Monday, October 11, 2004

Now for Something Completely Different

YTD: + $43726.21

We've been having some swell comments in one of my posts about SnG play. Chaos and Andy W believe that you should pass up small edges early on even to double up. I, Paul Phillip's like, don't agree. Here are my stats for why...please feel free to poke big holes in them: (We are assuming 9 handed, $109 entry; if you pass you still have the same chance of getting into the money as you normally do; if you double up you knock out a player)

Finish…Net $...% Place…EV……%P x2…..EV x 2

This makes the EV for not doubling up in the SNG to be +$28 with a ROI of 26%...very respectable. But after the double up this leaps to an EV of $55.54 with a ROI of 51%. Clearly you have to be very very sure it is a marginal edge if you want to pass it up.


Andy_Ward said...

Surely that's wrong. I was wondering if this is what you meant. The $109 is gone. You have to compare total return not profit.

Say we make this move twice. When we lose, we get nothing. When we win, we get $164. So over the two comps we have lost $54, right ?

Or is it late ? Ask me again in the morning :-)


chaos said...

Dave I'll have a look tomrrow: I'm a bit knackered and I'm playing a couple games. Assuming my logic before wasn't flawed (which it might be, I am tired), the situation is more worrying that I thought! Still we'll see, I'm sure this is something we can arrive at a sensible conclusion on.


Big Dave D said...


I would be interested in you explaining what is wrong with the calculation after u have had your beauty sleep - I didnt understand your last post at all :-)

But interestingly, your last point b4 moving onto this post actually also proves my point. If you are saying you should take the 60:40, then by most peoples' reckoning this is quite a slim chance...certainly in Phil H reckoning :-) And this was my original point...its damn hard, in most cases, to know for sure where you are in these close odd coups. So you aren't passing QQ and AK normally, or even except in very unusual circumstances. You raise, get reraised by an unknown and you should go allin with AK without a moments worry :-)



chaos said...

Ok I'm still up. I looked at the figures but they didn't appear to add up. But I'm sure they will look clearer in the morning.

Apologies for the big post: even by my standards it reads poorly, I made it up as I went along. I'll try and clarify the points further.

There were two points that discouraged the ‘1st hand all-in’ situation.

1. The negative $EV effect. Even a 55% advantage in all-in scenario only equates to a level EV on chips in most 10 runner STT’s i.e. Your chip EV is 110% of your starting chips. The one problem with this logic is that you start from a negative EV position anyway i.e. you’ve put in 1/9th of the prize money but only have 1/10th the chips. However, as illustrated by the in the smallest STT, the HU, taking a less than a 55% edge (using the same juice as the larger ones) is a losing strategy. This should point to something sinister, albeit a lot more marginal, when considering the ‘1st hand all-in’ situation.

2. Imagine 100 of these scenarios. For illustrative purposes assume an even split: win 50, lose 50. Now what this effectively means is that you have bought in double to 50 tournaments. You’ve effectively paid twice the entry and have twice the chips in these tournaments, starting from the second hand. It isn’t clear that this is a bad strategy until you imagine a scenario where you buy in for five times the normal buy-in. Now you can’t make a profit. In fact with the commission you are a guaranteed loser. Clearly you don’t want to be buying in this way at all whether it is 5 times or 2 times the buy-in.

Of course the latter is extreme, but its best way of illustrating what behaviour there is.


Andy_Ward said...

It's morning, I've had a cup of tea and that is definitely wrong. Two ways of looking at this :

1) If you lose, your ROI is not zero (as you are assuming) : it's -100%

2) Let me try to restate my original comment more clearly. Once again, suppose we play two Sit and Goes. Each time, a situation arises where you can either pass or call for all your chips, on a 50-50. If we fold both times, our expectation from the two comps is to return 137*2 = $274 for a profit of $56. If we call both times, then once we lose (returning $0) and once we win, improving our expectation for that comp to $164. Now we have lost $54 !

3) One more bonus try : the value of our chips if we fold is $137. The value of our chips is we call and double up is $164. The value of our chips if we lose is $0.

Come on, it's OBVIOUSLY wrong !!


Anonymous said...

Rule of thumb. Ignore the buy-in(* in 'during the tournament' calculations and just look the pay-out structure and chip amounts.

Once tournament is over, it's time to drag the buy-in amounts back to calculations.

for chaos: even the rake does not matter as there is nothing we can do to avoid paying it anymore. It's differnt in cashgames where it's easy to avoid rake by not winning the pot.


chaos said...

Morning all:

Well I’m struggling to believe in the figures here: I can’t imagine doubling up a good player’s chips can only leads to increase of $EV of 20%! Though it would support my case further if it were true.

Hi Aksu: I know where you coming from, but I can’t believe that the rake doesn’t affect the playing strategy just because everyone pays it. As I said look at the HU STTs: you pay 5% rake. If you take a shot at less than 52.5 % you are on a losing strategy: it is relevant. Imagine instead that you had to pay 50% or 100% rake: you simply could never adopt a strategy of calling all in for your stack early, it would be incredibly damaging long term. It isn’t easy to illustrate without going to extremes, but I’m convinced it’s highly relevant.


Andy_Ward said...


If the rake was 50% then it would be incredibly damaging to play at all. Exaggerating a point to demonstrate that a factor exists is all very well, but it doesn't tell us how important the factor is (or isn't) in real situations.

That's all I've got time for right now, am at work.


chaos said...

Andy, it serves to illustrate that the rake affects the playing strategy. Its relevance isn't confined as an after thought. This something you do in maths to get a sense of the behaviour. How much it should affect decsion-making, what situations you should pass? I'm not sure; but I'm willing to bet it's underestimated, becasue it's counter intuitive.

Similarly, in a 10 runner STT we know that the value of 1000 chips is worth less when accompanied by nine other 1000 stacks than it is when accompanied by 7 x 1000 and 1x 2000: i.e. a double up occurs. Since all of these 8 remaining stacks have increased in value the 2000 stack cannot be worth twice the 1000 stacks. Again this isn't intuitive but should impact on our decision-making.

Furthermore, this I suspect impacts the good player more so. If this player has a healthy ROI then it doesn't have much to do with knowing the value of QQ pre-flop at an early stage in an STT.


Anonymous said...

Interesting thread guys, altho it takes a bit of work to make sense of it all to start with ;)

Maybe I'm totally wrong, but do we not just need to divide Dave's $55.54 figure by a factor of 2? (as we are 50-50 to get into this situation when we make the call). That gives us $27.77 EV for the times we call, compared to $28 when we fold. So we should fold as Andy and Chaos are saying, but only just.

Or am I missing something?


Big Dave D said...


You're right of course...including the cost of the tourney has buggered the figures. I should stick to what im good at...losing buckets at PLO :-)



chaos said...

Sorry to see you took another hit Dave. I've had a fortnight to forget too w.r.t poker and sports betting; which of course means I won't. I remember a couple years ago some guy was quizzing Erik123 and asked him if he'd ever had a losing week, I think, he replied and said no, but I've had a losing day!(It could have been month/week, but I'm pretty sure it was week/day).

The table shouldn't be too hard to adjust. Just half the probabilities on the double up and introduce -50% for ninth place. That said I'm struggling to believe the probabilities given doubling up: winning up 3% to 19; last place is 8% in both cases. Nine handed with equal chips for our good player is 8%; eight handed with double the chips is also 8%.

There is enough here in the thread for me tp review my strategy. This information makes precious little difference to the end game, where the distorted approach needed is obvious, but in the early stages I think we are too easily fooled into thinking that the environment is normal: the normal rules of poker apply.

It would be very, very interesting if there was some simulation, modelling one could do, without such it may be tricky to prove conclusively.


Aksu said...

Hi Chaos,

I think I finally know where you coming from too. Still the time to think about the rake issue is prior entering and it is not a true factor to think about during the actual tournament IMO.

Lets take the extreme example 50% rake in HU match.

Case1: we know that there is still profit as our opponent is not from real life. Now we pass 60/40 shot's early. The reason is not the rake however. The reason is the opponent who we think will give us better changes in the future. We are maximasing our expected return using information about our opponent, stack sizes and payout structure.

Case2: We are in 50%raked tourny by accident against avg opponent. It's not right to pass 60/40 shot's now just because the rake is high. We need to maximise our expected return the usual way.

Does this make sense?


Big Dave D said...

To be frank, chaos, the win % were very conservative guesses, reverse engineering what I read on 2+2 as a good ROI, i.e. 20-30% per SNG. The trouble is if i put in more significant figures for the double up then the ROI and EV is just going to shoot through the roof, which (a) seems unrealistic (b) proves my case even more. So as I *thought* my conservative, flawed figures proved my point, I didnt try and put in more realistic ones.

I remember SpicyF once telling me he had lost 20+K over the weekend on UB, so I dont feel too bad about my slow decline. Of course I would rather be like Jim Britton, who once went on record on THM as saying he hadnt had a losing week in something like 11 months :-)



Big Dave D said...

Arrrggghhhh! Of course I *meant* that the EV for the double up was halved to reflect the chance of losing....I had it in my spreadsheet but didnt copy it across. Bugger. And you all assumed that it WAS ALREADY INCLUDED in the table :(

My idiocy and stupidty to one side, it still does seem to suggest that these close to even money shots are well worth taking. And if that is the case for SNGs, it must be even more the case for normal final table payouts. I think :-)

Aksu said...


1……… 0.16*500 ..... 0.19*500
2……… 0.14*300 ..... 0.17*300
3……… 0.16*200 ..... 0.19*200
........+_______ ..... +_______
=............ 154 ........... 184

ROI ......... 141% .......... 169%

According to your 'conservative' numbers I get $30 jump to EV. So doubling up is worth $30. Conservative indeed :-)

Good night,

Big Dave D said...

As I seem to have turned myself into a living, breathing, straw man argument :-) would anyone like to plug in some real numbers? To at least save my future embarrasment???


PS I'm gonna have to spoil your run on that plo8b tourney one of these days, aksu :-)

chaos said...
This comment has been removed by a blog administrator.
chaos said...

Dave in no way do your conservative figures suggest you should be taking on these even money shots, if I’ve interpretted them correctly. If you look at Aksu’ interpretaion. Without doubling ROI is 141%. Flip the coin it is 0.5 * 0 + 0.5 * 169 = 84.5%, but I don’t believe it is that bad.


First of all my comment that players shouldn’t treat the juice is an after thought, is of course true, but wrongly implies that many do. What I meant was that it shouldn’t just be a forethought: it affects strategy.

Case 2 I agree with enirely and unconditionally (I think): cash is usually straight forward! Case 1 I agree with in principle but not in practice(generally).
In the sense that this was a single one-off event or perhaps a tournament I would agree with you: there is no case to argue. Not, though, when there is a conveyor belt of games.

Most of us play with that in mind: we do not play as if it was our last or only opportunity. This is why many of us make thin calls, I feel.

In the HU scenario without rake you would take on many thin positions because you can move on to another opponent. Assuming you were playing this non-real player repeatedly you would take on the 60-40 advantage without rake, but with it you can’t: it’s a losing strategy. So for all practical purposes in a series of HU matches the rake will effect your decision-making because how quickly you win money is relevant.

I’m sure that this is an issue present in all players and because there is another game just around the corner we are inclined to gamble the odds slightly in our favour.

I’m not sure that I made that clear, or that it was clear to me; I knew it didn’t sit right, but I also was sure it was an issue.

So in summary I’d say this:

There are two reasons to consider avoiding the marginal all-in STT’s
1: You may have a better chance of outplaying your opponnent later.
2: All-in, or big stack collisions benefit other players not involved*.

If EV/time is the basis of your decision-making then the rake must influence your in-game decision-making, since your goal is not to maximise STT EV.

This has been an extremely useful thread, at least to me. I believe the issues are larger than I thought. Unfortunately, we aren’t close to coming up with numbers but get a sense of what I think should change. Changing my game to one that I’d rather not play may prove a little tricky and hopefully won’t impact on other forms of poker. That said, I still prefer cash!

That a player goes all-in first hand with four other people with O chip EV will find himself with around negative 25-30% before rake was rather startling and revealing. It is extreme of course and can’t be compared to doubling up; at least though the 5 timer stack has a high chance of pushing on in the later stages.


* and therefore by definition damages those involved.

chaos said...

Another thought....

Ignoring such unimportant issues as skill, position, large blinds etc the following might make sense:

'Any pot in a tournament that results in an increase in the standard deviation of the stack sizes will increase the EV of the players not involved in it. When a pot decreases the standard deviation, the reverse is true'.

Ok it is late. But for example in an STT if you play 1 round and you have the same stack you started with then your EV will have gone up assuming the other nine players don't have the same number of chips as well.


Anonymous said...

I think one significant factor that is ignored in most odds discussions is that we are NEVER playing odds exactly. Factored in to any coin flip where you play the QQ against AK is the very real chance that someone successfully disguised his AA or KK and you bit. Your "small edge" isn't 100% dependable. For that reason alone, the EV should tilt well away from calling all in with QQ on the first hand. You can be confident, but certainty is a myth...

Hypotheticals are all well and good, but no one ever plays a hypothetical tourney, and no bank accepts hypothetical cash...

Andy_Ward said...


It occurred to me half way through all this that I was talking about EV per tournament and you were talking about EV per hour. I don't like "per hour" approach with S+Gs ; I haven't got time to go into it now but I will do on my blog at some point.


Of course you're right but we do have to simplify in order to find a baseline to work from. In practice yes, we estimate our odds against the range of hands that our opponent(s) might have. I've got to tell you though QQ should very rarely be passed pre-flop in Sit and Goes because your opponents can turn up all sorts of awful hands.


chaos said...


The first two reasons for not making thin plays are independent of time and relate only to maximising STT EV, namely:

1: You may have a better chance of outplaying your opponnent later.
2: All-in, or big stack collisions benefit other players not involved*.

The third point, that for some reason I didn't label label as 3, of course isn't:

3: If EV/time is the basis of your decision-making then the rake must influence your in-game decision-making, since your goal is not to maximise STT EV.

I'm not sure that the time-factor should ever be ignored theoretically, but it may encourage poor play. No doubt though that this is part of the D-M process for many players.


chaos said...


Perhaps your comment hints at the question of how these issues, if true, manifest themselves in a change of game strategy. Since, as you say, we never know for sure what position or odds we are in, so we can't know what to decline.

This is of course true, but in big positive decisions that you feel on the cusp of making, should perhaps instead be declined. Thats not all: it's not just big decisions. One's general play may need to be pruned a little or perhaps a lot in the early stages. Some calls turn into folds, some raises turn calls or folds (in the case if steals,say).

On another point. Last night I played an STT. Very quickly 2 people were gone and another guy had about 5% of his stack left. There was one stack of 3k and another of 2k. The rest of us were lingering around SP. My EV had gone up, but it didn't 'feel' that way. It felt as though it had got worse: four players fighting for 3rd place. Of course it is nonsense, but it is naturally disappointing to appear to 'lose ground' so quickly.

It is counter-intuitive. With a certain degree of fear and disapointment present in our minds it is only natural that we are more likely to take risks, when the opposite strategy is required.


Seed said...

I have read this thread and admit to not understanding it one bit. I think some math is being applied in "creative" ways. Anyway... I can add the following information.

I coded a simulation of SnG tournaments for another purpose. I have modified it to look at this question.

The simulation has 10 players. Player 1 is marginally better than player 2 who is marginally better than player 3 etc. In this simulation, each player starts with $100,000 and is given $500 for first, $300 for second, and $100 for third in 10,000 $100 dollar tourneys.

After 10,000 torneys the players end up like this:

Player Win ITM
Index Wins % % Bankroll
0 1181 11 31 $182800
1 1189 11 31 $185400
2 1155 11 30 $154600
3 1047 10 30 $132300
4 1021 10 29 $100700
5 1009 10 29 $85700
6 892 8 29 $68000
7 936 9 29 $75600
8 798 7 28 $12000
9 772 7 28 $2900

Now, in each tourney I added a 50/50 bet between player 0 and player 9 (the best and the worst players) for all of their chips on the first hand. Following are the results:

Player Win ITM
Index Wins % % Bankroll
0 957 9 25 $-22800
1 1154 11 31 $185000
2 1136 11 31 $166400
3 1122 11 31 $160400
4 1027 10 32 $159300
5 1046 10 31 $133900
6 991 9 30 $120600
7 936 9 31 $121700
8 911 9 30 $81400
9 720 7 24 $-105900

The following conclusions can be drawn:

a) Good players should not make all in bets to start tourneys on 50/50 shots - PLAYER 0 gets trashed.
b) Bad players should not make all-in bets to start tourneys on 50/50 shots - PLAYER 9 gets hammered.
c) Good players should not care if other players make all-in bets to start tourneys on 50/50 shots - PLAYER 1 does not see much difference.
d) Bad players should be very thankful when good players go all-in early in tourneys on 50/50 shots - PLAYER 8 gets a great benefit. Actually, players 2-8 seem to get increasing benefits.

Next I made the 50/50 shot into a 60/40 shot with the advantage to the better player. Here are the results

Player Win ITM
Index Wins % % Bankroll
0 1158 11 30 $163400
1 1211 12 31 $201100
2 1126 11 32 $187200
3 1083 10 31 $156000
4 1064 10 31 $164400
5 1040 10 30 $122900
6 907 9 30 $83100
7 912 9 29 $71100
8 902 9 31 $103400
9 597 5 19 $-252600

Player 0 doesn't get hit as hard, but he still gets hit. Player 9 gets hammered again. All other players are happy.

Finally, I switched the odds to the 60/40 in the bad players favor:

Player Win ITM
Index Wins % % Bankroll
0 735 7 20 $-204400
1 1192 11 31 $196800
2 1103 11 31 $171600
3 1127 11 32 $189500
4 1092 10 31 $172200
5 1010 10 30 $122800
6 991 9 31 $130900
7 1001 10 31 $125900
8 882 8 30 $72900
9 867 8 28 $21800

Anyway, I hope you found this interesting.


Seed said...

BTW... sorry for the poor formatting, the columns are "Player Index", "Wins", "Win %", "In the money %" and "Bankroll" respectively.


chaos said...

Hi Seed,

Interesting stuff. I'm sorry I don't have time to comment now. Perhaps you would care to mention what isn't clear to you. Incidentally your conclusion covers point 2, but you also address point 1. I'm not sure how you easily you could cover the third point.

bye for now


btw I resent not resemble that remark about creative maths!

Seed said...

You said, "Interesting stuff. I'm sorry I don't have time to comment now. Perhaps you would care to mention what isn't clear to you."

Thanks. I don't have a specific thing that isn't clear to me. Basically, my tiny understanding of the ebb and flow of tournaments and the swings of cards makes it hard for me to understand how even the medium sized sample of data or math applied to the first hand can can predict future results. A poker tournament is a chaotic system... ironic considering your handle isn't it:) I believe that these systems are best analyzed with simulation or VERY large samples of data.

Your conclusions make sence and my creative maths comment was not directed at you nor anyone in particular. I believe you were saying that, if two players going all-in against each other increases the +EV for the other 8 players then it must also decrease the +EV for the two players who go all in. This agrees completely with my simulation.

You said, "Incidentally your conclusion covers point 2, but you also address point 1."

Yep. Your first two conclusions were proved out.

You said, "I'm not sure how you easily you could cover the third point."

With the $9 vig, and no 50/50 bet up front here are the results (same columns).

0 1235 12 31 $110200
1 1197 11 31 $85500
2 1070 10 30 $42000
3 1100 11 30 $38100
4 947 9 29 $-13700
5 912 9 28 $-49000
6 975 9 29 $-3000
7 862 8 29 $-32600
8 840 8 29 $-45400
9 862 8 29 $-32100

With the 50/50 bet here are the results.

0 933 9 25 $-119400
1 1230 12 32 $120800
2 1162 11 32 $122000
3 1100 11 32 $85800
4 1034 10 31 $49500
5 969 9 30 $6200
6 1008 10 32 $64100
7 917 9 29 $-21300
8 888 8 29 $-22200
9 759 7 24 $-185500

You said, "btw I resent not resemble that remark about creative maths!"

Didn't mean to make you resent or resemble anything. Sorry.

Best Regards,

chaos said...

I'm being extremely rude again, I have to cut short. I'm going to write something more exaplanitory if I can, I think this thread has been confusing.

Well you don't need to use enormous samples to infer conclusions. I did it without it: your work backed it up. The logic can point us in the right direction. Naturally I can't vouch for the integrity of your software, but it certainly appears to be telling us what we/I expect to find, which is pleasing. If it has integrity then the tool you have is invaluable.

Unfortunately you haven't covered point three and I'm not sure you can currently. Point 3 highlights that players may adopt a strategy of maximising EV/hour. This means they do not seek to maximise STT EV: they may take a hit to earn more money per hour. However, the strategy to maximise $/hour is affected by rake. The strategy to maximise STT EV isn't affected by rake. At least that is my claim.

Thanks for your input Seed, you've added another dimension to the thread.

cheers chaos

Anonymous said...


Your simulations are interesting, are you completley confident of the results? They seem to be telling us that taking a 50-50 on the first hand turns the best player at the table into one who has a -ve EV in said tourney. Can this really be true?


Seed said...

You said, "Unfortunately you haven't covered point three and I'm not sure you can currently. Point 3 highlights that players may adopt a strategy of maximising EV/hour. This means they do not seek to maximise STT EV: they may take a hit to earn more money per hour. However, the strategy to maximise $/hour is affected by rake. The strategy to maximise STT EV isn't affected by rake. At least that is my claim. "

Sounds right to me. The difference is that the rake is payed up front. It's gone. So, in a SnG you want to maximize the average money you take away from the tourney no matter what the rake is.

In a ring, a best play could be affected by the rake because the the rake is payed based on that one hand. An extreme hold-em example would be a hand where only BB and SB are still in it. The pot is 2xBB. It's the river and a royal flush is on the table. SB bets all-in with his huge stack. BB folds because the rake will cost more than getting his BB back. In a tourney, BB would call because the rake is already paid.

God, don't you hate when people go all-in when they know the pot is going to be split!

Anyway... you are right that I don't have the means to simulate this but I agree with you.

Seed said...

Butch said, "Your simulations are interesting, are you completley confident of the results? They seem to be telling us that taking a 50-50 on the first hand turns the best player at the table into one who has a -ve EV in said tourney. Can this really be true?"

I am very confident, yes.

Note that, in this simulation, the best player is only marginally the best player. I think these results would be much different if he were definitively the best player. I will try this at home tonight for giggles.

chaos said...


'The difference is that the rake is payed up front. It's gone. So, in a SnG you want to maximize the average money you take away from the tourney no matter what the rake is.'

I've addressed this a couple of times, this isn't necessarily true at all. Maximising your STT EV does not necessarily optimise your hourly rate. To optimise your hourly rate you likely must play sub-optimally w.r.t. to STT EV. This turns the rake issue on its head: it now affects which strategy you choose and how you play your game. The rake is not the same in each choice of strategy. Should I average 2 or 3 STT's an hour?


Strategy A: 30% return ; 2 STTs per hour; $100 buy in.

Strategy B: 25% return; 3 STTs per hour; $100 buy in

Strategy A or B which do you choose? It depends on the rake:

Rake 5%: Strategy A yields 2x(30-5) = $50/hour
Strategy B yields 3x(25-5) = $60/hour

Rake 20%: Strategy A yields 2x(30-20) = $20/hour
: Strategy B yields 2x(25-20) = $10/hour

Two differnet rakes, two differnt solutions.

Optimisng STT EV always leads to Strategy A, optimising EV/hour can lead to either. Therefore, rake effects strategy!

Butch, I guess it would have to be marginal. But perhaps not, I've an open mind. This is what we must hope to understand.

I'm off shortly, but I'll look in later.

Cheers chaos

Seed said...

OK, Butch!

Player 0 is now a lot better than the other 9. Without a 50/50 bet up front, he is finishing in the money 64% of the time and winning 28%. He's making a killing, earning $1,281,100 over the course of 10,000 SnGs.

0 2868 28 64 $1381100
1 1126 11 28 $-1400
2 981 9 27 $-79600
3 916 9 26 $-108400
4 860 8 26 $-112000
5 738 7 25 $-179200
6 673 6 25 $-197900
7 645 6 25 $-189400
8 656 6 25 $-194300
9 537 5 25 $-218900

Put in the 50/50 bet up front and look at what happens. He halves his profit. Hmmm... interestingly he halves his profit by taking a 50/50 shot up front. I wonder if that is significant.

0 1861 18 40 $535100
1 1162 11 30 $66900
2 1144 11 30 $59200
3 1058 10 29 $12800
4 890 8 28 $-58100
5 929 9 30 $-6600
6 830 8 28 $-75900
7 745 7 28 $-106700
8 621 6 27 $-143000
9 760 7 24 $-183700

BTW... the simulation plays NL Hold-em SnGs by Party Poker rules, 10/15 blinds to start escalated every 10 hands. Hands are played out in full with an appropriately moving button. In this case, players 1-9 are playing pretty much randomly with random bets, raises and calls (differing random behavior accounts for the differing win percentage). Player 0 has a difficult situation on his hands with all of these crazy players against him so he chooses a very basic strategy to play with. Only play premium hands and only bet out or call when you hit top pair or better on the flop. Only raise with two pair or better. Don't chase flushes or straights but if you happen to hit, make the other random players pay for it with big bets that are randomly called.

Andy_Ward said...


Two problems with the "per-hour" approach in S+Gs, in brief :

1) If you are considering a gamble early on, you have to take into account that while losing reduces the time taken for this S+G, winning increases it. That's not the same as Heads-Up games where the time is reduced win or lose.

2) It's extremely optimistic to believe that, as in your example, reducing the time taken per S+G by 33% (from 30 mins to 20 mins) will only reduce your RETURN from 130% to 125%. It's more likely that your profit will be severely hit, seeing as the buyin and the rake (you're right, it is a factor) remain constant.

For these reasons I prefer to concentrate on EV per tournament when playing.


chaos said...

Hi Andy,

re point 1: Yes you are right it is different in HU; however I don't beleive the relationship between winning and losing here is linear on time: losing an all-in bet means 0 time, but I very much doubt that doubling up doubles up the average time spent, 50% max I would guess.

The second point was clearly an example to illustrate the principle as I was going out the door. Nevertheless it stands up ok. It looks worse when you break it down becasue it looks as though I'm trying to claim 20% on profit on 20 minutes a tournie. You've assumed I'm playing them consecutively. I was actually thinking on the lines of playing two tables at once. Thus Strategy A averages one hour a tournament and Strategy B 40 minutes. The ratios remain the same but the feel is different. As I said it was just a proof of priciple to illustrate that playing strategy is affected by rake when optimising $/hr. It illustrates the point I've been trying to make quite well.

Finally the issue is not just about going all-in thin. It's about a lot of thin situations: thin calls, thin bluffs, thin raise etc. These issues don't just relate to the big situations: these situations emphasize the issues.


chaos said...

That said it's hard to know how much of an issue it is, but for me there's no doubt that an attitude of 'oh f**k it there's another STT around the corner does exist': it's the reason I've thrown them in a couple of times!

On this perhaps confusing comment:

'Any pot in a tournament that results in an increase in the standard deviation of the stack sizes will increase the EV of the players not involved in it. When a pot decreases the standard deviation, the reverse is true'.

The standard deviation is just a measure of how much the stacks deviate from the average. So to begin with, the average is 1000 chips with 10 players. Each stack is 1000 chips so the SD is 0. If one stack loses 100 chips then the SD has gone up. If it gets them back off the player it's gone back down again.

Essentially the bigger and smaller stacks are, the more variance and hence the greater the standard deviation. Based on equal skills, the if the SD goes up then the players not in the pot gain higher EV.

If you are in a field with an average stack then the higher the SD, the higher the EV. In that case should the on-line casinos put in standard deviation has a metric in the tournamnet stats department?

I'm off for a couple of days.


Big Dave D said...

Chaos..Dont go ...this is fun!

I finally plugged some sensible numbers into my EV spreadsheet and surprisingly, or not, it came out with roughly the same figures as Andy W did. 50:50 turns a just under 30% ROI guy into a losing one; 60:40 keeps him winning but worse than just passing. Interestingly, a 70:30 shot gives him quite a significant increase in EV. I'm not sure what this means for playing hands, but it certainly makes passing a QQ or AK except under hugely exceptional circumstances a big mistake, against typical foes.



Seed said...

Andy's spreadsheet agrees with my simulation. I modified the test from my original post where Player 0 was only marginally better than the other players to change the first hand bet to a 70/30 shot.

Player 0's ROI goes way up, mostly funded by the fool who is going all-in with weak cards.

0 1659 16 43 $528200
1 1163 11 31 $96100
2 1119 11 31 $82600
3 1058 10 30 $34900
4 1021 10 31 $51200
5 1009 10 30 $22500
6 954 9 30 $10500
7 864 8 30 $-14800
8 909 9 30 $5300
9 244 2 8 $-716500

So, a 50/50 shot makes a marginally winning player into a big loser. A 60/40 shot makes him continue to win but with a lower ROI. A 70/30 shot makes him a big time winner, seriously boosting his ROI.

You must have a nice spreadsheet, Andy! How does it work?

Seed said...

Dave, why wouldn't you pass AK? I would think this is most times less than a 70/30 bet against most foes all-in at the first level. Don't you find that the majority of these players are holding pockets? Especially at the higher stakes tables??? I don't know, I was just curious what your experience has shown.

My take on all this is to pass anything but KK or AA... maybe QQ!

Oh, and BTW, sorry for calling you Andy in the previous post:) I don't know anyone here so I am getting confused.

Anonymous said...

Thanks for running all tehse models guys. I find the results surprising, and they will certainly change my approach to SNGs if I ever start playing them seriously. My initial feeling was that it wouldn't make that much difference to the EV. But it seem to be massive


Big Dave D said...


The spreadsheet is just a standard calculating EV affair, just this time I put some serious thought into what the numbers should be, then multiplied them by 50% when he has doubled up. I suspect Andy uses something from some of the software he has written, which can be found on his site.

I need to think more clearly about what the implication of the 70:30 rule, as we can now call it. I think it means QQ is a v v v clear call, against the whole range of possible hands which in my experience may be AK-Q, sometimes AJ, down to 88 on the pair front. This would especially be the case when facing a massive reraise, which are often weaker than just a more normal sized reraise or raise. AK is more contentious. Again it probably is better against a "move you out" raise then a "keep you in raise" if you know what I mean.



Andy_Ward said...

Believe it or not I was just guessing from my own experience.

One point that Chaos made that's very important to remember is that this doesn't just change all-in decisions ; it affects a lot of the smaller decisions in that you just fold marginal hands in the first two levels (eg AT), and a lot of the time with AK you would rather just call a single raise and take a flop (providing the raise is large enough so that you're unlikely to be more than three-handed), and if you miss then you're done with it.


chaos said...

Hi guys,

I've been a way for a couple of days and it looks as though Dave may have been converted! Not much more I can add, it really comes down to sensitivity and as such only models, simulations or large real life data samples can take this further: none of which I have access to.