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 

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Equity related question 
#1




Equity related question
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 call or fold?
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#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....
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#3




blinds+antes? how many places paid? BI of the sng?
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doomasiggy looking gully in the joint if ya'll ppl ain't talking 'bout large money 
#4




Sorry,
50/100 blinds, no ante, $1 bi, 3 places paid
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#5




yeah call. 6 handed he's probably rejamming like 77+/QJs+/KQs+/AJo+/ATs+ here. Plus it's a one dollar comp so he might be jamming 74s for anyone knows.
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doomasiggy looking gully in the joint if ya'll ppl ain't talking 'bout large money 
#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
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#7




He had A7s and flushed the flop.
A couple of hands later he busted my KK with AA and I was out. Was just wondering with the blinds quite low and being the chip leader whether it was correct.
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#8




It's fine. He's shoving a lot worse so you're ahead often enough that it's a call.
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doomasiggy looking gully in the joint if ya'll ppl ain't talking 'bout large money 
#9




You could fold then use the 1500 to shoot a 250 bet at him every time its his big blind.
Fully loaded 6 shooter.....
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Benny Binion ~ "Good food, good whiskey, good gamble." 
#10




Cool, just reading Collin Moshman SnG Strategy and there is an example where he says to fold QQ to an allin from a player with an equal stack at the bubble. I know it's a different scenario totally but trying to learn ICM better.
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#11




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'gg' 
#12




Yes, someone on here recommended it a while back. I've had it a while and it's getting more useful each day.
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#13




what is he shoving in that spot? hard to do readless, but why would he shove qq, kk, aa, there?
the 15bb shove screams acerag or small pair call
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#14




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.
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#15




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#16




Many paid. The chance of other pay this allin SB is great. Ai becomes more lottery.
I think it would be good to keep the chip leader. Other hand, in better positions, come.
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#17




re: Poker & Equity related question
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!
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#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.
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#19




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#20




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.
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#21




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 ..
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#22




The math must be wrong. 1.2 to 1 pots odds with 49% equity AQ+ 10 10+ is a clear call.
$1.02 to win $1.20 every coin flip. And he shoved with A7 suited, adding that as the bottom of his range takes your equity to 57.5%
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#23




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.
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.
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!
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#24




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
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#25




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.
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#26




again thats not right, you cant have 89% v 1010+ AQ+ with AK, that is more than AA has against any range. the pot odds is also incorrect.
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#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
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#28




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.
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#29




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?
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#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
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#32




1300:1800 does not = 1300/1800
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#33




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




re: Poker & Equity related question
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
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#35




3100, we have to call 1300 (1500200) but otherwise yea looks fine
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#36




I would fold holding 3,500 theirs no reason to call it off.
theirs no way im not cashing from 3,500  you can control your table with ease but if you lose the toss (which you will half the time  you will lose your dominance and be back in a dog fight
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Anything is possible... When you Believe 
#37




i dont understand why your folding though cotta?
yes you can control the table, but how often are you going to fold a dominating hand like this? what if he starts shoving every hand, if the odds are correct to call by not making the call your losing money, everybody is about to go into shove and fold mode, and AK is not the sort of hand i would be folding once your there remember opponent shoved 15BB, his range should only hold AK  AA  KK, but what if you wait a bit longer say 2 more minutes blinds go up, he now has 7BB with same stack size, are you still folding? because according to you, no matter what hand you get the risk of going out on the bubble is bad (as it was opponent wasnt taking into consideration UTG position, because he did a "resteal" when opponent wasnt stealing, and if your not stealing the blind then the call is definately the option to go for" this is the stage of the STTs where players stacks mean hardly anything, you yourself only have 30BB, how often you going to raise fold AK when them blinds go up, early on in STT there is reason to fold this pre, but right now i cant see how you can ever justify it, odds tell you you only have to win 40% of the time to be profitable. now if you are min raising and folding to a shove from UTG you might aswell start to open fold AK from UTG, because your leaking so many chips by doing this. then again im a MTT specialist not STT so maybe the same rules dont apply with ICM? i dont know, but as far as equity is concerned which is what this thread is about, were trying to figure out if he had enough equity to fold, or should it have been a call
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#38




First, pot odds: most people just learn the trick that we need X% equity to call where X = Call/(Call+Pot), but where this COMES from is an EV equation. EV(Call) = (Win %)x(Potsize)  (Lose %)x(Betsize) Lose % just = 1  Win %, since we must either win or lose the hand. Also, to breakeven on the call, EV(call) must be >= 0. So: EV(Call) = 0 = (W)x(Pot)  (1W)x(Bet) Now it's just algebra from here: 0 = WxPot  1xBet + WxBet 0 = Wx(Pot+Bet)  Bet Wx(Pot+Bet) = Bet W = Bet/(Pot+Bet) Tada!!! So that's where you get that handy trick. So in this case, the blinds are 50/100, we make it 200 UTG, and the SB jams 1,500. The BB's 100 is also in the pot. So pot = 200 + 100 + 1,500 = 1,800. We must call 1,300 to win 1,800. Our POT ODDS are 1,800:1,300 or ~1.38:1. This means that for every 1.38 times we lose the pot, we must win 1 time to breakeven. You can think about it like > if we play this spot 2.38 times, then we must WIN one time, but we can lose the other 1.38. So we must win 1 time out of 2.38. Note this is the exact same equation as above. 1/(1+1.38) = 42% (rounded) 1,300/(1,300 + 1,800) = 42% (rounded) So our EQUITY against villain's range must be 42% AT LEAST to break even. Onto your equity calculation. This is wrong in all sorts of ways every time you tried to do it, so instead of trying to correct each mistake, I'm just going to walk through the calculation. Let's start by assuming that you've ranged SB correctly, and he has TT+/AQ+. Namely, he can have TT, JJ, QQ, KK, AA, AQo, AQs, AKo, AKs. If we didn't know our own hole cards, then each pocket pair would have 6 combos, each suited hand would have 4 combos, and each offsuited nonpair hand would have 12 combos. BUT, we have AK, which means we block some combos. For simplicity, I'm not going to worry about suitedness here, since it will only change the equities a little bit. We have about 43% equity against TT, JJ, and QQ, 30% equity against KK, 7% equity against AA, and 72% equity against AQ. For AK, we will win such a small % of the time, and chop such a high percentage, that I will just call our equity 50% against AK combos. The key to determining equity is a weighted average. TT  6 combos JJ  6 combos QQ  6 combos KK  3 combos (we have blockers for everything aside from TT and QQ) AA  3 combos AQ  12 combos AK  9 combos = 45 combos total So we can say what % of his range is TT, what % of his range is JJ, etc. TT > 6/45 = 0.1333 JJ > 6/45 = 0.1333 QQ > 6/45 = 0.1333 KK > 3/45 = 0.0667 AA > 3/45 = 0.0667 AQ > 12/45 = 0.2667 AK > 9/45 = 0.2 Note that these sum to 1, since this is what his entire range is comprised of. Now to find our equity, we take our equity against a given hand times the chance that he holds that hand. This is our weighted average. Total Equity= (% TT)(Eq Vs TT)+(% JJ)(Eq Vs JJ)+(% QQ)(Eq Vs QQ)+(% KK)(Eq Vs KK)+(% AA)(Eq Vs AA)+(% AQ)(Eq Vs AQ)+(% AK)(Eq Vs AK) Equity = 3x(0.1333)(0.43)+(0.0667)(0.30)+(0.0667)(0.07)+(0. 2667)(0.72)+(0.2)(0.50) (note that I just multiplied by 3 to deal with TTQQ, since the combos and equities vs. those hands are the same) Equity = 0.1720 + 0.0200 + 0.0047 + 0.1920 + 0.1000 Equity = 0.4887 = 48.87% We have nearly 49% equity against that range, and need only 42% to make a +chipEV call. But note that we are losing the hand more than half the time. Whether you want to flip is your choice. But also consider that his range is probably much wider than this with a 15bb shove.
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My Poker Vlog: https://www.youtube.com/channel/UCZF...eudgbdpLD7slQ Originally Posted by TylerN: scourrge bro u sir are a wisdom like god 
#39




^ +1 this is the long version of the calcs i did
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#40




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#41




direct quote from your earlier post
" The Pot The pot is $1800 giving us $1500/$1800 or 83% pot odds, or 1:5. " 83% is 1500/1800 so this is exactly what you did, just saying
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#42




I still don’t understand pot odds – that may seem like an obviously statement but I understand what each is saying – I get it, I really do – but I’m reading a book on Poker Math right now that says this: “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). I understand the two methods in this post: X=a/(a+b) Or X =a/b The question is which one is right? I always thought it was x=a/(a+b) too, until I read the book cited above. X=a/b In such a case as the books’ example from above, we have to call $10 to win a $20 pot, thus 20:10 becomes 2:1 and converts to 1/3 in fractional form. Therefore to call in this situation we need to win 33% of the time. X=a/(a+b) Now if I do the math the other way, then I get $10 to win $30, thus 30:10 which becomes 3:1 which is further represented as 1/4, or 25%. In our example from the OP this was an allin pot, meaning no action was pending after our call. Do we use x=a/b in that situation and reserve x=a/(a+b) for situations in which the villain has chips left? Quite a bit different, so which way is right? If you say x=a/(a+b) then I’m going to cite a published poker author that disagrees; is the book wrong?
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#43




Its a tempting call... but there is no need to risk your chips and lose the chip leader position.
I would let him take the cents there... and take him out later, lol
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#44




"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).
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#45




Pot odds means: The amount we risk (amount we have to call) to (ratio) the amount we can win (the pot). So yes, if the pot BEFORE the bet is $10, and he bets $10, then the pot is now $20, and we are facing a $10 bet.
We have to call $10 (risk) to (ratio) win $20 (pot). This means we are getting 20:10, or 2:1 ODDS to call. This is not the same as the EQUITY we need. EQUITY is the percentage of the time we will win the pot. If our ODDS are 2:1, then we need at least 33% EQUITY to make a breakeven call. Why? Because the ODDS we are getting 2:1 dictate this. BREAKEVEN EQUITY = Bet/(Bet+Pot) = (Right side of ratio)/(Left side of ratio + Right side of ratio) = 1/(2+1) = 1/3 = 33% But like I said, the breakeven equity equation stems DIRECTLY from a standard EV equation. You are reading a math poker book but you don't seem to be understanding. Imo, go slower, go a chapter at a time, and do practice problems so that you know you are understanding the concepts and can apply them correctly.
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My Poker Vlog: https://www.youtube.com/channel/UCZF...eudgbdpLD7slQ Originally Posted by TylerN: scourrge bro u sir are a wisdom like god 
#46




thank you guys i hope i can at some point get a better understanding of the maths involved in this simple equation lol, definately need to pick me up 1 of these maths books
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#47




Call ofc only 2 hand beat you pre flop aa kk.Dont raise under the gan whit ak if you fold when someone reraise you...
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#48




You still have your pot odds wrong.
The pot here is the blinds 150, plus the min raise of 200, plus his 1500 (1850) He has called your 200 and raised you 1300. You must put in 1300 to win a pot of 1850. The ratio between these numbers is your pot odds and has nothing to do with what you have already put into the pot or the total amount when your 1300 goes in as well. 1850 divided by 1300 is 1.42 (to 1) You are also not in any danger of elimination as you had 3500 at the start of the hand.As stated before with AK you have 49 % equity against 10 JJ QQ KK AA AK AQ, Which makes this a clear call.
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#49




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#50




[x] Done all I can for this thread
[ ] People reading my post correctly [x] Sigh
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My Poker Vlog: https://www.youtube.com/channel/UCZF...eudgbdpLD7slQ Originally Posted by TylerN: scourrge bro u sir are a wisdom like god 

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