The situation: You are playing a deep stack tournament with 300BB starting stack. Let's suppose you have exactly 300% ROI in this field, in this specific tournament. UTG goes all-in on the first hand, everybody folds until you in the BB, you look at your hand and see Aces. Let's suppose you have exactly 80% equity against his range (to ease the calculation).

Is it worth it to call or the fold get you more EV in the long run? What is the ROI limit when you should definitely fold this hand?

What's with the same situation, when the player goes all-in and accidentally shows his hand (but not dead) QJs and you got AKs (everything is the same, except you have 60% equity)?

Wow excellent question. Excitedly awaiting responses.

Agreed. I've always been curious about this but was never able to articulate it in the way OP did.

Tough to answer, because if you fold 80 or 60 percent edge, your ROI will no longer be 300%

If you'r folding aces you would never have 300% ROI right?..


60% edge is a tough one... would love to here what people have to say about this

Snap fold both, ESP if UTG is me

what if utg is joe tehan?

lol dude why are you calling out joe tehan... your kind of a clown yourself

It's probably impossible to have a 300% roi, un less you can se your opponents cards.

It clearly depends on the field size. If the tournament is a winner-take-all sit and go with 4 entrants, it means you are able to always get the money in with your opponents drawing death. If it is a huge field, your ROI most likely comes from the sum of a lot of +EV decisions that are individually less profitable in a smaller tournament.

@Evan

Unless your opponents are muppets, it's impossible to be a big winner in a 4-handed winner takes it all SNG - if you only get it in, when your opponents are probably drawing dead.

I don't believe anyone could ever be even close to have a ROI of 300 in todays games. If you are a huge winner online you probably have a roi around 30.
I believe guys like Doyle had a huge ROI back before internetpoker. But I have no idea how big. But it was probably over 100.

Snap the AA, fold the AK.

300% ROI against any field is unrealistic especially in this day and age of hyper aggro monkeys.

You have to draw the line somewhere for spots where you wouldn't pass up edges if you think you have a good ROI vs a field; I think for me that would be 70-30 and up.

As another guy mentioned. Even though you are a brilliant pokerplayer you are not a supernatural machine. You cannot decide not to get it in with 70% equity, and still be a winner.

The question was NOT that if 300% roi is possible or not. It was the presumption, just get over it....jeeeez.

The fact that it isn't possible should actually stand for something. If we take some theoretically unattainable ROI(like 1000%) then yea we're always folding aces cause we assume our edge comes from raping everyone with blind steals and no one ever fighting back. It's impossible to just run over a table like that nowadays so edges are much smaller and you have to take gambles.

How can you be a big winner when passing up 4:1 opportunities?

I think that part of why the ROI is so high is the ability to dominate with >>> avg chips. Obviously a 300% ROI reflects going very deep when hitting the money. Doubling up early would seem to be a good way of getting a leg up on that.

I would take the AKs opportunity as well. If we are truly 300% ROI in this tourney then it means there is a lot of dead money. A guy going all-in with QJs at this point in the tourney is brain dead. I would love the opportunity to be able to take all of his chips in one hand rather than let somebody else do it. And it would likely lead to other opportunities to get it in good against smaller stacks while they are still around.

Kind of similar spot passing up the nuts but postflop i remember year or so ago ...

WSOP ME first level

Hero has JTss board AKQhh, may have been on the flop or the turn. After the action clear both players held JT.

Old guy folded his JTss face up. - At the time was mind blowing anyone considered folding but the maths showed that if the other old nit was only piling JThh then a fold wasn't wrong.



Anyone have a link to that thread?

What if every pot we played in a tournament we were all-in pre with 80% equity? What would be our approximate ROI in the tourney? I feel like the OP is a math problem, not a discussion about some macro-strategy.

If that tournament had 1000+ runners itd be like 1000%+ roi (estimating, but it would be huge)

Trying to avoid allin situations, where you can bust out, even if those huge plusev(in chips), and find a bunch of small and medium pots where you risk maximum the 10% of your 300bb. Thats how for example...imo.

using the semi silly winner take all coin flip tournament estimate, getting it in with 80% every hand in a 1024 person tournament, you win the tournament 10.7% of the time, so your ROI=100%*(.107*1023-.893*1)=10,895% Pretty sure I can do better than this (if I get it in with 100% every time I'd have a 100,000% ROI), so I'd fold.

Ok, but its a normal tournament, where you can play postflop, without the risk of busting out. You can build your stack comfortably, and it has more EV(300% roi) than playing a 80-20 for your whole stack, which -as you calculated- means a maximum 100% roi.
Nope?

Steve has the right idea, a log based approximation.


----

Here are the gory details for anyone who wants to know, cliffs at bottom:


Under the implicit assumption given by Steve, as log(your_stack/total_chips) approaches 0, trueev(stack)/icm(stack) approaches 1 linearly.

Let R be your roi (in ratio... so for example, if you have a 100% roi, your stack is worth double what it normally is, and R=2) in an N person tournament. Then if you have the opportunity to double up with probability P, you take it if P*M(2)*( R^[(log 2/N)/(log 1/N)] ) > R.

By M(2), I mean what ICM says the factor that the value of your stack has increased by in an N player tournament when you double up on the first hand. This depends on the tournament's payout structure: if it pays p_i for ith place, then ICM predicts your equity as sum_i p_i 2(N-i)/(N(N-1)), and M(2) is equal to that divided by your prior equity of sum(p_i)/N. (This is exact in the first hand case but isn't exact throughout, a better prediction overall might be M(s) = ICM(s,s,...,s,n%s).)

Anyways, for example, take the most recent Sunday Kickoff, which had N=1539 players. Then M(2) with that given payout structure can be calculated as 1.9897, and you should take a flip that wins with probability P when P(1.9897)( R^(0.9055) ) > R, or whenever the chance of winning the flip is better than R/(1.8017*R + 0.1880). This is surprisingly weak: for example, when R = 1 (no ROI), you take the flip if you are better than 50.26%. When R = 2 (100% ROI), you take the flip if you are better than 53.66%. When R = 3 (200% ROI), you take the flip if you are better than 55.76% to win. When R = 4 (300% ROI), you take the flip if you are better than 57.29% to win. Notice, to answer the AA question, you don't take the flip if R is 137 or more (13600% ROI).

As another example, take a 9 man sng. Then M(2) with that given payout structure can be calculated as 1.825, and you should take the flip with probability P when P(1.825)( R^(0.6845) ) > R. When R=1 (0% ROI), you take the flip if you are better than 54.79%, when R=1.1 (10% ROI) you take it if you are better than 58.49%, when R=1.2 (20% ROI) you take it when you are better than 62.08%, when R=1.5 (50% ROI) you take it when you are better than 72.32%, when R=2 (100% ROI) you take it when you are better than 88.06%, when R=3 (200% ROI) you never take it. To answer the AA question, the breakeven point is about 74% ROI.

-------

Notice that in large field tournaments, even if your ROI is insane, based on the ICM interpretation of equity, you should take relatively thin flips. That is because your ROI with twice as many chips is just as insane. However, as the field thins, even a small ROI means you have incredible min-edge requirements to achieve before taking a flip.

I didn't check my work so well so this could be wrong but I believe these results are accurate.

Cliffs: In the most recent Sunday Kickoff with ~1500 players, you need about 53% to take a flip when you have a 100% ROI, and you need a 13600% ROI to fold AA. In a 9 player tournament, you need about 60% to take a flip when you have a 20% ROI, and you need a 74% ROI to fold AA.

Can't imagine folding any of those.

If you are folding AA pre, you should also also be folding top-set on a board with draws etc.... can't see how you can achieve 300% (or to be honest even 10% ROI) if you aren't willing to get in with this kind of edge.

In 99.999999% of tournaments you will need to put your tourney life on the line at some point or the other, and a 80% edge in lvl 1 is just about the best time for that. It means you can take all those other small edges in the future without being afraid of busting out.

Apart from all this, even discussing folding AA pre in Lvl 1 is beyond ******ed....

calling may get you more ev in the long run. as you can play more situations with more chips and have more life.

however if for instance you were at a table where you could rob most pots, you might make more folding and doing that.