This is a discussion on Equity related question within the online poker forums, in the Tournament Poker section; 9 handed SnG, 6 players left, quite passive game, am chip leader with 3,500. Dealt AKo I min raise from UTG and SB shoves allin 1,500 Is it 



#2




Probably a fold... i mean you're already chip leader... you've got a lot of hands to play. Yes it would be nice to eliminate another player but save the money... especially since you're not getting good odds on a call... with a min raise invested (im assuming only 200 max invested at that point)... not worth the 1300 to make a call. But without notes on the guy... no reads on any previous plays... you just never know....

#6




well being chip leader and with only 3 players ak is a hand i would call an all in, Only way you are calling almost dead is if he has pocket rockets, with lower pairs its still 50/50 and if he has A with lower kicker, Well your in good shape

#14




re: Poker & Equity related question
There should be a lot of stuff in CM book about equity. But basically the more chips you have, the less they are worth. So when you have the big stack, the chips you lose hurt you a lot more as it will affect your equity position a lot more than the gain in equity you recieve if you win.
Having said that, this is an easy call. Sounds like it just wasn't meant to be. I've been in situations like that plenty of times, you can't do much about it apart from loading another games and getting on with it. 
#17




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Well I would say call without much hesitation, but let’s do the math: Let’s assume the SB only 3bet shoves TT+, AQ, and AK (pretty standard I think). Villain's Range There are 12 combos that make up AQ There are 9 combos that make up AK (we have two of those cards). Then there are 24 combos that make up all pairs TT+ (again, we have two of those cards) That means we are ahead or dead even with 21 combos of his range. We are behind 24 combos of his range. We could further reprise this number since we really don’t want to call if he has AK and say that we are ahead of 12 combos, even with 9 combos, and behind 24 combos. The Pot The pot is $1800 giving us $1500/$1800 or 83% pot odds, or 1:5. Equity vs. Pieces of His Range If he has TT we have 42% equity – there are 6 possible TT combinations, giving us 2.52% equity. If he has JJ we have 42% equity– there are 6 possible JJ combinations, giving us 2.52% equity. If he has QQ we have 42% equity– there are 6 possible QQ combinations, giving us 2.52% equity. If he has KK we have 30% equity– there are 3 possible KK combinations, giving us .9% equity. If he has AA we have 7% equity– there are 3 possible AA combinations, giving us .21% equity. If he has AQ we have 72% equity– there are 12 possible AQ combinations, giving us 8.64% equity. If he has AK we have 2% equity– there are 9 possible AK combinations, giving us .18% equity. 2.52% + 2.52% + 2.52% +. 9% + .21% + 8.64% + .18% = 17.49% The Math Since there are 49 combos that the villain can have we divide 49 into 17.49% (17.49%/49) and come up with 35% equity. Our opponent is allin so implied odds are not a factor and I must say that I’m surprised by the results – I said call off the top of my head and I think I was wrong. We have 35% equity against his range and we really must have greater than 83% to make this call and it would be for 42% of our stack. The golden rule is never to be afraid of flipping for less than half your stack but we’re not sure we’re flipping here are we? Surprisingly (at least to me), this is a fold! 
#18




Sorry I didn’t see the A7s part of the post until after I posted, but…
Let’s add Ax suited into his range here. There are 13 suited ace combos in the deck, we have already accounted for 2 of them with our AQ and AK estimations. That leaves 11 possible Ax suited combos; just for kicks let’s assume he will 3bet shove with all of them (not too far off target since he did do it with an A7). That’s adds 11 more combos that we have about 67% equity against. This gives us 7.37% equity versus this range of hands. Adding our new range into our equation results in the following: 17.49% + 7.37% = 24.86% There are now 60 hands in his overall range so we take 24.86%/60 and come up with 41% equity – this is still a fold – we need more than double that to make this a +EV call. 
#19




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#20




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Also you never need more than 50% equity to make a call, and the pot odds offered approach a limit of 50%. for example only AA has more than 83% equity (and only just) KK has 67.4% equity. 
#21




re: Poker & Equity related question
hello ssbn743 , i got confused on one thing bro the way u calculate ur pot odds .
pot odds should be 1800 to 1500 i.e 1.2 : 1 as the pot is 1800 and u have to call 1500 to win the pot ,because pot odds is defined as ratio of current size bet to cost of contemplated call i.e how mutch can i win with what stake .. 
#23




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Step 1  Make Accurate Assumptions So the one thing I will say right off the bat is that this is what happens when we overestimate our opponent’s range. OP didn’t really give us an idea of what kind of player we were dealing with, so with an allin raise OOP I have to assume the default – which is the stone cold premium range. Quote:
Remember that 2:1 pot odds is 1/3 in fractional form. This is something that is often confused. So 1:1 would be 1/2. Or in this case, we’re getting 5/6 on our money, or 5:1. We’re getting 1 in 5, or damn close to 83% pot odds. That means you need to be good better than 5 times out of 6 to make this +EV. Remember the first number is the number of times something will not happen and the second number is the times that it will. We will lose 5 times and win 1 time, 5:1. You’ll also notice that adding the two numbers together will result in the denominator from our 5/6 fraction. Using your 1.2:1 example, we can make the fraction 1.2/1, multiply by 10 (10/12), and reduce to 5/6, which will come out to 5:1. We all should know that there is no hand poker that will be good 5 times out of 6, so this is a fold. Assuming we have calculated our opponent’s range correctly, which we did not in this case. Quote:
He could have 0 combos of suit A (because we have the Ace) He could have 10 combos of suit B (minus 1 combo because we have the King of this suit) He could have 12 combos of both suits C and D This means he could have 34 combos of Ax suited. We do still have 67% equity against all hands in the range which will give us 22.78% against that range, 17.49% + 22.78% = 40.27%. Now there are 83 hands in his range, so 40.27%/83= 48.51%  which is still long ways off from the 83% we need. Now let’s assume differently: With an allin raise OOP we have to assume at least some premium combos are in his range, but let’s say that he could only do this with AA KK or any suited Ace: AA – 3 combos, we have .21% equity versus this range KK – 3 combos, we have .9% equity versus this range AXs – 34 combos, we have 21.44% equity versus this range. .9% + .21% + 21.44% = 22.55% equity versus his range. Then we take 22.55% divided by the total number of hands in his range (38) 22.55%/38 = 59% equity  Still an easy fold because of the ratio of the pot! Although I admit I would have called at the table as well, but the math does not support it! If this is wrong – someone is going to have to tell me where! Quote:

#24




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It can be clearly shown that the amount of equity we need to call converges to 50%. this is intuitively logical as that is both the minimum needed to value bet, and the limit of the pot odds equation. example, if you shove 1million bb into a pot of 1 and I have exactly 50% equity, I show a profit of .5bb on my call in terms of cEV. therefore it can never be correct to fold with greater than 50% equity in an all in situation. (or any other hot n cold situation) pokerstoving gives us 49% equity v our opponents range, Im not going to go through working it out manually but your method seems different and definitely incorrect as the answer it gives is extremely off. The method I would use would be sum ((equity v hand) x P(hand)) to workout our overall equity. Another non congruent piece of logic you used was assuming an irrational shoving range, its illogical to assume villain would shove A7s but fold AJo or 99 
#25




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Figuring the pot odds as such: $1500/ ($1500+$100+$1500) is not correct. Pot Odds “The idea of pot odds starts with comparing the size of the pot with the size of a bet we must call….So pretend we’re on the flop in a hand, and the pot is $10. It’s the villain turn, and he bets $10. The pot would now be $20 and it’s $10 for us to call. We’d be getting 20:10. We then reduce this to 2:1. We’re getting 2:1 odds on our call.” (“Poker Math That Matters” pg 59, 2010). This pot is therefore calculated as $1500/ ($1500+$200+$100), $1500/$1800, 5/6, 83% or 5:1. Doing the math as you have $1500/ ($1500+$200+$1500) does result in 42% pot equity; but that’s not right. Implied odds are not a factor here since the villain doesn’t have any chips left; therefore we need a hand that is going to win greater than 83% of the time. Obviously that can't happen preflop so we must then consider his range and consider it hopefully wide enough to make this call against a range. Nonetheless the premium range consisting of TT+, AQ, and AK results in the following odds: There are 6 combos that make TT There are 6 combos that make JJ There are 6 combos that make QQ There are 3 combos that make KK (We have one of the Kings) There are 3 combos that make AA (We have one of the Aces) There are 12 combos that make AQ (We have one of the Aces) There are 8 combos that make up AK (We have an Ace and a King) We have 42% equity against TT – There are 6 total hands he can have – (42%/6=7%) We have 42% equity against JJ – There are 6 total hands he can have – (42%/6= 7%) We have 42% equity against QQ – There are 6 total hands he can have – (42%/6= 7%) We have 30% equity against KK – There are 3 total hands he can have – (30%/3=10%) We have 7% equity against AA– There are 3 total hands he can have – (7%/3=2.333%) We have 72% equity against AQ – There are 12 total hands he can have – (72%/12=6%) We have 2% equity against AK – There are 8 total hands he can have – (2%/8=.25%) There are 44 total combos he can have here in the premium range. So, adding these numbers together =39.583%. Then we divide by 44, (39.583%/44=89%) We have 89% against the highest range in the game and need 83% to be +EV – Call, and I’m sorry I got the numbers jacked up. I knew it sounded wrong from the start but couldn’t figure out why. 
#27




lol its funny, now i only have a little bit of knowledge about "equity" and i know alot about pot odds
The rules everyone is stating here is for a cash game scenario, as long as you have 50% equity it is a call etc etc but in a MTT its completely different logic, we dont just calculate the pot odds and call for every flip, that would be insane instead we look at risk and reward which is how much equity we have in the pot already, + how much we stand to gain + how bad a loss would affect us The maths here is two different kinds of maths, lets just say worst case scenario, opponent can do this with a hand like J 10s the pot odds would say we are a 60% favourate here and so we would make a call and in cash would definately be a call, but in an MTT if you called every all in with AK, knowing they had hands as bad as J 10, then you would lose by the 2nd  3rd race mathmatically as a result we should always be looking at the equity we have in a hand against the equity we stand to gain, and if he hasnt got a minimum of half your stack usually making too many calls like this is given us very little gain against a huge loss if we lose i hope i have understood this correctly and if ssbn could comment, because i could be wrong as i dont 100% understand how equity works, i just believe that is what he is referring to in his maths 
#28




re: Poker & Equity related question
I think the rational decision would be a fold...but thinking that you have a pretty good hand , you could consider a call. It's risky , but you know what they say "There would be no game without the risk". This is what makes the game so beautiful.

#29




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So Duggs, there’s the math, where is it wrong? I have the book right in front of me that tells me to do the math exactly like that. I agree, 89% sounds ridiculous, also we’re both wrong with our pot odds, since we already have $200 in the pot it’s only $1300 for us to call ($1300 / $1500+$200+$100) ($1300/$1800), 13/18, or 72% , 13:5 in favor of the pot. I would really like to understand this – initially I said call here, just as most did, but then I did the math and said fold. In the time since I think I got some of those numbers screwed up, I had the right numbers in the post but apparently jacked up the calculator. And now, I’m coming up with a ridiculous number, 89%, that can’t be right; can it? But I can’t figure out where it’s wrong; anyone? 
#30




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#31




ssbn you are ignoring the money you put into the pot, that weighs into the pot odds, it should be noted that 1300:1800 is equivalent to 1300/3100 in the same way that 1800:1300 is equivalent to 1800/3100
you are also dividing the equity of each hand by the number of combos, this is wrong. the correct formula is SUM P(EQ) to determine our equity where SUM=summation of all the terms P(EQ) where P= probability of each hand within the range (hand combos/total combos) EQ= equity of each hand combination v our hand 
#33




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and if i can understand it who knows i might be able to come up with the answer lol 
#34




ok after relooking at the opponents opening thread,
you have min raised 200, he has shoved 1500 from sb. so 300 is in the pot, he shoves for 1500 giving us 1800 and so our odds should look like this we call 1200 to win 3000 which is 6:15 (or 40%) so pot odds offer 40% cus we only need to win 40% of the time to make this a profitable call one thing i have noticed and always remembered is you have to remember to add on what your putting into the pot, and it looks like you have forgotten to do this, unless of course im missing something again xD 
