You're Playing Tournaments Wrong! Here's why

You're playing tournaments wrong, and here's why. Back in the day, we started off with HUDs, push-fold charts, simple calculators, and guesswork. Then we created solvers, but it was impossible to solve ICM for large field MTTs, so we used chip EV simulations instead. Now, recently, we've developed the technology to calculate ICM strategies for large field MTT scenarios. This begs one important question though: at what point in the tournament does ICM become significant? When should you switch? We ran an experiment to find out.

simulations instead now recently we've developed the technology to calculate ICM strategies for large field MTT scenarios this begs one important question though at what point the tournament does ICM become significant when should you switch we ran an experiment to find out

First of all, what is the Independent Chip Model? At its core, ICM just translates the value of a stack from chips to dollars, and this is important because it impacts every one of your tournament decisions. You see, it's not a one-to-one ratio. ICM essentially looks at the size of each stack in a tournament and figures out how often each stack will place first, second, third, fourth, and so on. It has no preconceived notions of player edges or strategy or positions. It's just a placement probability formula. The fundamental difference between an ICM calculation and a chip EV calculation is that chip EV seeks to maximize chips, whereas ICM seeks to maximize dollars. These two goals do not always align. The fundamental trade-off of ICM is that it sometimes sacrifices chips to win more money, and this is because of a concept called risk premium. Sometimes in MTTs, survival is worth more than maximizing chips, so it can be worth avoiding marginal spots to survive longer. This formula was invented in 1987 by Mason Malmuth, originally derived from Harville, who used it for horse racing. Despite its age, it took us over 35 years to fully utilize it. The reason for this is that the original ICM calculation is recursive, and this means that as you add more and more players, it becomes more and more difficult to calculate it. So if you had a tournament with thousands of players, it was almost impossible to calculate ICM. That was until recently we teamed up with Helm of Melcher, developer of Holdem Resources Calculator, to run an experiment. You see, HRC has developed technology to calculate ICM with hundreds or thousands of players remaining instantaneously, so we wanted to see at what point should you switch from chip EV solutions to ICM solutions. At what point does this significantly impact your tournament results? Well, let's find out.

one-to-one ratio ICM essentially looks at the size of each stack in a tournament and figures out how often each stack will place first second third fourth and so on it has no preconceived notions of player edges or strategy or

So here's how we're going to set up this experiment. We're going to run a 200-player MTT freezeout. Fifteen percent of the field is paid, and you can see the payout structure on the right-hand side. In order to make this simple and fast, it's going to be a push-fold tournament where the big blind is always set to one-seventh of the average stack, and the big blind will update every time a player is eliminated. Now remember, our goal is to figure out when switching from chip EV to ICM is a plus, so we're going to simulate six different types of strategies all playing in the same tournament, and every player knows and adjusts to each other's strategy. Let's meet the contestants. At the top, we've got ICM 100. This is a pure ICM strategy that uses ICM calculations from the get-go. At the very bottom, we've got CEV 95 to ICM final table. Now, what does this mean? Well, for example, the CEV 25 to ICM 75 indicates that this player type uses a chip EV strategy until a quarter of the players in the tournament are eliminated. At that point, it will switch to an ICM strategy for the remaining 75 percent of the tournament. And so by testing these different strategy types, we can see how well each strategy performs and figure out when it becomes significant to switch from chip EV to ICM.

of ICM is that it sometimes sacrifices chips to win more money and this is because a concept called risk premium sometimes in mtts survival is worth more than maximizing chips so it can be worth avoiding marginal spots to survive

Here are the results. As you can see, the pure ICM strategy at the top did the best, winning a return on investment of 3.3 percent. So this means for every buy-in they entered, they gained 3.3 percent of that buy-in back on average. At the very bottom, we've got this chip EV slash final table strategy, who is losing 13 percent of their buy-in. And so the question is, at what point does switching from ICM to chip EV become significant? It seems to start to drop off at around somewhere between 50 percent of the field remaining to 37 percent of the field remaining. Now, this game is a surprise to me because remember, the bubble is at 15, yet we're seeing significant changes to the ROI even somewhere between 50 and 37. So this indicates that ICM impacts your strategy much sooner than most players previously thought.

recursive and this means that as you add more and more players it becomes more and more difficult to calculate it so if you had a tournament with thousands of players it was almost impossible to calculate ICM that was until recently we

Here you can see the data in more detail. On the left, we see the strategy types followed by the return on investment and a 95 percent confidence interval. We can see a steady drop-off as the prism strategy dominates the field, followed by a decreasing return on investment as it switches later and later. If you want to see more information, all of our graphs and all of these charts will be in an article detailed below. Check the description. Another way we can visualize the data is to graph the in-the-money placements by strategy. So the pure ICM strategy at the top here places in the money 16.3 percent of the time, and we can see a smooth progression down to the chip EV strategy at the bottom, which is only placing in the money 10 percent of the time. Now keep in mind, the baseline probability with 15 percent of the field paid would be to place in the money at least 15 percent of the time, and we can see that it starts to decrease at around the 25 percent of the field remaining mark. At that point, players who haven't switched sooner are often going to end up placing in the money less often as compared to an ICM strategy that switches sooner.

from Chip EV solutions to ICM Solutions at what point does this significantly impact your tournament results well let's find out so here's how we're going to set up this experiment we're going to run a 200 player MTT freeze out 15

Each color along each of these rectangles represents the placement. Here we've detailed how often each placement will occur for each type of strategy. So for example, in this ICM 100 column, we can see how often they're busting and how often they're placing, for example, first, second, third, fourth, and so on. Something interesting occurs here. We'll notice just how often the chip EV 95 strategy on the right is busting 89 percent of the time, as shown in the top right corner. But something else I wanted to do with this data, instead of just looking at the placement probability, was compare it to the baseline probability. So a baseline probability is just how often would some player place first if you just picked a player out of a hat. So the chip EV strategy, for example, is busting 5.2 percent more often, but they're also placing first more often, and this actually makes sense. This is what we expect because a chip EV strategy maximizes chips, and according to ICM, your probability of placing first is simply your chip portion in the tournament. So this type of player plays too risky. They aren't accounting for risk premium. As a result, they are placing less often, but when they do hit a good run, they are more likely to get first or second. However, that's not nearly enough to make up for all the EV they lose by not placing in other areas of the money. Conversely, ICM 100, this pure ICM strategy, is busting 1.5 percent less often and placing in the money overall much more often. We can see that proportionally speaking, they're much more likely to place in the money, bubbles 16.3 percent of the time, they're busting in 24 to 30, which means they're hanging on, hanging on right until at least they get some payment. And this is important because placing in the money more often indicates that you're going to increase your EV, but there's always a trade-off between maximizing your stack and surviving.

and the big blind will update every time a player is eliminated now remember our goal is to figure out when switching from Chip EV to ICM as a port so we're going to simulate six different types of strategies all playing in the same

Lastly, we can graph each of these placement probabilities according to how much money they make. So here I've used a 100 buy-in, and here's the expected value of different placements. So for example, ICM 100 percent, when they bust, on average they're busting 83.69 at the time, so they're losing 83.69. And we can see throughout this how often each player is going to win or lose and how much each placement impacts your value. Again, the chip EV strategy is placing first or second more often, but they're busting a lot more often and placing in those middling sections less often overall as well.

95 to ICM final table now what does this mean well for example the cev25 to Isam 75 indicates that this player type uses a chip EV strategy until a quarter of the players in the tournament are eliminated at that point

it will switch to an ICM strategy for the remaining 75 of the tournaments and so by testing these different strategy types we can see how well each strategy performs and figure out when it becomes significant to switch from Chip EV to

ICM here are the results as you can see the pure ICM strategy at the top did the best winning a return on investment of 3.3 percent so this means for every buy-in they entered they gained 3.3 percent of that buy-in back on average

at the very bottom we've got this chippy V slash Final Table strategy who is losing 13 of their buy-in and so the question is at what point does switching from ICM to chippyv become significant and it seems to start to drop off at around somewhere

between 50 percent of the fields remaining to 37 percent of the field remaining now this game is a surprise to me because remember the bubble is at 15 yet we're seeing significant changes to the ROI even somewhere between 50 and 37. so

this indicates that ICM impacts your strategy much sooner than most players previously thought here you can see the data in more detail on the left we see the strategy types followed by the return on investment and a 95 confidence

interval we can see a steady drop off as the prism strategy dominates the field followed by a decreasing return on investment as it switches later and later if you want to see more information all of our graphs and all of

these charts will be in an article detailed below check the description another way we can visualize the data is to graph the in the money placements by strategy so the pure ICM strategy at the top here places in the money 16.3 percent of the

time and we can see a smooth progression down to the chip EV strategy at the bottom which is only placing in the money 10 of the time now keep in mind the Baseline probability with 15 percent of field paid would be to place in the

money at least 15 percent of the time and we can see that it starts to decrease at around the 25 percent of the field remaining Mark at that point players who haven't switched sooner are often going to end

up placing in the money less often as compared to an ICM strategy that switches sooner each color along each of these rectangles represents the placement here we've detailed how often each placement will occur for each type of strategy so for example in this icm100

column we can see how often they're busting and how often they're placing for example first second third fourth and so on something interesting occurs here we'll notice just how often the chippy v95 strategy on the right is busting 89 of the time as shown in the

top right corner but something else I wanted to do with this data instead of just looking at the placement probability it was compare it to the Baseline probability so a baseline probability is just how often would some player place first if they you just

picked a player out of a hat so the chip EV strategy for example is busting 5.2 percent more often but they're also placing first more often and this actually makes sense this is what we expect because a chip EV strategy

maximizes chips and according to ICM your probability of placing first is simply your chip portion in the tournament so this type of player plays too risky they aren't account for risk premium as a result they are placing less often but when they do hit a good

run they are more likely to get first or second however that's not nearly enough to make up for all the EV they lose by not placing in other areas of the money conversely ICM 100 this pure ICM strategy is busting 1.5 percent less

often and placing in the money overall much more often we can see that proportionally speaking they're much more likely to place in the money bubbles 16.3 percent of the time they're busting in 24 to 30 which means they're

hanging on hanging on right until at least they get some payment and this is important because placing in the money more often indicates that you're going to increase your EV but there's always a trade-off between maximizing your stack

and surviving lastly we can graph each of these placement probabilities according to how much money they make so here I've used a 100 buy-in and here's the expected value of different placements so for example ICM 100 percent when they bust on average they're

busting 83.69 at the time so they're losing 83.69 and we can see throughout this how often each player is going to win or lose and how much each placement impacts your value again the chip EV strategy is placing first or second more

often but they're busting a lot more often and placing in those middling sections less often overall as well which overall results in them losing a lot of money so we see this smooth progression of expected value from the

pure ICM strategy to the players that switch later in the tournament lastly by taking those expected value data points we've calculated earlier we can graph the in the money expected value by strategy and so here we can see how

often and how much money you get from each placement and every strategy seems to follow a very similar line except for one the chip ev95 slash Final Table strategy is way off base placing everywhere less often busting more often

and as a result for their work they are placing first and second more often but like I said not enough to make up for all the money they lost by overplaying their stack earlier in the tournament good science involves isolating

variables and repeating your experiment so that's what we're going to do here instead of a 200 player phrase out we're going to simulate a 1000 player phase out to see how that impacts the results same setup as before six different

strategies seven big blind average stack let's see how they did here we can see the return on investment by strategy for the 1000 field MTT and again a smooth progression from the pure ICM strategy down to the chippy V Final Table

strategy and we can see it's losing quite a bit at the bottom and marginally winning at the top our question originally was at what point does switching make the most sense and here it seems that switching earlier in the

event so 50 players remaining is approximately when it starts to impact your results to any significant degree we can see that the 37.5 percent strategy is winning quite a bit less often than the above strategies and the Quarterfield strategy is winning

significantly less often half as often as the pricm strategy so I think this just reinforces the idea that you need to switch to an ICM solution much sooner in order to maximize your results again all of this data and all of these tables can be

found in an article linked below check it out so here's the 1000 field MTT seven big blind pushfold 15 of the field paid and we can see the strategy return on investment and confidence intervals again we can graph the in the money

placements by strategy we see the same smooth progression where the pure ICM strategy is just placing in the money more often Overall winning more money overall and as you go down down the very bottom the chippyv final table strategy

is losing a lot more money overall we've graphed the expected value of different placements here this is for a 100 buy-in and at the very bottom we can see the total expected value given a 100 buy-in and we can see where that EV is coming

from and I really like these charts despite them being kind of confused using to look at just because it's interesting to see where your expected value comes from in a tournament and a surprising amount of EV just comes from

placing in the middle of the tournament just making it to the money rather than trying to go big or go home the strategy that does try to go big or go home is the chippy V Final Table strategy who is

placing you know fourth third second first reasonably often but also busting a lot more often and losing a lot of money as a result of overplaying their stack again we've graphed those results here so each of these lines represents each strategy and

the height of each line represents the expected value of each payout that the strategy gains and we could see one outlier which is of course the chip EV strategy the rest are following a very close progression it should be noted

however that it's more difficult to see the difference between other lines when there's one player doing significantly worse because they make everything else look smaller in comparison next up let's try more strategies this experiment was run to a much lower

sample size so there's more noise in the results but instead of six strategies we're going to simulate nine different types of strategies this one is run on a 90 player MTT freeze out 13 players paid here we can see the results but it's

better to look at these graphically we can see a smooth progression from ICM 100 at the top and cev pure at the bottom so cvpirin never switches even on the final table they are still playing a pure CV strategy and losing a lot of

money 17 of their buy-in is lost and we can see that the other strategies have actually increased their Roi and this is just basic whale Theory right more bad players in the tournament exist the higher your return on investment for the

other more sound strategies now this one isn't quite as smooth for example we see that the ICM 62.5 strategy is winning slightly more often than some of the strategies above it but this is well within the margin of error as outlined

in the table above you need a pretty big sample for these to converge but overall we see a very smooth progression players who are switching earlier in the tournaments are of course going to win more money for experiment four we're going to vary

the stack depths of it so we'll use the same 90 field MTT frees out as before 13 players pay but this time we're going to test three different tournaments one is going to have the big blind set to

one-fifth the average stack so a five big blind push-fold event then we'll do a seven big blind push fold event and a 10 big blind push Vault event and we'll compare the results for three different stack depths to see how that impacts the

strategies first up here are the results for the five pick blind push-fold events so they're much shorter here and this will give us more variance in the results which is reflected in the confidence intervals on this graph and

again we see the same smooth progression a bit more noise the pure ICM strategy of course winning the most and where it starts to really matter for this event is around the 37.5 maybe 50 left Mark that's where the drop-off

starts to begin next up we've got the seven big blind push fold event same smooth progression and the drop-off starts to begin somewhere between half the fields remaining and 37 of the fields remaining again keep in mind it's

about 15 percent of the field played it's actually 13 players so not quite 15 but pretty close you can see the same smooth progression a little bit more noise in the ROI distribution but same pattern overall lastly we have the 10 big blind pushfold

event now 10 big blinds is inevitably going to play much tighter as a push fold strategy compared to five pick blinds and therefore there's going to be I think a little less noise in the results which is shown by the fact that icing 50

through Isam 100 are all gaining the same Roi the drop-off begins somewhere between 50 and 37.5 percent players remaining and the chip EV slash Final Table strategy of course still losing horrendous amounts of money let's address a common misconception

many players believe ICM assumes the tournament stops and is paid out after the calculation but this is not the case estimating the value of stacks is not the same thing as stopping a tournament imagine that you're looking at a cash

game instead of a tournament and you want to figure out the expected value of some hand on the flop would you say that the hand stops after you've assigned an expected value to it no that's silly assigning a value to

some hand or some stack does not assume that the hand or the tournament stops I think this misconception stems from the fact that ICM doesn't account for future positions which is where future game simulation comes into place so ICM has

no preconceived notions of what the big blind will be next round or who's in position who's out of position it just looks at the value of stacks we can use future game simulation to resolve this and the way this works is by simulating

one round and then another round and then another round and so on so for example if under the gun is very short stacked they're more likely to bust next round and therefore that can impact your strategy on the previous round similarly

if for example the big blind is increasing next round that can change your decision on the current route but despite future game simulation and despite all of this ICM predicts placements accurately even when no player is aware of ICM and this is why

it's often used to make deals at final tables but let me prove this to you let me prove that ICM works even when players aren't actually aware of the concept we're going to run another experiment two player groups one with

Half Stack and one with full stacks and everyone is playing chip EB strategy so no player in this tournament is using an ICM strategy no one knows what that means they're just playing chip PV trying to get the most chips possible

the big blind is 1 7 of the average stack same setup as experiment one so here we see the results for the Half Stack and full stack strategies and at the top we can see for example top two

percent indicates how often each of these Stacks places in the top two percent of the tournament you can see the simulated results and icm's prediction just based on stack depth and we can see that they are identical in

the top 15 percent this is in the money we can see some very small variation but overall ICM is extremely accurate in predicting how often half stacks and full Stacks will place in the money overall bottom row shows the expected

value and we can see that ICM predicts the expected value of each stack size within 39 cents per 100 buy-in so extremely accurate despite the fact that no player is even aware of the concept of ICM it's still a good indicator of

what your stack is worth so I should point out ICM is not the only tournament Equity formula there are other versions that are pretty good in fact helmuth Melcher explored a lot of these in an academic paper which I'm

going to link in the description so here we're comparing how three different tournament Equity formulas do against a perfect strategy they figured out the perfect strategy using brute force and a lot of calculations which are not feasible for really any situation

outside of an academic study so how well did the original ICM calculation that's Harville this first row here due against the perfect strategy well it lost about one percent of its buy-in on average which is actually pretty good next up

we've got Weitzman which is a decent formula it's a slight Twist on the original ICM idea but it's losing 2.6 2.7 percent of its buy-in and lastly we've got Robert's formula which is performing about as good as the original

ICM formula it's stronger in some places weaker in others tends to do better against the perfect strategy but loses heads up against ICM so the question is why not switch to Robert's formula the thing is it's not as efficient ICM is

one of the only tournament formulas we know which can be scaled to large field MTT events but it should be noted that ICM is not perfect it's not the only formula and it's not a hundred percent accurate given equal skill Edge but it

is very very darn close if you want to explore this data more the paper is in the description like I said where they did a lot of other experiments comparing different tournament Equity models okay so I've shown you a lot of different

charts and in numbers but the real question is how does it actually impact your strategy well lucky for you GTO wizard has MTT pre-flop solutions for many tournament stages ranging from final tables to the last three tables 25

37 and 50 of the fields remaining so let's go and explore a few of these different tournament phases and compare how your strategy changes as the tournament progresses for this first example let's examine how low Jack's opening strategy changes as

we progress through the tournament every player has a 20 big blind stack and you can see the tournament phase in the top left corner here we're looking at the chip EV Solutions here we see the same solution when 50 of

the field remain so half the players have been eliminated here is 37 percent of the field remaining 25 percent and the final table I'll go through that one more time and pay attention to what's happening in the range

chip EV 50 37 25 final table interesting hey it's becoming more block or heavy more asex hands and fewer pocket pairs in suited connector tie pants so why is that as risk premium increases more of your EV is derived from stealing the blinds

rather than post-flop play post flop implied odds decrease due to tightened stack-off conditions and a higher risk premium as a result these drawing hands are traded out for hands that block three bets and block calls instead and so that's why we see the shape of

the range change for this next example let's examine how big blind's defending range changes facing the low Jack open so LoJack has opened two chips folds the big blind and here we see the strategy where 20 big blinds effective starting with the chip

Evolution as shown in the top left corner when 50 of players remain we can see it's already much tighter there's already a fair amount of risk premium and a lot of these hands were very close to start with

37 percent of players remain 25 percent final table that is a drastic difference wow look at that one more time chip EV AP the players are gone 37 for Maine 25 percent final table as you can see it gets much much tighter even halfway

through a tournament so ICM clearly has a significant impact early on and you should be switching to ICM Sims sooner rather than later lastly let's examine how button strategy changes facing a small blind three bet this time we're 50 big blinds deep

and again you can see the solution in the top left corner so button opens 2.1 chips small blind three bets and here's how button responds lots of calling some jamming not a lot of folding all right how does their strategy change

when 50 of the field remains well it's already much much tighter wow 37 percent 25 percent final table that's an enormous difference we went from defending two-thirds of our range to one third of our range so even if you don't agree with my

simple push-fold experiments that I was running earlier if you give a solver the option for complex post-flop play it's already going to play much tighter and much more conservatively even halfway through a tournament I think a lot of MTT Pros have been using

chip PV simulations for the majority of stages throughout the tournament and it's only recently that we've gained the technology to calculate simulations for early and mid-stage tournament events that account for ICM let's summarize the goal of these experiments was to

find out when ICM significantly impacts your results in a tournament when should you switch from Chip EV solutions to ICM Solutions we demonstrated that players who switched to ICM sooner consistently outperformed players who switched later we tested multiple structures and field

sizes we tested multiple stack depths we demonstrated that ICM predicts placements even when no player is aware of the concept of ICM and lastly we demonstrated that silver strategies changed drastically even halfway through an MTT ICM appears to have a statistically

significant impact on your results somewhere between 50 and 37 percent of the field remaining for a 15 payout structure at Hazard guess that The Sweet Spot is approximately three times the number of players who are paid but it

might be the case that when you account for complex post flaw play The Sweet Spot occurs even well before that if you guys want to examine this experiment go check out the article Link in the description we've posted all of

the tables and graphs there so you can go and scrutinize this if you want to run your own experiment I suggest you pick up a free trial of HRC the best ICM tool on the market you could pick up a free trial up until

January 22nd and I'd like to give a big shout out to helmuth Melcher who helped me run these simulations and is also the developer of HRC if you have any questions post a comment down below or join our Discord

anyway that's my video guys I hope you learned something new I hope you start using ICM and as always happy grinding