What I think is an extremely complex decision

[Oxford_HRV]

I have  a 30% roi in the big 109. This is taken as a "concrete" fact.

I have a 5% edge shoving the button with K9o  with 12bb. Do I take the 5% edge. Will it hamper my overall long term roi? In theory, if I took every spot that was plus ev my roi might be lower than someone who only took 20%+ roi spots. How do we decide on that? What spots are too marginal too take and when/how/why do we decide to take the spot? I mean in a certain tournament you could make a 20% roi + play and it would never matter if you'd finalled a particularly big Sunday Millions for example.

i dont get how you have a certain 5% edge shoving the button with 12bb and K9o?

this question feels like the answer relies purely on the times villain will hero fold better and how much you can repeat the same move.

I don't play very much poker, and therefore take more variance than you. This would most likely make me fold more close scenarios than if i played full time, when you are considering your edge i think you have to consider variance aswell. Therefore the better your ROI the more you are winning and variance is proportional to this so you should encounter less variance in these small edge spots?

[theprawnidentity]

I think you're missing the point a little bit Oxford.  We're assuming for the sake of the argument that the figures quoted are fact.  It's just a hypothetical situation evaluating whether or not we should take less of an edge in one particular spot than we have in a tournament overall.

Also in a situation with a small edge we would encounter more variance, not less.  For example if we rolled a dice and 4 numbers were our outs, we would bust more times on average than if 5 numbers were our outs.

[rfgqqabc]

I think you're missing the point a little bit Oxford.  We're assuming for the sake of the argument that the figures quoted are fact.  It's just a hypothetical situation evaluating whether or not we should take less of an edge in one particular spot than we have in a tournament overall.

Also in a situation with a small edge we would encounter more variance, not less.  For example if we rolled a dice and 4 numbers were our outs, we would bust more times on average than if 5 numbers were our outs.

Yeah I just made it up, it was more about what rois are compromised of and how this is affected by taking a decision we know is lower than our actual total roi. I think it would probably be possible to solve certain situations for our roi in a push/fold spot, but working out our actual roi is a lot more difficult.

[buffyslayer1]

Age old question I guess and ofc its hard to determine how much of a 'edge' we have in any give spot.

The way I always looked at this issue is just how profitable of a spot it is full stop and how that correlates to our overall 'edge' idoesn't matter (our 'edge' is made up of all the times we have the ability to make a profitable play and exploit that)

K9o for 12bb given perfect calling ranges (and no ICM factors) nets us around 30 chips profit on a shove.

That might not seem a lot on the surface but 30 chips is of 0.3bb on one hand, if we had this spot 100 times and made the same play our expecatation on the play would be 30bb/100 hands.

If this was a cash game spot and we could just play out this spot for the rest of our lifes I am sure we would all take a jam here and be very happy about it and retire off the winnings. Most regs are very happy with 5bb/100 I would imagine

As already mentioned somewhere making this much profit when we have just 12bb is also a factor its absolutely huge to make this many chips on a play regardless of stacksize anyway but off a 12bb stack if we don't take it, well I would question actually if we could be a winning player tbh. As I don't think anyone in the world can make up for the loss of ev here by 'waiting' for better spots. This is the better spot!

Even if we take a hand thats not so +ev say the worst K here, K7o it make us 1.4 chips in the play, again not that many chips but still would work out to a winrate of 1.4bb/100 on this one spot.

As you can tell I am a advocate of taking every spot we can to maximise ev, I love it when playes give up +ev spots because of their 'edge' well guess where that edge/ev goes. straight to me

[Honeybadger]

I have thought about this exact issue in the past. It seemed confusing at first... is it right to turn down a 5% (or smaller) edge if our expected ROI in the tournament is 30%? It turns out that we SHOULD take every edge, because our ROI is made up of all the edges (both big and small) combined.

Having a strategy based on turning down small edges will reduce your overall ROI. However, it will also reduce variance - which means that whilst your ROI is smaller, you are more likely to get close to that reduced ROI in any given tournament than if you took every edge and maximised your ROI.

Take it to an imagined extreme. Imagine you are playing a HU SNG and opponent is forced to open jam every hand blind. You should call according to Nash (which is 51.4% of hands with 100bbs according to Tomsom who ran it through some fancy program for me last night). If you think to yourself "wow, he is jamming every hand blind - I can fold some of the more marginal hands like Q7s in order to wait for a better spot" then you are not doing anything wrong as such. But you ARE reducing your ROI in this HU SNG. You are, however, MUCH more likely to hit that (reduced) ROI if you sit on your hands and wait for a much better hand before you call his jam. If you were able to play an infinite number of these HU SNGs with me guaranteed to jam every hand blind then you should just go ahead and take every tiny edge and maximise your overall ROI. However, if I said to you that I would play you one HU SNG only for a million quid and that I would open jam every hand blind... well in that case your best play is to wait for a better hand than Q7 (or whatever) because if you lose with Q7 you will not be able to take advantage of bigger edges later on (I am only playing you once). But if I am going to play you infinite times (and you can afford it!) then you are not risking losing out on making future bets that are far more +EV than calling with Q7... so you should snap up every edge and maximise your ROI.

BTW, just as an aside... the widely held premise that reducing your ROI/EV necessarily increases your variance is completely incorrect. Everyone seems to trot this out as if it is true, but it is definitely wrong. Reducing your ROI means you are more likely to have a losing streak, but this is not the same as saying you have more variance.

To prove this point, let's use another imagined extreme. Imagine that in a tournament or cash game you adopt a strategy of always folding every hand preflop, without even looking at your cards. This definitely reduces your EV/ROI! However, you will experience precisely NO variance. You will always hit your ROI in a tournament - i.e. you will always lose your buy-in. And in a cash game you will always hit your expectation every single round of the table you play - i.e. you will lose exactly 1.5bbs. The only variance you would ever experience is when you get a walk in the BB.

[Honeybadger]

If you think to yourself "wow, he is jamming every hand blind - I can fold some of the more marginal hands like Q7s in order to wait for a better spot" then you are not doing anything wrong as such. But you ARE reducing your ROI in this HU SNG. You are, however, MUCH more likely to hit that (reduced) ROI if you sit on your hands and wait for a much better hand before you call his jam.

The pedant in me feels obliged to mention that this ^^^ is completely wrong. In a single HU SNG it is impossible to hit your ROI. You either end up way above EV or way below EV depending on whether you win or lose. I guess what I should have said is that you are more likely to WIN the HU SNG.

The general point I was making still stands though, despite my sloppiness in the quoted bit above.

[Honeybadger]

Another point to mention is that there is a big difference between ROI for a specific tournament and ROI overall. And in the same way there is a big difference between bb/100 in a specific hand of poker and bb/100 overall.

If you take a very small edge for all your chips in a tournament then - at the point at which you choose to do so - it is possible that your ROI for that particular tournament is less than your overall ROI (i.e. your expectation when you first sat down to play the tourney). Taking this small edge still maintains your overall ROI though, and turning it down will reduce your overall ROI.

In the same way if you are a 5bb/100 winner in cash games, you may get in a spot which - on average - nets you 1bb/100. You can't think to yourself "well I am a 5bb/100 winner, so I can't take a 1bb/100 edge in this particular hand". If you do this then you will no longer be a 5bb/100 winner.

To help you get your head round this issue you need to remember that so many hands you are dealt, whether in a cash game or a tournament, have a negative EV. The reason for this is because you have to post blinds and antes. Just being dealt in on your BB is -EV. So taking even a tiny edge is essential to make up for all the -EV spots you are in.

Part of the reason why this whole issue is so difficult to comprehend is IMO because the fact that a single tournament is a discrete unit and this encourages us to see things in 'tournament life' terms rather than seeing one tournament as just a tiny part of your overall play. Same with thinking of cash games on a session by session basis. Really it is all just one long game, but our minds are conditioned to focus on session by session or tourney by tourney results.

[wazz]

I do wonder whether anyone has ever taken a spread of 6max cash winrates and worked out a way to apply them to tournaments to see how they would translate (under certain theoretical conditions of course).

One thing to remember, if you're going to apply the practical considerations of this theoretically flawed logic, is that unless you're the kickassiest player around, you should generally only be passing edges at the beginning of tournaments, due to the evolutionary pressure of tournaments. If you have a 30% roi, that's over the whole tournament, and bad players tend to bust before good ones. So if you got to play the entire tournament out against the same level of field at the beginning, you might have a 75% roi. If you had to play the entire tournament against the likely field you'll encounter on the final table, you might only have 10% roi. You could even have a negative roi and still have a positive one overall. Passing up any edge when you're only a small winner will have a much more significant (negative) effect on your roi than early doors, where the kelly-criterion-like logic of 'assurance of being able to find better future spots' has more impact, also given depth of stack.

[Oxford_HRV]

how i think with the variance being smaller here is by being 'outside the game' this one spot may have only a 5% edge so its a high variance play but if you sustain a long term positive roi your outside game variance is smaller so thinner spots become more profitable? if that even makes sense

[wazz]

how i think with the variance being smaller here is by being 'outside the game' this one spot may have only a 5% edge so its a high variance play but if you sustain a long term positive roi your outside game variance is smaller so thinner spots become more profitable? if that even makes sense

It's a common misconception that variance decreases when you have a higher winrate. While variance and winrates are both a function of playing style, they don't directly affect one another. One source of profit for a winning poker player is taking on variance that others aren't willing to - in a sense, offering insurance, i.e. if someone wants to fold when they're getting the right price to call (all-in) but folds to decrease variance, you get an increase in EV. Or in other terms - a professional gambler provides an entertainment service to the amateur.

While it might seem that increasing your winrate decreases variance, this is only due to a misunderstanding of what variance means. People usually measure variance by how bad they run, not how good they run. So a stronger winning player (disregarding playing style) will have smaller downswings than a breakeven or losing player, but will have bigger upswings - positive variance.

[Oxford_HRV]

how i think with the variance being smaller here is by being 'outside the game' this one spot may have only a 5% edge so its a high variance play but if you sustain a long term positive roi your outside game variance is smaller so thinner spots become more profitable? if that even makes sense

It's a common misconception that variance decreases when you have a higher winrate. While variance and winrates are both a function of playing style, they don't directly affect one another. One source of profit for a winning poker player is taking on variance that others aren't willing to - in a sense, offering insurance, i.e. if someone wants to fold when they're getting the right price to call (all-in) but folds to decrease variance, you get an increase in EV. Or in other terms - a professional gambler provides an entertainment service to the amateur.

While it might seem that increasing your winrate decreases variance, this is only due to a misunderstanding of what variance means. People usually measure variance by how bad they run, not how good they run. So a stronger winning player (disregarding playing style) will have smaller downswings than a breakeven or losing player, but will have bigger upswings - positive variance.

[rfgqqabc]

EV (»?«)   2.50 BB/100
Standard deviation (»?«)   100.00 BB/100
Hands(»?«)   100000
Expected winnings (»?«)   2500.00 BB
Standard deviation after 100000 hands (»?«)   3162 BB
3.16 BB/100
70% confidence interval (»?«)    [-662 BB, 5662 BB]
[-0.66 BB/100, 5.66 BB/100]
95% confidence interval (»?«)    [-3825 BB, 8825 BB]
[-3.82 BB/100, 8.82 BB/100]
Probability of loss after 100000 hands (»?«)   21.4598%
Probability of running at or above observed win rate (10.00 BB/100) over 100000 hands with a true win rate of 2.50 BB/100 (»?«)   0.8853%
Probability of running below observed win rate (10.00 BB/100) over 100000 hands with a true win rate of 2.50 BB/100 (»?«)   99.1147%
Minimum bankroll for less than 5% risk of ruin (»?«)   5991 BB



EV (»?«)   5.00 BB/100
Standard deviation (»?«)   100.00 BB/100
Hands(»?«)   100000
Expected winnings (»?«)   5000.00 BB
Standard deviation after 100000 hands (»?«)   3162 BB
3.16 BB/100
70% confidence interval (»?«)    [1838 BB, 8162 BB]
[1.84 BB/100, 8.16 BB/100]
95% confidence interval (»?«)    [-1325 BB, 11325 BB]
[-1.32 BB/100, 11.32 BB/100]
Probability of loss after 100000 hands (»?«)   5.6923%
Probability of running at or above observed win rate (10.00 BB/100) over 100000 hands with a true win rate of 5.00 BB/100 (»?«)   5.6923%
Probability of running below observed win rate (10.00 BB/100) over 100000 hands with a true win rate of 5.00 BB/100 (»?«)   94.3077%
Minimum bankroll for less than 5% risk of ruin (»?«)   2996 BB


Winrate seems to affect how often we lose over 100k hands. I understand that variance is the same in the context of the game, everyone has 80% equity with aces vs kings so it seems to me like variance is affected by winrate over the long term, but not on a hand by hand basis.

Say we both play a guy who shoves 100% of hands no matter what. You decide to call with top 15% and I decide to call with the top 30%. I win more long term, but will have larger downswings and bigger upswings. I think thats right but it seems to contradict your previous statement. (Which does make sense btw). This topic has really made my head hurt but thanks to both Wazz and Honeybadger for their great posts. I'm aware this is pretty abstract and probably useless really, but sometimes you have to think about the cool shit. If you don't explore, how can you find greatness.

[Longines]

This topic has really made my head hurt but thanks to both Wazz and Honeybadger for their great posts. I'm aware this is pretty abstract and probably useless really, but sometimes you have to think about the cool shit. If you don't explore, how can you find greatness.

This.

[Rupert]

Winrate seems to affect how often we lose over 100k hands. I understand that variance is the same in the context of the game, everyone has 80% equity with aces vs kings so it seems to me like variance is affected by winrate over the long term, but not on a hand by hand basis.

Nope.

Two players same variances, one has a graph like this in the long run |_ (breakeven) another has a graph like this |/_ (yay, winner). Variance is a measure of the fluctuation around that line e.g.

Click to see full-size image.

Obviously you don't usually get peaks and troughs so evenly around the mean because cards still, despite being 2014, don't have a memory.

To a poker player, variance is often used incorrectly as a way to bemoan luck/say how well they are running. While it's very possible in poker to run several standard deviations below or above the mean, in the long run it does converge to true winrate (how long is the long run is a well documented question, but not the topic).

[Rupert]

w.r.t OP: haven't done any maths on it but pretty sure taking a 5% edge with a 12bb stack is gonna make you lots of money. And I think taking most edges is gonna be the best decision. Most of the reason you have a 30% ROI is because you aren't constantly giving up 5% spots "waiting" for the 80% spot.