose to him since we're sitting in a pretty good chip position as it is.
so instead of needing about 39%, i'd bump it up to about 44% (this is still not taking into account the fact that we don't want to take a fair gamble because of tournament implications, so in reality it should be still a little higher). i hesitated to even put a number on the size of the fudge factor here b/c i really haven't done the math, but i wanted to discourage people from thinking it should be 0.5% or 15%.
SB hand #2: heads up with a micro-stack
SB/hero (11000)
BB/villain (2500)
blinds are 600/1200 with ante 75, and stacks are before posting anything. now, if villain has half a clue, he's calling with anything when hero pushes. we'll assume that he will call, and if you think he might fold, then open up your pushing range a little extra. (also, we'll ignore the possibility of hero just completing in the SB).
now hero knows that if he pushes, BB will call. there is 600 in dead money from each of their SB's (as discussed above, only count 600 of the BB as dead money because hero still has to match the other 600), and 150 in antes. that makes 1350 in dead money, and hero still has to put in 1825. the easiest way to figure out that it's 1825 is to add up what hero currently has to call (600) plus the amount that BB has left in his stack after posting everything (1225).
if the dead (1350) were equal to the amount SB has to put in (1825), then it'd be 33%. double the dead would be 2700, so it's between 33% and 40%, but closer to 33%. call it 36%. even a lowly 73o is 36.6% against a random hand (i searched in vain for a website that listed this kind of info so i could provide a link, but just wound up using sngpt instead). so the point here is: fold less often than you might think in the SB with micro stacks.
the disclaimers
we've assumed the whole time that you'd be ok with taking a fair gamble, such as a 1/3 chance to have 1800 with a 2/3 chance to go broke compared with just having 600 for sure. obviously this is not true in a sit n go, but it's more wrong some times that others. if it's early in a sit n go and you've lost 2/3 of your stack, you're not going to very unhappy at all about taking a coinflip for your stack (in fact, if you have hourly rate concerns, you might welcome the flip). but if you're on the bubble with stacks of
hero 5000
villain 6500
shorty 800
shorty 1200
then taking a flip for all of your chips with the big stack villain is an absolute disaster.
i won't give any numerical guidelines b/c it's a whole extra barrel of worms, but add a small fudge factor in most situations to the result that you get from the method i've described, and sometimes add a large or very large one, and sometimes don't even bother looking at pot odds.
if you want to learn more about when tournament situations dictate that you need to avoid big confrontations, a good starting point is independent chip model: http://sharnett.bol.ucla.edu/ICM/ICM.html.
hero 5000
villain 6500
shorty 800
shorty 1200
then taking a flip for all of your chips with the big stack villain is an absolute disaster.
i won't give any numerical guidelines b/c it's a whole extra barrel of worms, but add a small fudge factor in most situations to the result that you get from the method i've described, and sometimes add a large or very large one, and sometimes don't even bother looking at pot odds.
if you want to learn more about when tournament situations dictate that you need to avoid big confrontations, a good starting point is independent chip model: http://sharnett.bol.ucla.edu/ICM/ICM.html.
posted by pokerschwab at 11:18 AM
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