TL;DR introduction:
When people get to around 1000 posts they often try to make a post giving something back to the 2p2 community. I would like to thank the people who have helped review my hands over the last few months. Partly thanks to them I am winning online at microstakes:
http://pokerprolabs.com/players/lektoraj/pokerstars
and I am also doing well in small stakes turbo live tournaments over a small sample
http://www.olympic-casino.sk/poker/r...g.view.77315/3
Anyway, as a microstakes player I am not qualified to post my general theory of poker like some others have, but I hope the following will help someone anyway.


Start of post:

Kill Everyone introduces the concept of the "Bubble Factor", a way of quantifying the skew in the $ equity gained/lost after winning or losing a flip against a particular player.

e.g. On the bubble of a satellite paying 2 places (each place worth 300 dollars), with even our equity is worth 200 dollars. If we win a flip, our equity goes up by 100 dollars (we qualify), if we lose, our equity goes down by 200 dollars (we lose) so we have a bubble factor of 2 (200 divided by 100) against the other players. The book suggests dividing our (chip) pot odds by the bubble factor to get the ($) tournament odds e.g. to make a call.

It extends the principle to talk about "average bubble factors" as a way to measure how ICM-heavy particular structures and particular points in structures are. These are expressed as what the bubble factor between the players would be if there were even stacks with a particular number of players left. To help people playing their particular games, I have calculated the average bubble factors for different stages of common games. If there is something you would like to see added, please post the payouts and I will try to put it in (I can do up to 50th place with up to 40 payouts). There are no guarantees for accuracy but the results I have got agree with the few examples given in Kill Everyone.

First number is players left, second number is bubble factor

Classic Sit & Go. Payouts 50-30-20
2 1.0000
3 1.3333
4 1.8750
5 1.5385
6 1.3889
7 1.3043
8 1.2500
9 1.2121

Pokerstars 18-man, or my live tournament when fewer people come 40-30-20-10
2 1.0000
3 1.5000
4 1.8000
5 2.0000
6 1.6667
7 1.5000
8 1.4000
9 1.3333
Then
10 1.2857 11 1.2500 12 1.2222 13 1.2000 14 1.1818 15 1.1667 16 1.1538 17 1.1429 18 1.1333

Pokerstars 45m $1 (7 paid). Where I started donking and have recently returned after fixing my more serious leaks in the 25 cent games.
2 1.0000
3 1.3428
4 1.5596
5 1.7136
6 1.8143
7 1.8687
8 2.0433
9 1.8075
FT2 10 1.6587 11 1.5562 12 1.4813 13 1.4242 14 1.3792 15 1.3428 16 1.3128 17 1.2876 18 1.2662
FT3 19 1.2478 20 1.2317 21 1.2176 22 1.2051 23 1.1940 24 1.1840 25 1.1750 26 1.1668 27 1.1594
FT4 28 1.1526 29 1.1463 30 1.1406 31 1.1353 32 1.1303 33 1.1257 34 1.1215 35 1.1175 36 1.1137
FT5 37 1.1102 38 1.1069 39 1.1038 40 1.1009 41 1.0981 42 1.0955 43 1.0930 44 1.0907 45 1.0884

^ 8 handed is the steepest bubble of all listed tournaments except the satellite. Notice that the bubble factors ITM are still really high. At least at the low end of the micros the other players don't seem to realise this and go crazy as soon as the 8th man goes out.

Pokerstars 180m $2.50 Turbo - 27 paid
2 1.0000
3 1.4613
4 1.5383
5 1.4942
6 1.5156
7 1.5475
8 1.5384
9 1.5392
FT2 10 1.5350 11 1.4570 12 1.3989 13 1.3539 14 1.3180 15 1.2887 16 1.2644 17 1.2438 18 1.2263
FT3 19 1.2897 20 1.2703 21 1.2534 22 1.2384 23 1.2252 24 1.2133 25 1.2026 26 1.1929 27 1.1841
FT4 28 1.4125 29 1.3920 30 1.3735 31 1.3566 32 1.3412 33 1.3270 34 1.3140 35 1.3020 36 1.2908
FT5 37 1.2805 38 1.2708 39 1.2619 40 1.2534 41 1.2455 42 1.2381 43 1.2312 44 1.2246 45 1.2184

^ People who play these will be able to say more. It is unexpected (at least to me) that the biggest ICM pressure actually peaks at 7 handed, not the FT bubble or the min cash bubble and it is lower and a lot steadier than than the 45s.

Last night's live tournament. Bigger pay jump between 2nd and 3rd than between 1st and 2nd. They were paying bonuses for Full House and Flush, possibly taking them out of the first prize.
It paid (in euros) 154, 117, 75, 42, 29. We chopped at 6 handed so we never got to play the 3-handed bubble.
2 1.0000
3 1.5316
4 1.7460
5 1.6738
6 1.9541
7 1.6860
8 1.5355
9 1.4392
10 1.3722
11 1.3230
12 1.2852
13 1.2554
14 1.2312
^ It's interesting that this weird structure doesn't have a 3-handed bubble much bigger than some of the PS tournaments.

Satellite for 5 seats
6 5.0000
7 3.0000
8 2.3333
9 2.0000
10 1.8000
11 1.6667
12 1.5714
13 1.5000
14 1.4444
15 1.4000

I hope this can help at least some people. The thing that has helped me most is understanding that being under ICM pressure isn't a yes/no kind of thing. We are already under mild ICM pressure a couple of tables away from the money and we are definitely still under it even after we min cash. We don't take our buy-in into account when playing because it is a sunk cost. The money we have already won is the same - the opposite of "sink" is "refloat", so we could call cash already won as "refloated" so just as we ignore the sunk cost of the buy-in we should ignore the refloated gain of money already locked up. Winning zero more dollars from now on is always among the possibilities and (at least in 45s) we are always on the bubble of the next money to be locked up.

Great post.

I saw this numbers before. But not is such details. Very helpful for better understanding what is going on in SNGs.

how did you calculate the average bubble factors when there were more than 20 players ( wich tools did you use) ?
I did calculate those for less than 20 players few years ago but i didn't know tools to do it quickly for more players ( i could do it with icmizer but it would take too long and im too lazy ).

i kinda wish you didnt post the average bubble factors for 180m cause most players think ICM is less important than it really is lol.
do you have those numbers for 90 men sng? (that would spare me a lot of time)

Just my own thing. You enter the prizes and it lists the average bubble factors for the numbers of players left. I may put the tool up on my website. I'm trying to work out if its a net plus for my business from the SEO point of view (the business is not poker related so the tool page would have a link back to the main page of my business but the front page would not link to the tool).

I feel a bit like that about the 45s. But we are mostly not playing against people reading 2p2, and getting these ideas out into the 2p2 community will improve the advice we get back from the more experienced players when we post hands - so when people are talking about 7-handed in a 45 they won't say "call because we are already ITM". Locked-up money should be ignored just the same as money already paid to enter the tournament. Also I want my participation on 2p2 to be a two-way street as far as is possible when other players are more experienced.

These figures are interesting, but the player still needs to get a feel for his own ICM/bubble factor position in the specific spots against specific players. It's also more important to get game or player reads on what villains think about ICM and laddering. It's no good thinking we can jam into someone because the villain is over an ICM barrel if he thinks he can call loose because he is already in the money. The usefulness of this stuff also depends on the extent to which ICM is an accurate model for tournament equity.

Pokerstars 90 man $2.50 (13 paid)
2 1.0000
3 1.3313
4 1.6335
5 1.6636
6 1.6701
7 1.6242
8 1.5832
9 1.5681
FT2 10 1.5582 11 1.4758 12 1.4146 13 1.3674 14 1.8023 15 1.7046 16 1.6281 17 1.5666 18 1.5161
FT3 19 1.4738 20 1.4380 21 1.4072 22 1.3804 23 1.3569 24 1.3362 25 1.3177 26 1.3012 27 1.2863
FT4 28 1.2728 29 1.2605 30 1.2493 31 1.2390 32 1.2295 33 1.2208 34 1.2127 35 1.2051 36 1.1981
FT5 37 1.1915 38 1.1854 39 1.1796 40 1.1742 41 1.1691 42 1.1643 43 1.1598 44 1.1555 45 1.1514

^ So there is a big bubble at 14 handed to get in the money after which you can play a bit looser and then the most ICM pressure is at 6-handed. I think from this we can see that a "start worrying about ICM when we get to FT2" strategy is not optimal.

good thread, thank you

first of all thanks a lot for the 90s numbers

really? i tought most regs were reading 2p2 but i will take your words since you must know better than me.
for how many players can your programm calculate these numbers? it seems like a great tool

nice thread

There are only ever a few people in this sub forum at a time and several hundeds playing in stars mttsngs. What is your definition of a reg? I got into a discussion in nvg with someone who defines it as someone with no other job but I would define it as someone who is at least breakeven at the given stake - so I am a reg at micro mttsngs but would be a recreational in the Sunday Million. The average roi per entry in the dollar tournaments is minus 9 percent (i.e. the amount of the rake) so probably most people are not regs even on my definition. Also the stronger players are not generally English speakers.

It can currently do up 40 prizes and 50 places.

Interesting post, thank-you

Here are the numbers for a three man satellite (mentioned in another thread)

4 3
5 2
6 1.667
7 1.5
8 1.4
9 1.333
10 1.286
11 1.25
12 1.222


and also a 6 man SNG, missing from the original post - 65-35 payout ratio.

2 1
3 1.538
4 1.304
5 1.212
6 1.163

I don't know where I was in January, that I missed all this. Great work.

I'm surprised the 45s have such high BF even itm, and how they're higher than on the 180 FT. I'm not surprised that the 180 actual bubble is still not a very high BF compared to other formats, personally I hate the 180 payout structure.

If I have to do this much work when I get to 1K posts I'm going to start writing less.

I've started playing 27 man's because there isn't much volume in the reg speed 45s above $1. Came here to look up the average bubble factors and found it was missing.

Pokerstars 27 man - $3.50 (5 paid)

2 1.0000
3 1.4608
4 1.6990
5 1.5996
6 2.0132
7 1.7223
8 1.5612
9 1.4589
FT2 1.3881 1.3363 1.2966 1.2653 1.2400 1.2191 1.2016 1.1866 1.1737
FT3 1.1625 1.1527 1.1439 1.1361 1.1292 1.1228 1.1171 1.1119 1.1072

- so like the other smaller MTTSNGs it has a significant money bubble with the small jump between 4th and 5th providing a small breather before the 4th-to-3rd bubble.

When I still played 180m I played the "semifinal" table way looser than the average reg since I figured with the payjumps being as they are you really don't want to start final tables with average stack. Result was that I had slightly less final tables then some but since I was "in the right side of ICM problems" a lot I got way better result distribution from the final tables and much higher ROI than average reg.

Is the 4th position's BF correct?
Could you post $1 180-man (Stars 15m blinds)?

Yes, - just checked it now.

It's hard to justify why in words other than "that's what the computer says" because ICM is often non-instinctive, but the gap between 3rd and 4th is more than double the gap between 4th and 5th. So it's kind of the bubble of the top 3 (within the top 3 itself - the gap between 1st and 2nd only slightly bigger than the gap between 2nd and 3rd - so it's not about playing for first so much).

The numbers for the 180 15 minute are essentially the same because they are based of the same percentage tables - just they round differently. Here they are anyway:

Pokerstars 180 man $1 - 15 minute levels

2 1.0000
3 1.4606
4 1.5376
5 1.4938
6 1.5153
7 1.5474
8 1.5380
9 1.5392
FT2 1.5347 1.4568 1.3987 1.3538 1.3179 1.2886 1.2643 1.2438 1.2262
FT3 1.2894 1.2701 1.2532 1.2382 1.2250 1.2131 1.2024 1.1928 1.1840
FT4 1.4119 1.3915 1.3729 1.3561 1.3407 1.3266 1.3136 1.3015 1.2904
FT5 1.2801 1.2705 1.2615 1.2531 1.2452 1.2378 1.2309 1.2243 1.2181

very interesting!

can you add 27 man?

Post 13

I have a question about these.

The pay jump from 3 to 2 is almost double and is the same jump from 2 to 1. Obviously no bubble factor from 2 to 1 because there is no one else to go out. But why so low between 3 to 2?

It seems to me that a huge amount of profit in these relies on getting 1st or 2nd where other tournaments I am used to coming 3rd is still a good pay day.

When you are three handed it's linear:

Second and third pay same (Winner takes all) = bubble factor 1

Second and first pay the same (e.g. satellite for 2 places) = bubble factor 2

Second pays halfway between first and second = bubble factor 1.5.

This means we have to try laddering more and playing more carefully ICM wise in Flat-payout system like 45`s and intended to go for top3 @ 180s?

All other things being equal, yes. Although "top 3" is just an arbitrary cut-off point I assume inspired by there being 3 medals in the Olympics, 3 places on the podium in F1 etc. It's certainly not the case that at 4-handed you should play it like the bubble of a satellite offering 3 places - nor that you can ignore ICM when you are 9 handed.

One interesting thing about the two you mention though is that when you actually get to 3-handed, the situation is reversed and there is more incentive to ladder up to 2nd place in the 180s than there is in the 45s.

Hello!

Nice post!

I wonder if the table size dynamic has some effect on this, or, as I'm thinking, if it's already taken into account when calculating the BF.
I read somewhere else we loose up when it's down 19~22 because of the short tables.
But the BF seens insensitivy about this.

PS: sry if this has any sense o.O

^ It's not really related to bubble factors.

If you are on the button and everyone folds, how many people "everyone" is shouldn't really affect your opening range IMHO - the important things are your hand and the fact that you still have the two blinds to act.

So generally, you play looser in later positions and when you are short-handed the missing positions are the early ones, so your average VPIP/PFR is higher.

TY for this!