Positive EV vs. survival in Tourneys

[triplc]

Hi all,

there have been several threads recently in which debates have arisen surrounding making plays when you have positive (tourney chip) EV. For example, if I hit a four-flush on the flop, should I call an all-in bet (when covered) if the pot is laying me the correct odds. This particular post does not attempt to cover the situation when you are not putting all of your chips at risk, but we can branch out to that topic here as well if folks want to.

Here's my take on it...feel free to blast away, folks.

In a ring game, when you decide to chase a four-flush (1.9 to 1 to hit by the river) because the pot odds are correct, you are talking about real dollar EV, and thus it is correct to chase the four-flush because in the long run you will win more real dollars than you lose, which is what we all strive to do. However, in a tourney (multi or SnG) you are not playing with real dollars, but tourney chips. So, the decision has to be based upon the real-dollar EV vs. the tourney chip EV.

For example...you flop a four-flush with T1000 and a player who covers you pushes all-in. The pot is laying sufficient odds for you to call (let's say 3-to-1 to make it simple). Even so, two out of three times you are going to bust out, and once you are going to quadruple up. So, do the 3000 chips you win one time make up for the two times that you bust out? I don't think so, especially if you are one of the better players at the table, and figure to have a spot sometime soon when you have the best hand. What if the pot odds are 4-to-1? 5-to-1? Do you chase it now? Are there any odds that would make you chase it?

What about a gutshot straight draw. Say the same scenario but now the odds of making are 5.1 to 1 against and the pot is laying to 8 to 1 odds (far-fetched in NLHE, but possible). Here, you are gaining 8000 chips once, and busting out 5 times. Granted, the 8000 put you in great position to win the one tourney, but does that outweigh your survival in the 5 others. In this case, I'm even less inclined to do this because I am going to bust out 5 times out of six.

These are contrived examples, and in reality there is a lot more to consider, such as stack size, how close to the money, blind size etc... But most recognized (Sklansky, Cloutier/McEvoy) experts feel that protecting your stack is more important that positive tourney chip EV, especially if you are one of the best players at the table, and you are putting your entire stack at risk in a drawing situation.

Does this change for multis vs. SnGs? Do the two different structures (one being quick and the other requiring more time invested) mean you think about this issue differently?

Interested to hear the debate. Flame away.

CCC

[Kurn, son of Mogh]

Most of the advice says don't chase small edges in a tournament. The question then becomes how to define small. A lot depends on your read of the opponent (are you really behind) and the possibility of other outs.

If you play x SNG's during the season, passing up 3-1 pot odds every time when a 7-5 dog is going to cost you money in the long run.

But, as Dennis Miller would say. That's just my opinion. I might be wrong.

[agenbite]

In a tournament I don't believe you should put all your chips at risk on any draw. In my opinion, draws are only profitable in a tournament (long term) when you see them for better than the correct odds (pot laying you 3:1 or better to play a 4 flush on the flop, for example). This is usually only the case very early when the blinds are puny and the table is full of limpers, of course.

Cloutier says he never plays draws in tournaments. If you never did I don't think it is a mistake. Sort of like never playing low pairs. I'm more prone to muck them early unless I see a flop for free in the BB.

I'm tighter than most, so I'd like to see what others have to say too.

[VVildo]

This is an issue that has been bugging me for a while, especially in the 4-flush situation. I tend to not go on draws as well. So the situation is reversed for me. I get good cards early in the tournament, let's say Kings, and raise it a good amount, let's say to 100 when blinds are still 15/10. I get a couple callers (probably because I play on the kiddie tables on Party) and we go to the flop with a 300 chip pot, pretty large in the early stages of the tournament. Flop comes all rags, but there's two cards of the same suit. What do I do?

Right now I'd be very happy just picking up the pot as it stands, so I'm not concerned with trying to bait people into calling. In this vein, and in the confidence of my overpair, I want to go all in and get rid of any people that are on a flush draw. However the odds are only 1.9:1 in my favor. So if I get calls by those flush drawers I run the risk of getting myself thrown out of the tourney pretty early, even though this is a +EV situation (correct?).

So take it to the other extreme. I just check or call on the flop and see what comes on the turn. If it's that cruical 3rd suited card then I just tossed away a large pot when I had the (presumably) the best hand on the flop. If it doesn't help the flush draw do I bet a lot now and hope that they don't want to stick around just for one more card?

The only other alterative that I can think of is to bet a sizeable amount on the flop, but not so much that you screw yourself over for the rest of the tournament if that suited card comes on the turn. If the card comes on the turn then you just lost more money than the 2nd option. However if it doesn't you can bet again and hope that the flushers will fold this time. The problem with this method is that you're probably giving the drawers correct pot odds to call on the flop, so you're setting yourself up for failure in a way.

Opinions?

[Utah]

The problem is that each chip you acquire becomes less and less valuable. I dont know the crossover point when the draw overpowers the odds and where you dont mind being all in, but there is a point. For example, if 2 players are all-in and you have a straight flush draw with overcards then a call would most likely by correct.

Time also is a factor if you are a winning player. So if you bust out the first hand then you can just join another SNG, which I believe has the effect of rebuying.

There is an interesting although incomplete discussion of tourney chip value in Masons "Gambling Thoery and Other Topics" book.

[AleoMagus]

I just made a post about this in the thread "Bubble,Bubble,...toil and trouble"

I am not going to say all the things I said there again here, but I will answer the rhetorical question I posed at the end of that post.

The question was, with AA in the BB on the first hand of a sng, do you call if everybody else goes all in?

It is definitely a +EV situation (chip values). AA wins about 1/3 of the time against 10 random hands and you are getting 9-1 odds on your call.

Problem is, by calling you will then get Zero dollars 2/3 of the time. You will get $50 (assuming a $10+1 party sng) about 33% of the time (taking all split pots out of the equation for simplicity)

this means you will on average win (2/3)(0)+(1/3)(50)
which equals about $16.67

If you fold, you will get 2nd probably 90% of the time because you will be so shortstacked and 1st 10% of the time.
(again this assumes only one opponent who win the big all-in fest)

this means you will on average win (9/10)(30)+(1/10)(50)
which equals $32

It should be obvious from this that +EV decisions are not what really matters all the time. The apparently -EV decision of folding AA will actually make you almost twice as much in the long run.

Regards
Brad S

[agenbite]

Well, in your case of having AA count my vote as an adamant yes (call). If by some bizarre set of circumstances you are a few spots from the money in a large multi-table tournament, and would bust out of it by virtue of having one of the smaller stacks in that case, then I may possibly fold AA. Especially if it were one of the big tournies (Stars' $200 Sunday event, for instance).

Would anyone make the call in that specific case?

Heads up or against 3 or less opponents I believe I make the call no matter what, when, or where.

[Utah]

I believe miss the value of time of the course of tournaments. Lets say this situation came up over and over again.

You will make more money over time going all-in preflop with AA. It simply takes you too many hands to get to the end of the "folding option" to make it worthwile over time.

The reason is that it will take you at least one more hand to collect your value. The best option to do that is to go all in, hope you opponent calls and hope that you lose.

This way in 2 hands you have made 30 dollars. and you are ready to do it again. However, I have already went all-in with another AA and I am now ahead of you.

However, it is at best 50% likely that you will lose one hand one and reality it will be far more hands, since the opponent can fold a weak hand and you only pick up tiny blinds.

So, you can see that pushing in with AA is a far best choice under certain circumstances.

[AleoMagus]

My post is claiming this exactly - That over time, you will lose more by calling everybody's all in with AA.

The math I have given describes this. I have simplified it yes (because of split pot possibilities and even 2nd & 3rd place prize money)

Rest assured though, over time you will lose more by calling the all-in. I will describe this again as I fear my post was misunderstood. In my example, it is the first hand and in the big blind you are dealt AA. Every other player at the table goes all in. This means that if you call, in all likelihood, the tournament will be over on the first hand. Against ten random hands, this means that you will win about 1/3 of the time. Over the long run then, you will win about $16.67/tourney. Actually, it will be more because of 2nd and 3rd place finishes and split pots

It will not, however, be as much as you will win by folding. By folding, you will win - over the long run - $32 on average

I know this example is hypothetical. I sure have never been in a tourney where everybody pushed all in preflop, but it is hypothetical to make an important point. This situation paints a very clear +EV situation under normal circumstances which is clearly a mistake in tournament play!

These kinds of situations do come up, and more often than I think people on here realize. I am amazed lately by the amout of "is +EV the right way to play tourneys" posts I am seeing. I seriously recommend you guys all go get TPFAP and mason's 'Gambling theory and other topics'.

I am reading your post again and I have to say I just don't understand what you mean by some of your statements. Yes, you will be ahead of any one given player with AA, but you will not be ahead of the whole table. Survival should be your key concern here.

I don't know how to put it any other way. Anybody who thinks calling with AA here is correct is just plain wrong. It is most definitely the right play in a ring game, but it's not going to be correct in a tournament.

Regards,
Brad S

[AleoMagus]

lol. Looking at your earlier post Utah. I guess you have read Mason's book. Perhaps my post was just unclear.
I hope the first response clarified that I am talking about situations where EVERYBODY goes all in, and why I am using such a hypothetical example.

Regards,
Brad S

[eastbay]

You might want to read the recent couple of threads regarding my "call/fold" model for evaluating chip EV vs. chip risk.

I think the qualitative ideas that came out of that analysis are correct. Knowing where to draw the line quantitatively in full-scale poker is another story.

eastbay

[CrisBrown]

Hiya Brad,

But that's part of the EV calculation, is it not? You don't simply look at the EV of betting/calling, but also at the EV of folding. In this case, calling is +EV, but folding is even greater +EV, so the correct decision is to fold. But I don't see that as an exception to the "+EV is the right play" principle.

Fossilman says that early in a tournament, real dollar EV ($EV) and tournament chip EV (TEV) are basically the same. Early on, then, basic ring game strategy applies. It's not until you're in or near the money that $EV and TEV begin to diverge, and at that point the $EV:TEV ratio decreases as stack size increases. I.e.: the chips you lose are worth more than the chips you win ... a good reason not to chase draws or make loose calls. I'm going to assume he knows what he's talking about, although I can't offer a mathematical proof. (Perhaps he can.)

When I first came to this forum, I attempted to prove the converse: that, for example, doubling up early doesn't much improve your chances to win a SNG, therefore if you face a double-or-gone situation, you should fold. Fossilman and several of the other posters convinced me that this was not correct; that if you had a clearly +TEV chance to double up, it was a mistake to fold. The argument is probably back in the Tournament Forum archives somewhere.

I think to some degree this also depends on the structure of the tournament. In a PokerStars two-table SNG, there are 27,000 chips in play. By the time you're nearing the bubble, the blinds are often 200/400+25 or more. So you need to build a solid stack along the way, or you'll be in all-in-or-fold territory just when you're at the bubble ... not a comfortable situation.

By contrast, the lower buy-in SNGs at Party have only 8000 chips in play, so one or two big hands will usually get you into the money. In that situation, it's better to avoid risks unless you're so short-stacked that you have no other option, and instead wait to pounce on a big hand.

To some degree, the correct strategy also depends on the dynamics of the tournament you're in. In a very "fast" game, with a lot of loose-aggressive players, it's better to sit tight and let the rabbits eat each other. A big stack's $EV is less than at a tight table, because the stacks are so volatile in a loose-aggressive game. You gain $EV every time a rabbit busts out, so it's better to wait.

By contrast, in a tight game, a big stack's $EV is greater than in a loose-aggressive game, because your steal-raises get more respect, so it's easier to maintain a lead. You have to pick up little pots along the way, because there aren't going to be a lot of big ones unless you get monster vs. monster or monster vs. monster draw. So while you're picking up little pots with bluff and semi-bluff steals, you have to be on the lookout for those monster draw opportunities and the chance to double through a big hand. When one comes along, if the pot odds are good enough, the shot at a dominating stack is worth the risk.

All in all, I just don't think there's any one, fixed answer to this question. Like almost everything else in poker, it's situational.

And that, BTW, is why I mention the buy-in when I offer a hand for analysis, and why I mention what buy-ins I play. What works at a $55 two-table SNG on Stars might be horrid at an $11 SNG on Party, because of the different structure and typical table dynamics. The advice which is "best" for a given player is probably the advice of successful players at that site, and at that buy-in.

Cris

[Henke]

I think there are some errors in your assumptions. First of all, you say that aces will win 1/3 of the time against random hands, but that it will never get 2nd price in an all-in contest? If we assume that it will snatch second place about as often as it will snatch first, we get that the EV of folding needs to be higher than about 26.67. To accomplish this, we'll need to snatch second (after folding) about 18% of the time, which basically means that we don't want a split pot more than about 70%-80% of the time. That seems to be a reasonable assumption though, so I'll have to agree with your conclusions after all /images/graemlins/smile.gif

[Henke]

[ QUOTE ]
Fossilman says that early in a tournament, real dollar EV ($EV) and tournament chip EV (TEV) are basically the same. Early on, then, basic ring game strategy applies. It's not until you're in or near the money that $EV and TEV begin to diverge, and at that point the $EV:TEV ratio decreases as stack size increases. I.e.: the chips you lose are worth more than the chips you win ... a good reason not to chase draws or make loose calls. I'm going to assume he knows what he's talking about, although I can't offer a mathematical proof. (Perhaps he can.)

[/ QUOTE ]

Fossilman is correct in his statement, but, since in this hypothetical situation everyone is going all-in, it's no longer "early on" in a tournament. Instead, we instantaneously moved to the bubble! So having 10% of the chips left with just 1-2 opponents means that your chips has increased alot in value.

[Bozeman]

3 handed in a SnG among equal players, you need about a 1-10% percent better hand than ChipEV would indicate (depending on stack sizes). If you are the smaller stack, it can vary from 2-10%. Note however, that 3 handed is a situation where you are playing for 1st or 2nd, and 1st is worth a lot more. Overall, this curve reaches 0 at headsup, gets close to zero at 10 handed, and has a maximum at 4 handed.

As your edge increases, the edge you need to call allin can go up considerably, to about 10% more than for the equal player calculation (at 3 handed, other #'s I haven't done yet).

Craig

[Henke]

About 23.5% of the starting hands are suited. With only two opponents seeing the flop, that means that on average 1/2 (probably the better half /images/graemlins/wink.gif) opponent will have two suited cards. Since there are four suits, that gives a probability of about 1/8 that you're up against a flushdraw.

If we assume that our opponent has at most 5 killer-outs, then if you bet about half the pot, it should be enough to kill his implied odds (assuming you start with T1000). That would leave you with about T750. If the flushcard comes on the turn, you might still want to bet about half the pot, and you would still be left with 450 if you lost. If it doesn't come, a pot-sized bet might be correct. In this case, it would mean all in.

I'm by no means an experienced NL-tournament player, so it would be great if someone with more experience would comment on this...

[AleoMagus]

Yeah, I definitely simplified the math by leaving out 2nd & 3rd place finishes on the all-in call (and split pots). I suppose folding will not be twice as profitable in this respect, but I think we are agreed. It is more profitable

Regards,
Brad S

[AleoMagus]

Yeah, I guess it is a part of the EV calculation.
Maybe that's where +/- EV calculations seems to stop short sometimes. I, for one, often decide on whether or not something is +EV and just do it in the heat of the moment without also considering if alternative (and completely different) plays are even better.

That said, I think that the strictly chip value EV of folding AA in that situation is still negative. I certainly would not do it in a ring game. It would seem that the definition of EV is mixed. I'm not sure if I am using it correctly or if others are. You seem to be implicity taking chip values and $values into account and coming up with a true and ultimate +/- EV. I'm just saying that sometimes +/-EV calculations are wrong in tournaments if you are only looking at chip value.

As far as stack sizes are concerned, with so few chips on the table in a one table sng, startegy changes are often required very early on. It is not altogether rare on party's sngs that one player has a third or half the chips on the table in the first round. Single table tourneys feel a lot like the bubble from the start sometimes. In my aces example, I think this is especially true (as pointed out already by another poster)

Very interesting thread

Regads,
Brad S

[Henke]

As far as stack sizes are concerned, with so few chips on the table in a one table sng, startegy changes are often required very early on.

If you are refering to chip-values here, then I think you're wrong. However, a tighter and more conservative play might be in order because a) you play better short handed than your opponents, or b) a large % of the opponents will bust out because of stupid play.

Regarding b), I don't really know how big the % would have to be, but it is surely related to the chipwize EV of the specific hand.

[AleoMagus]

I've been thinking more and more about this. If by the third hand of a sng, the stacks look like this
1.800
2.800
3.785
4.15
5.1570
6.2400
7.785
8.845
9.out
10.out

would I not be correct in altering my play slightly against the big stack/the small stack? Perhaps I am drawing more conclusions than I should because (your suggestion) there are so many bad players who will bust themselves out. Maybe this is the biggest reason why tight play is right.

I've also been thinking about my aces example some more. As far as partypoker is concerned, players who simultaneously bust out are awarded prized based upon chip count when going into the pot. I assume that this means all the losing players would split 2nd and 3rd prize. In this case, my conclusion to fold would still be correct. If, however, 2nd and 3rd were awarded based upon a secondary criterion of hand strength, it might still be correct to call as aces will still be second best or third best a lot.

I suppose this does not change my original point - you can't just blindly follow usual chip EV calculations.

Getting back to opponent considerations, I also have considered some things. If I was up against the ten best sng players in the world, I would definitely call with the aces.

This goes back to an earlier example (another similar thread) where I suggested folding QQ even if you knew your opponent had AK (first hand all-in during a sng). It is ordinarily +EV, but if you think you have similar or better odds of making the money anyways, why risk busting on the first hand. If however, your odds of making the money are low (tough competition) you would probably call.

I'm just thinking out loud here, but perhaps the biggest things to consider when changing strategy early are not stack sizes, but opponent strength. Of course I know it all depends on a lot of things.

It's all got me thinking anyways.

Regards,
Brad S

[AleoMagus]

Ok. Ok. lol. I finally got it
Sorry to post so many times on this thread.

I see what you are saying. I am thinking about profit/tourney while you are thinking about profit/hand. By calling, you will, of course make more per hand.

I will attempt a counter-argument however. Suppose I just don't bother playing any other hands after the AA fold. Suppose I just take 2nd? Will I not still be making $25/hand - more than by playing the aces.

I am already doubting myself here because I think the 2nd/3rd place consideration and split pots might push the aces above $25/hand. Still, I am not inclined to give in just yet.

There is also the consideration that we may only be able to play a definite number of tourneys each day, despite the time we have avaliable.

Very interesting objection, no matter how long it took for me to wrap my brain around it.

Regards,
Brad S

[Henke]

[ QUOTE ]
I've been thinking more and more about this. If by the third hand of a sng, the stacks look like this
1.800
2.800
3.785
4.15
5.1570
6.2400
7.785
8.845
9.out
10.out

would I not be correct in altering my play slightly against the big stack/the small stack? Perhaps I am drawing more conclusions than I should because (your suggestion) there are so many bad players who will bust themselves out. Maybe this is the biggest reason why tight play is right.

[/ QUOTE ]

Oops! I didn't mention in my last reply that I was refering to strategy changes compared to a cash-game. The correct strategy allways depends on stack-size (for example, don't try to steal the blinds if the big blind is all-in). My point was just that at the beginning of a one-table tournament, fossilman is right, and your chips approximately equals their share of the buy-in/prizemoney. Thus the correct strategy at the beginning of the tournament should be quite similar to a cash-game with the same players, same stacks etc. However, if you know you're far better than your opponents when shorthanded, your chips gain some value. Also, if you somehow know that some big % of your oppoents will go all-in (so that you will get close to or in the money regardless of the outcome), your chips gain value. This is what happened with the AA and everyone moving all-in.
[ QUOTE ]
I suppose this does not change my original point - you can't just blindly follow usual chip EV calculations.


[/ QUOTE ]
Correct.

[ QUOTE ]

This goes back to an earlier example (another similar thread) where I suggested folding QQ even if you knew your opponent had AK (first hand all-in during a sng). It is ordinarily +EV, but if you think you have similar or better odds of making the money anyways, why risk busting on the first hand. If however, your odds of making the money are low (tough competition) you would probably call.

[/ QUOTE ]

Hmm.. Tough one... I tried to apply the Malmuth model (http://forumserver.twoplustwo.com/showflat.php?Cat=&Number=369811&page=&view=&sb=5&o =&fpart=all&vc=1) to extract the probabilities of finishing in first, second and third place. That gave these numbers: 20%, 17.8% and 14.4%. With those values, a call would have EV 10.3854, which is slightly better than a fold (which obviously has EV 10). But of course, the Malmuth model assumes that you are playing against opposition that are equally skilled as you are. I don't really know what adjustments that has to be made if you are better than the opposition. But, if we assume that we have an adequate bankroll, then passing up a +EV move the first hand should be bad. If we loose, there's allways another SnG. So to maximize EV/hr, I think a call is in order.

[AleoMagus]

Excellent post, which clears up a lot of my confusion.

I think that the last paragraph in your post hits right to the core of so much of the debate on this forum recently and would actually answer the question of survival vs EV for many.

Do we want to maximize our $/hr OR do we want to maximize our $/tourney.

Truth be told, I can see reasons for answering this question either way, but it's hard to deny that online... there always is another sng to get into.

Regards,
Brad S

[triplc]

I think the shorter nature of SnGs shouldn't change the way we play poker. For me, every SnG is an attempt to last into the money and (God and cards-willing) win the thing. At what point should we decide to gamble, simply because our situation in the current SnG is unfavorable and our hourly rate might go down if I get bounced in 5th or 4th instead of 8th or 9th?

Should I make a rule that if I haven't hit any cards for 15 minutes, and am one of the shorter stacks, that I should just go all-in at the first coin flip opportunity, or when I get a decent draw. Will this really increase my hourly rate?

In my opinion, there is a strict correlation between $/hr and $/tourney, although I am anxious to hear from others with better data on this issue. I guess its just a matter of pride for me that I am unwilling, even when shortstacked, to stop playing solid poker until the blinds begin to dictate that I need to start taking chances.

I believe firmly that you need to maximize your dollars per tourney, or, to put it another way...you should always be trying to play your best poker, and not give in to the "I'll just play another one if I get busted" mentality.

CCC

[Al_Capone_Junior]

This is not about calling an all-in with a draw, but the discussion on this post, and the one directly after it, are on the same subject - calling all-in when there's a chance it will knock you out.

http://forumserver.twoplustwo.com/showthreaded.php?Cat=&Number=508495&page=0&view=ex panded&sb=5&o=14&fpart=

Basically I need a considerably better than 0 EV to make such calls, 5c on the tournament dollar is not enough to risk getting knocked out. 60c, yes, I will take that almost every time, as long as it aint the bubble.

al

[SossMan]

I know it's a little off topic, but I think that while the AA wins against 9 randon hands 33% of the time is valid, I don't think that 9 all-in's on hand 1 of a tourney represent "random" hands. My guess is that the other two aces are most certainly dead. I'm sure many of AA's wins against 9 random hands come from spiking a set somewhere along the way.

This only enhances your argument that mucking preflop is higher $EV than calling.

[Utah]

I am not sure what the analysis really says about how to play or how would it relate to a more common situation such as going all in against a raise and a reraise with KK on the first hand. I just think it is an interesting avenue to explore.

You cant simply quit and take second place, at least not online - for which I was basing this analysis. Online, you need to lose to take second. So, you need to look at the minimum number of hands to lose with - which is 1 (you go allin and the opponent calls and you win). Lets say you and your opponent both go allin every hand until the end. You get:

Lose - 50%
Win/Lose - 25%
Win/Win/Lose - 12.5%
etc.

The odds are that it will take multiple hands even under the best scenario. Even with one additional hand, you are now at an even proposition on a per hand basis with going all-in.

I need to think about this some more.

[Cosimo]

Q: let's say you get AA every time you enter a tournament and everyone else always goes all-in on the first hand. How do you make the most money over the long run?

A: who cares? I don't think analyzing this scenario provides useful information, because you WONT be dealt AA every time. You have to assume that you'll only make average ROI in the next tournament.

In the first tournament you are dealt AA, everyone goes all-in. Your choices are to call and win $16.67 on average, or fold and win $32 in five minutes (or however long a short-stacked HU match lasts). Should you go all-in, your EV for the remaining five minutes is ROI*5/avg-tourn-length. This is most likely less than $32. If you are looking to maximize $/hr, then folding is the best option. I think maximizing $/tourney is a poor goal.

I'd push in on a draw here if I cover my opponent by a good bit AND there's already dead money in the pot from a preflop raise, blinds, etc. Most likely there's someone else out there with 1500-2000 chips, so if I take a lead with 6000 chips I've still only grabbed a small bit of equity. If I fold here, I expect my average ROI from the tourney.

[Utah]

A: who cares? I don't think analyzing this scenario provides useful information, because you WONT be dealt AA every time. You have to assume that you'll only make average ROI in the next tournament.

You miss the point completely. The goal of analyzing this scenario is not what to do with AA everytime the previous 9 players go all in on you.

Models start out simple to illustrate a point, explain a phenomenon, or to provide a launching point for further exploration. Economic models do this all the time and nobel prizes are based on them, even htough the models have nothing to do with reality (e.g., Miller-Modigliani Capital Structure Model in a World Without Taxes).

Maybe this over-the-top model can provide useful analysis on whether to go all in with high pairs against 1 or 2 players already allin in the early rounds of an SNG Tourney.

[Bozeman]

"Maybe this over-the-top model can provide useful analysis on whether to go all in with high pairs against 1 or 2 players already allin in the early rounds of an SNG Tourney."

It can't.

[Cosimo]

I'm going to agree with Bozeman here, tho I'm going to expand a bit more. Utah, I understand your point about starting small, believe me. I know exactly what you are talking about.

However, if your simplification misses an important element (that being that you WONT be dealt AA every single hand), then the simple model leads to incorrect conclusions. You have to be able to expand the model to include additional elements. The model that I am arguing against is the one that says that you get AA every single hand.

What is the goal of this scenario? To prove that calling produces a higher $/hr for the thirty seconds that you are at the table? I'm missing something here; fill me in.

Or, maybe, I'm just quickly concluding that this model is too warped to provide useful information on going all-in versus 1 or 2 players early in a sit-n-go. What is the measure of that choice? By what metric do we decide that calling is a good play? I choose net $/hr; I think a scenario that assumes AA on the first hand every time isn't useful for my goal.

[AleoMagus]

this thread is about whether survival considerations ever take precedence over normal EV calculations. This example is merely an extreme illustration that it happens.

Regards,
Brad S

[AleoMagus]

it does not assume we get dealt AA on the first hand of every sng. It merely looks at all those cases and no other cases.

The point is, in all those cases, your $/tourney is greater if you fold. Your $/hand (and in turn, $/hr) is greater if you call.

This could very easily apply to coin flip decisions (or even loose starting hand selection) at the beginning of a sng as well.

as for responses like "it can't" - care to explain why?

Regards,
Brad S

[Utah]

You dont know that of course. and I would bet big money against you.

But your remark was a nice little quippy comment none the less.

[Utah]

Lets make it simple and get away from the AA hand scenario.

My whole argument summed up:
1) Wow, its interesting that folding AA has a higher EV than calling with AA
2) Hmm..., maybe not so fast. It depends on your assumptions
3) Hey, maybe this model has applications to real game situations (Bozemans brilliant and articulated rebuttal not withstanding)

The biggest apllication I can see is the effect of "mixing it up" early in a tourney taking into account: the affects on profit won of winning the tourney, the cost of busting out, the value of sitting out (surely, all players busting out gets you to second. However, what is the effect of 1-2 players busting out have on you getting to second. Can this override a normally positive EV play?), and the value of time.

Oh well, I guess Bozeman has looked at this and he already knows its a waste of time. One wonders though, if Bozeman would have yelled to Miller and Modigliani, "You idiots. Your model about corporate structure is a world without taxes is just stupid. Any idiot knows that there are taxes in the world!" right before they won the Nobel prize. (of course, you can throw in John Nash's simplistic - Nash Equilibrium if you dont like M&M and instead prefer a different Nobel Price winner.)

[Scooterdoo]

Unless I am short-stacked or have someone covered by a sizable margin I will almost never call an all-in on a complete draw even with strong odds. I will do it if I also have something, like a medium pair that might/could already be leading. Otherwise I figure any draw (the best case you're 3-1 to hit) is just not worth risking the tournament on. Of course I'll often push all-in on a draw when I think there is a decent chance that the move will get my opponent to fold and even if they call i have many outs.

[eastbay]

How did you arrive at these numbers, Craig?

eastbay

[Bozeman]

Check out:

Three handed allin call (http://forumserver.twoplustwo.com/showflat.php?Cat=&Board=tourn&Number=415745&Forum= All_Forums&Words=test%20intuition&Match=And&Search page=0&Limit=25&Old=6months&Main=415745&Search=tru e#Post415745)

In addition, you might be interested in:

Finish probability (http://forumserver.twoplustwo.com/showflat.php?Cat=&Board=probability&Number=369811& Forum=All_Forums&Words=134&Match=Username&Searchpa ge=6&Limit=25&Old=allposts&Main=369811&Search=true #Post369811)

[Bozeman]

Ok, I will amplify my statement.

Utah said, "Maybe this over-the-top model can provide useful analysis on whether to go all in with high pairs against 1 or 2 players already allin in the early rounds of an SNG Tourney."

I claim this model (9 players allin before you) is irrelevant to the case of whether to call allin with a pair when 1-2 players are already all in.

First, recognize that the situation of all players going allin before you and you having AA will not occur in your lifetime, and if it does, it will not make a difference to your average win rate what you do if it happens.

Second, recognize that the problem as stated is amenable to much more relevant analysis that is not too tough.

Third, recognize that 1 or two players left (after this hand) is not at all like 8 or 9. This second case is still a long way from the bubble.

Many people have done this analysis or arrived at their opinion from experience, but for completeness I will show some analysis:

Suppose for concreteness you have KK, and are facing 2 allins. Lets say the blinds (dead money) are negligible. There are two relevant cases: one or both of your opps. has AA, neither does.

a) you will have a stack of 3S chips in a 7 player game ~17% of the time, and be eliminated the rest of the time.
b) you will have 3S chips ~70% of the time, and be eliminated ~30%.

Suppose all players are equally skilled. By the Malmuth model, which favors small stacks, your big stack is worth 25.5% of the prize pool, while if you fold (barring ties), it is worth 10.2%. So while it is not worth 3x a starting stack, it is worth 83% of that. For this to be a +$EV call, you need to win 40% or more of the time (as opposed to 33.3% for +CEV). So if you are average, you need probability of one of them having AA of p given by p*.17*.255+(1-p)*.7*.255>.102 => p<56.6%. For the average player, we can safely assume that this is a +$EV situation, only if these two opponents always have QQ,KK,AA,AK or better is it -$EV.

Now, for a better than average player, it is a more complicated situation. I am of the opinion, and results I've seen and had support this, that is difficult to be better than twice as good as your opponents in a SnG. If you are twice as good as the rest (who are equal) your original stack is worth .169, if you fold .172, if you win this hand .341 (again from the Malmuth model which punishes the big stack). Now you should call only if you will win more than 50.4% of the time. This is true against a suited ace and a underpair, a suited ace and a suited connector, and almost true against a suited AK and a suited connector. So to evaluate this, it is only necessary to evaluate the probability that you are facing AA. p*.17*.341+(1-p)*.7*.341>.172 => p<36.9%. Alternatively, if your opps. both have Sklansky rankings of 1or 2 hands (tt-aa,aj-aks,kqs,ak), this is better to fold, but if they could have any additional hands, calling is correct.

Note there is some possible error introduced by separating between AA and not AA only, since KK is between ~77-87% to win against hands without aces or kings, can be as good as 94% against weak kings, and averages ~70% against Ax. The model above is approximate, but its qualitative results are good. This play, like all poker, is situation dependent.

Still, the most important factor is figuring the likelihood that you are facing the one hand better than yours. If you have AA, you can never fold here, and only if ALL your opponents are allin can folding AA be correct in a SnG (for the overthetop model, the only important factor is that almost everyone will be eliminated on this hand).

If you can show some relevance of the overthetop model, please enlighten me,
Craig

[DcifrThs]

[ QUOTE ]

Fossilman says that early in a tournament, real dollar EV ($EV) and tournament chip EV (TEV) are basically the same. Early on, then, basic ring game strategy applies. It's not until you're in or near the money that $EV and TEV begin to diverge, and at that point the $EV:TEV ratio decreases as stack size increases. I.e.: the chips you lose are worth more than the chips you win ... a good reason not to chase draws or make loose calls. I'm going to assume he knows what he's talking about, although I can't offer a mathematical proof. (Perhaps he can.)


[/ QUOTE ]

Cris,

What fossilman here means is what the whole point of TPFAP (tournament poker for advanced players) is about. It is why S&M jokingly refer to winning a tournament as a BAD BEAT. in the world series for example, you can win lets say $1m in real money but when you do that you will have over 2 or more million in $T. So what happens during the course of the tournament is that as you collect more and more chips, each additional chip is worth less and less. conversly, as you lose more and more chips, each additional chip lost is worth RELATIVELY more than it would be if you had more chips and were collecting them. Loose calls are clearly wrong (exceptions exist. im sure you can see'em but they have moreto do with situational analysis shorthanded or vs. a particular player). The mathematical proof that fossilman can probably give you revolves around the marginal value of each chip or rather, the value of each chip on the margin--if you can remember your econ classes this'll be nice and easy.


hope this helped
-Barron

[Utah]

As you requested:

You are missing a huge variable: time

Let looks at it very simply - What are the effects of an EV neutral tourney specific play, but that has the effect of shifting your placements in the tourney?

For example, the play makes you win more times but which is offset by the number of times you now miss 3rd place money by busting out early. We will assume that the EV neutral play takes into account any model you want for evaluating stack size, player ability, etc. Real simple math:

Old Model:
You get 1st 25% of time
You get third 25% of time
You finish 4,5 50% of time
1st pays $100, Third Pays 40
Your EV is $35

New Model:
You get 1st 35% of time
You get third 0% of time
You finish 8,9 50% of time
1st pays $100, Third Pays 40
Your EV is $35

For a conservative player like me, this has a MASSIVE effect on my hourly win rate. The best thing I could do for my game is to trade in my 4ths and 5ths for 8ths, and 9ths.

The reason is that there is an additional cost to playing an SNG tournament: That additional cost is the ability to play another SNG tournament

I do not care about my return rate per tourney, I only care about my expected win rate per hour (My average tourney ime is a little over an hour). Therefore, any EV neutral play that reduces my time per tourney is a big plus for my bankroll.

Heck, one could even see significant -EV tourney plays being correct if it shortened the time per period enough.

And thus, the relevance.

btw - I read some of your previous posts and I see that you have read Tom Fergerson. I dont know if you know him but he is a very nice guy and he helped me last year work through a complex game theory matrix as I kept getting stuck in the null value of a matrix (which I dont understand) as my variables and number of equations didnt match up after eliminating dominated rows and columns. He had a cool little program on his site that solved it (whereas the built in Excel matrix solver could not). After he helped me solve it he then told me that he had worked through the problem before with his son and he asked me if I knew who he was. Anyway, my not so interesting story of the day.