Vadiu: Translated and adapted from ChrisV SNG stuff: Partial SNG book (ChrisV) by Vadiu
Since I'm short on time, I'll translate in parts
Vadiu: In cash games, players measure losses and profits in terms of bigbets/100 hands, or bigbets/hour. This allows a comparison of win rates at the different limits played.
In SNGs, win rates are measured by percentages, called Return on Investment, or ROI. It's simply the total profit divided by the total buy-ins.
For example, if you made a profit of 660 after 100 SNGs of 50+5, your ROI would be 660/5500 = 12%
Marcelo: Net profit of $660? So you earned a total of $6160, correct?
Vadiu: correct. at least I understood that, it's the final profit after all the BI.
Vadiu: In most 10-person SNGs (9 in ps) 50% of the prize goes to the winner, 30% to 2nd place and 20% to 3rd.
The difference between tournaments and cash games:
At a cash table, if a player enters a hand in which he can lose $500 or win $500, with a probability of 50/50; the expected value is exactly neutral (disregarding the rake). At a cash table, the axiom prevails that a dollar chip is worth a dollar, in any context.
In tournaments, chips are not always worth the same amount.
Consider, for example, an SNG tournament with a buy in of $100 where everyone starts with 1,000 chips. In total, the 10,000 chips in play are worth $1,000.
At the end of the tournament, someone will have 10,000 chips, but they will only be worth 50% of the prize pool. The value of those 10,000 chips has decreased to $500.
In order to determine the correct plays in tournament situations (especially SNGs), we need to find a way of knowing the exact value, in dollars, that the chips are worth at that moment in the tournament. With this, we can make more favorable decisions, such as how many chips we should put at risk to achieve a theoretical estimated win.
Equity modeling, which we'll look at in the next few chapters, is one of the ways we can answer these and other questions.
Ras Lucas: I've never been able to play properly thinking about the value of the chips in SnG, I never stop to think about it at the time.
Vadiu: A player's equity in a tournament is their expectation, expressed as a fraction of the total prize pool, at a given point in that tournament. It's calculated by multiplying the chance (in %) that you might end up in the ITM positions and the percentage of the prize pool that position pays, and then adding up the resulting figures.
For example: let's say you have a 20% chance of finishing first, 25% of finishing second, 30% of finishing third and 25% of ending up out of the ITM.
Your Equity is:
0.2×0.5 + 0.25×0.3 + 0.3×0.2 = 0.235 or 23.5%
The total amount of equity in a tournament is constant, because the sum of the equity of all the remaining players will always be 100% = the entire prize pool.
However, any move that increases a player's equity will cause a decrease in the equity of one or more of the remaining players.
Since equity is a summary of your expected profit, it goes without saying that the aim of any move you make in a tournament is to increase your equity. You should never "play to be first" or "play to get ITM". You should make your moves simply with a view to increasing your equity, and consequently winning money.
Equity modeling is a method of estimating players' equity based on their chip counts and their relationship to the blinds. Later today, I'm going to write about the Independent Chip Model or ICM. One of the most widely used equity modelers for SNG players
Vadiu: SNGs and Multi-Table Tournaments (MTTs) have a very different structure. We could apply equity to MTTs using the ICM, but the sums would be much more complicated because they differ mainly in the number of people. The difference between cash games and tournaments is more evident in SNGs than MTTs for two reasons:
More difficult bubble situations in SNGs
The difference between 4th place and 3rd place in an SNG is 20% of the prize pool, which represents a dramatic change in deciding the right play. No MTT has a bubble with such a glaring difference, as the first to fall ITM usually receives little more than the BI.
Payout structure
30% of SNG players go ITM. MTTs typically only pay out the top 10-15% finishers, with the top 5% receiving 75% of the total prize pool. This makes the MTT structure much more biased towards the top finishers. The more the prize structure favors the top finishers, the more the MTT should be played as a cash game. In an MTT where only the first place winner takes the prize, the strategy is almost identical to a normal cash game.
Conclusion:
In an MTT, equity modeling is more complex and difficult both mathematically and intuitively. This is due to the differences in payout structures. Since using such modeling does not affect the correct decision in MTTs, most authors of books on No-Limit tournaments have chosen to ignore equity modeling, using only odds calculation.
The same is not true of SNGs. Calculating pot odds often gives us the wrong answers, especially in bubble situations. Using an equity model like ICM is therefore essential.
Vadiu: ICM is a model that I believe works very well in SNGs.
Today I will describe the method used to calculate equity in the LCI.
If you don't understand it now, that's fine, you can play by imagining the ICM as a magic formula. But this topic describes the magic behind the formula.
Suppose that, in a normal SNG, there are three players left - A, B and C - with stacks of 10k, 6k and 4k respectively.
->We'll assume that all three players have the same skills.
The process begins by placing them in the probability of finishing first. This probability is initially achieved simply by looking at the percentage of chips they have, in relation to the total. So:
A: 50%
B: 30%
C: 20%
Now, let's take each of these possibilities and mentally eliminate player A, leaving the other two in the game.
When we take A out of the game, there will be stacks of 6k and 4k left, with a total of 10k. This means that B finishes second 60% of the time and C, 40% of the time. However, as we want an overall result. As A finished 1st 50% of the time, we have to include the possibilities of the other two players, having (in order):
A, B, C: 30%
A, C, B: 20%
Then we need to do the same calculation, now eliminating player B, and then again with player C.
At the end of the process we would have:
A, B, C: 30%
A, C, B: 20%
B, A, C: 21.43%
B, C, A: 8.57%
C, A, B: 12.5%
C, B, A: 7.5%
All probabilities must add up to 100%
*->If we had 4 players left, we would have to add another level, eliminating the player who finished 2nd and repeating the process for C and D, and then multiplying the probability obtained for each of them.
Assuming we want to determine the overall equity for player A, we need to multiply the chance of A finishing 1st, 2nd and 3rd by the prizes received for each placement (expressed as a fraction of the prize pool).
Equity(A) = 0.5 * (0.3+0.2) + 0.3 * (0.2143 + 0.125) + 0.2 * (0.0857 + 0.075)
Equity(A) = 38.39%
According to the ICM, A's 10k stack is worth 38.39% of the tournament's prize pool
Marcelo: Bizarre man, really complicated calculation, now I get it.
prof_anselmo: Congratulations mate, the reasoning to arrive at these figures is quite complicated.
Vadiu: Complicated?!?! you'll see the next part I'm translating
Professional article
Vadiu:
Programs for LCI analysis (paid)
SNGPT - Sit-n-Go Analyzer
SitNGo Wizard - The SitNGo Wizard - Home
Free online calculator that calculates the ICM according to the size of the stacks entered
//www.bol.ucla.edu/~sharnett/ICM/ICM.html.
Vadiu: In the previous threads, we discussed that in a tournament, a chip won is always worth less than a chip already in your stack. One consequence of this is that there is a BIAS, a natural tendency against putting chips in the pot. In a cash game, to call a raise all in, a player needs to be the favorite to justify the call. In an SNG, on the other hand, we have to be more than just favorites. We need to be substantial favorites.
Thanks to ICM, we can calculate exactly how favorite we need to be:
Suppose you're playing an SNG where everyone started with 2k chips and the blinds are 10-20.
You're on BB with :2h :2d .
Everyone folds, except SB, who calls all in.
He accidentally shows you his cards.
He has :Ac :Kd . Should you pay allin?
->If you fold, you'll only lose the blind and you'll still have 1980, practically your starting stack. The ICM considers this to be 9,91%, slightly less than the 10,00% you started with.
->If you pay and lose, your equity is pretty obvious: zero. You're out of the tournament.
->If you call and win, you will have 4000 chips, while your remaining 8 opponents will have 2000. The ICM value for this is 18.44%.
What if we wanted to know the minimum probability where a hand wins, at the limit of what a breakeven call would be. (Breakeven means that the equity of paying equals the equity of folding)
Having:
E = the equity of paying and winning
E = the fairness of paying and losing
E = folding equity
P = the probability of winning
(For simplicity's sake, let's ignore the possibility of a split pot)
So:
E x P + E x (1 - P) = E
If E in this hand is zero, we can ignore this term, leaving us with:
0.1844 x P + 0 x (1 - P) = 0.0991
0.1844 x P = 0.0991
P = 53.74%
According to the ICM, we need to win 53.74% of the time to make that call. As :2h :2d only beats :Ac :Kd 52.34% of the time, drawing 0.31%. The correct move for this is FOLD
What's more, we can calculate exactly how much this call would cost.
The fairness of paying is:
P x E + P x E
= 0.5234 x 0.1844 + 0.0031 x 0.1000
= 0.0994
Subtracting this from E gives us 0.18% of the prize pool. On a SNG Buy in of $100, paying out here would cost us $1.80
In addition, the player with :Ac :Kd also loses:
P x E + P x E
= 0.4730 x 0.1844 + 0.0031 x 0.1000
= 0.0875
this gives a loss of 1,16%, costing $1.16 on an SNG of $100
But then you ask. If the total amount of equity in a tournament is constant, how do the two players lose equity? Where is the equity going?
The answer is that the equity is distributed equally among the other players in the tournament. In an SNG, every player has chips at stake in every hand. If you've ever been very short and had the pleasure of seeing someone else burst the bubble, you'll understand the idea.
Even if you're not involved in a hand, it's obvious that your equity has increased a lot. The same thing is happening with every hand of the tournament, even if unnoticed.
This net loss of equity is not limited to allin situations:
Assuming that two players have a 500-chip match in a sit where everyone starts with 2k chips, and assuming that they both have a 50% chance of winning or losing, their possible equities will be:
2500 chips: 0.1223
1500 chips: 0.0767
Averaging these values, we get 0.0995, which means that each player lost 0.05% of the prize pool (50 cents on a buy in of $100). This money was re-distributed to the other players who didn't take part in the match.
If, shortly afterwards, another similar confrontation takes place (with the same two players, where each has a 50% chance of winning 500 chips) there will be a 50% chance that both will end up with 2000 chips again, restoring the initial equity of 0.1 for everyone. But the other 50% times, the stacks became even more different:
3000 chips: 0.1438
1000 tokens 0.0524
For the player who started with 2,500 chips, his average equity after this hand is 12.19%, a loss of 0.04%. The player with 1500 chips is left with an average equity of 7.62%, a loss of o.o5%. Once again, the remaining equity is re-distributed to the players who were not involved in the hand.
CONTINUE...
Marcelo: Excellent analysis. This is one to note: you need to have a substantial advantage to pay for an all-in.
Simon: Excellent topic, but complicated to calculate. Now, in this situation of all in with pocket 2s, even if he showed me 34o I wouldn't call, not at the start of the tournament.
Vadiu: Moving on...
We must remember that the winning percentage can be altered, resulting in a balance in the equity gain between the two players. For example, if the short stack had a 100% chance of winning the second match, the result of the hand would be the opposite, with a net equity gain.
But if the bigstack was 100% favorite, the equity loss would be just as big.
->In the long term, things will tend to even out, the percentage of gains will tend towards 50%.
This brings us to the title of the topic, the bias against confrontation:
In an SNG, confrontations between players will, on average, result in a net equity loss for those players involved in the hand and an equity gain for the players watching. That's the bias, the players involved tend to lose equity in the long run.
To get involved in any hand, you must first be sure that you will win enough chips to overcome the bias of the confrontation, and the more chips you have in the pot, the worse the loss of equity will be.
So far, our examples of bias against confrontation have been simple. Before you start thinking that the concept is just technical and doesn't apply to the real world, let's look at this more extreme example.
This hand was taken from a real hand in an SNG $100+9
Cutoff: 460
Button: 550
Hero (SB): 13650
BB: 5340
Blinds: 300/600.
Cutoff and button fold.
Hero goes all in.
(The hero's hand is not important, as he would make this move with ATC (any 2 cards).
BB calls with his 22.
These are the LCIs for possibilities:
Opponent folds
Cutoff: 0.1063
Button: 0.1267
Me (SB): 0.4393
BB: 0.3278
Opponent calls and loses
Cutoff: 0.2502
Button: 0.2600
Me (SB): 0.4898
BB: 0.0000
Opponent calls and wins
Cutoff: 0.1032
Button: 0.1232
Me (SB): 0.3733
BB: 0.4003
Opponent gives cals and draws
Cutoff: 0.1053
Button: 0.1256
Me (SB): 0.4328
BB: 0.3362
Against a random hand, the opponent wins 49,39% of the time and draws 1,9%.
This gives the following equity for the call:
Cutoff: 0.1749
Button: 0.1899
Hero (SB): 0.4312
BB: 0.2041
By calling instead of folding, the opponent loses 12,37% from the prize pool. That's more than an SNG buy-in, which he lost in a single hand.
Unfortunately, the hero doesn't benefit from this generosity, with an equally substantial loss of equity, although less than that of his opponent.
The real beneficiaries of this move were the other two shortstacks who didn't even play.
In an SNG, it's quite common for bad decisions made by your opponent to cost you money. On the other hand, if the villain doesn't understand this bias against confrontation, you can just watch your equity increase as the other opponents ignorantly digress.
THE END!
I hope you enjoyed the article and the translation. Cheers and enjoy the game:coolgleam:
Vadiu: Anyone who wants to continue reading, I'm translating another article here:
//pokerdicas.com/forum/torneios-sit-go-sng/1689-davsimons-sng-strategy-guide.html#post15426
Vadiu: haha I'd forgotten about this article, it's really good for those learning about icm...
bumped for consideration
Marcia: Look, I play Six Max Cash Games and I don't measure my losses and profits in terms of bigbets. In fact, I've created a little table in Excell to keep track of my bankroll and I've already programmed one of the table's columns to calculate my winnings and losses in terms of percentages of the investment made.
You see, if I enter a table with 5 dollars, for example, and leave with 10 dollars, I've made a profit of 100%.
This business of calculating the percentage of profit motivates me and in general I win because it's not very difficult when you know how.
But there are times when bad luck strikes and we don't win for several tables in a row. I have a strategy for this and I tell myself that when I lose x I'll leave.
afsalagoas: Marcia,
How many tables do you play a day?
Theseus: Up! digging up this topic a real treasure, Great translation!
Tex Wilde: Vadiu, where did this partial sng book come from? Was it taken from Moshman's book or what?
fonteles: Dezosso Vadiu.
Critical poker concept, tournament equity. The value of chips is relative, deflating and inflating their value as the equity of all the opponents clash against each other or against each other. Chips also don't correspond to the value of money. That's why this concept is critical, right? Our intention is not to make money?
In the cash game, if I play a coin flip, roughly speaking I don't lose or win money over a series of games (breakeven), I just lose time. Moshman says in his masterpiece that the equity of a coin flip is different from the equity of a tournament. It's wrong to get involved in an early stage STT coin flip because 50 % of the time I lose an entire tournament yet to be played, and doubling my chips in the other 50 % I win doesn't mean I've doubled my equity.
"The loser of this race has lost chips of greater value than those the winner receives," says Moshman. Winning the 50 % of equity in the showdown - or doubling up early, a justification used by the donks who call an all-in with AK, but when it doesn't hit, they whine and say that it's the guy who went all in with a pair of twos who's the donk - never justifies the fact that you've given away the other half of your equity, which would be more than just a coin flip, but a tournament, in the other 50 % that you lose.
That's why stockpiling is a master strategy. The more you conserve your chips, the more they will inflate in value. They'll be worth more because when the weak opponents battle it out in a rough coin flip at the start of the STT, your equity will increase. In the world of equity, nature is explicit: nothing is lost, nothing is created, everything is transformed. The person who was eliminated didn't take the equity they lost with them, nor did the lucky opponent who won the race absorb all of it. The winner received a good deal of equity, but all the other opponents received some too. And as more opponents get involved in coin flips and leave the tournament, each eliminated player donates much more equity than their predecessor, seventh place for example, and their chips will be "worth" more and more as their equity in the tournament increases.
"You gain equity (aka money) with each opponent that gets eliminated."
Vadiu: excellent post fonteles
Heartbreaker:
Suppose that, in a normal SNG, there are three players left - A, B and C - with stacks of 10k, 6k and 4k respectively.
->We'll assume that all three players have the same skills.
The process begins by placing them in the probability of finishing first. This probability is initially achieved simply by looking at the percentage of chips they have, in relation to the total. So:
A: 50%
B: 30%
C: 20%
Now, let's take each of these possibilities and mentally eliminate player A, leaving the other two in the game.
When we take A out of the game, there will be stacks of 6k and 4k left, with a total of 10k. This means that B finishes second 60% of the time and C, 40% of the time. However, as we want an overall result. As A finished 1st 50% of the time, we have to include the possibilities of the other two players, having (in order):
A, B, C: 30%
A, C, B: 20%
How did you arrive at these figures? I'm doing some calculations, but the values don't add up.
Tex Wilde: How did you arrive at such figures? I'm doing some calculations, but the figures don't add up.
I developed these accounts in my post on ICM.
//pokerdicas.com/forum/torneios-sit-go-sng/9202-post-especial-an-approach-on-icm-with-emphasis-on-fifty50-do-ps.html
Heartbreaker: I developed these accounts in my post on ICM.
//pokerdicas.com/forum/torneios-sit-go-sng/9202-post-especial-an-approach-on-icm-with-emphasis-on-fifty50-do-ps.html
Yes, the formulas are better explained! I'm starting to understand the ICM better, but I'm just getting started:confused: I still can't see myself doing all these calculations in less than 20 seconds (the time I have to make a decision). I have an initial doubt.
1st - Is the calculation influenced by the number of opponents making the decision? For example, can a push situation in the SB, assuming that the table runs in fold, be a fold situation if you are in MP1, for example? Is this taken into account in the ICM?
Vadiu: he considers the probability of folding the next opponents, but he doesn't consider "being eaten" by the blinds or earlier
Tex Wilde: Yes, the formulas are better explained! I'm starting to understand the ICM better, but I'm just getting started:confused: I still can't see myself doing all these calculations in less than 20 seconds (the time I have to make a decision). I have an initial doubt.
1st - Is the calculation influenced by the number of opponents making the decision? For example, can a push situation in the SB, assuming that the table runs in fold, be a fold situation if you are in MP1, for example? Is this taken into account in the ICM?
Yes, it has a lot of influence. The more players there are to act, the more likely you are to get a call.
Original author: Vadiu.
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