Conjecture and Question

[fro_dude]

I imagine that the 40K equity developed for the start of a tournament has taken into account occurrences of extreme variance, ie. Doubling up or busting out on the first hand. Therefore it is easy to assume that your equity will rise, but as far as it doubling is definitely an overestimate.

[BitterChris]

I am not sure about the first double specifically, but it seems correct since if you carry it out (if you somehow doubled up every hand) your expectation would decrease proportionally, since at the end you would end up with only a fraction of the money even though you had all the chips.

[BigPoppa]

I would say it doesn't come even close to doubling.

While you, of course, need chips to play; the player's positive expectation is not due to the chips. It is due to his skill.

If his expectation were proportional to chips, then losing a quarter of his stack would decrease his expectation by $10,000. This is not the case. Again, his skill is the main difference here.

I would say that to double his expectation would require an increase in chips several-fold.

[Richas]

Suppose you are a great tournament player. Perhaps one of the best. You enter a $10,000 buy-in tournament and when the first hand is dealt, since you're such a great player your expectation is $40,000 even though you only have $10,000 in tournament chips. Now a very unusual first hand takes place and you double up. That is you now have $20,000 in tournament chips. My conjecture is that your expectation does not double even though your chip count has. So instead of having an expectation of $80,000 it may only be $78,000, or $75,000, or some other number less than $80,000, but it will definitely be less than $80,000.


Hi

Being English and new to tournament poker I have found myself thinking about this quite a lot so apologies if this is too long or is somehow a result of my complete poker ignorance. I just do not think the question has been answered properly, so I will have another go. I hope I am not covering ground that everyone has worked through before.

I can promise a small Tiger Woods analogy and Sir Isaac Newton gets a mention too.

The reason that I don’t think the question has been answered properly is that the conjecture mixes up two things – chips and expected value. They are very different things but we tend to use chips as a proxy for expected value in order to protect our sanity.

OK – we know that we start with $40,000 EV and $10,000 chips so clearly they are not the same. We get a transfer of chips to us of $10,000. Cool. We know where it came from – the first guy out of the tournament, the chips make it easy to follow the money – the total number of chips is unchanged and we know where they all are. Now the total expected value of all current competitors added together has also stayed the same (it equals the prize pool) but we don’t know where it all is now. We could try recalculating our EV but I think it is probably better if we look at it another way and try recalculate the expected value of all he other players and see what is left for us.

The poor sap who is currently wondering how to get to the car park without anyone noticing has generously donated to the remaining players all of his expected value. We have two possible extremes here. We could have just knocked out another great player with an EV of $40,000 or we could have knocked out some eccentric, rich (I wish) English bloke who has only ever played two online free rolls with an EV of approximately $0.01.

As the chips are not the EV – just a proxy for it – we know that the EV has not all just switched over to us – we do know though that the total EV remains unaltered overall.

Let’s start with the unluckiest pro ever. We have just knocked out one of the people we expected to take prize money – how cool is that? Our EV has gone up quite a bit - but so has everybody else’s EV. This guy, by the form book, was destined to be the nemesis for a lot of players and as he was at our table we were a prime candidate. Taking him out has helped everyone else at our table as well as us. Imagine it two of the best at your table – nightmare.

Ok we know that our EV has gone up but not by all of this guy’s $40,000 - the others in the whole tournie and the others at this table got some of the extra EV vested in him as a great player (as an aside maybe they are just getting back some of their EV that they lost the moment two superstars were seated with them).

Now let’s look at the English guys $0.01 of EV – where did that go? Well nobody much cares really but we do care where his chips went. They are with us. Lovely. I don’t think our EV has only gone up a cent, I think it is quite a bit more. We are now the table chip leader, we have in our stack the price of one bad beat. Fantastic. We can think about bossing the table and some of the EV from the other players near me has just come to me, more than this some of the EV from the guy who will join our table soon has come to me, and the guy we will be playing in an hour. Everyone really.

We can see how the proxy of chips measures the affect on everyone’s EV if we look at average stack size. Before the English guy left for the airport the average stack was $10,000 now everyone else has $10,000 and we have $20,000 – everyone else has a below average stack. This is a proxy measure of everyone else’s EV going down a bit. As the EV taken from the English guy was so insignificant this transfer of EV from everyone else is the more important bit here.

Ok to sum up – the total of chips and the total EV for all players remains the same. Some chips have moved in a very simple way but the EV calculation is much more subtle and complex and it has affected everyone in the tournie not just us and the guy with the red face.

Here is the Newton/Einstein bit. Instead of golf balls think about gravity.

The greater the mass the greater the gravitational force being applied to all other objects in the universe. In our case we have a closed universe of all the participants and their chips. When we got the extra $10,000 in chips our gravitational pull increased quite a bit having an effect on all other players and their chips – including a much greater affect on those closest to us.

When our closed universe was created we came to it with a greater gravitational pull than most because of our skill (density?), now we have more mass, more force. By beating an expert player we relieved some of the forces pulling on everyone else (and us) by beating Englishman the significant affect is just our greater pull on everyone else as we have a greater mass of chips.

There is also the whole Einstein time thing to ponder upon now that we have bent the space time continuum a bit (maybe another sleepless night) but for now what does this make me conclude about the conundrum……………. Well it might be right and it might not!

In general I think it is right that it will be less than $40,000 EV that I get from the $10,000 in chips. Certainly if the EV of the tearful one is only $0.01 I cannot possibly have gained $40,000 of EV. If however the one I knocked out was the absolute nuts the Tiger Woods circa 2000/2001 of poker then pheww how much EV did that guy have? Maybe I gained a bit more than $40,000 even when everybody else has had a bit of his EV too.

Ok I think that is about it except to say that I think the rules are a bit different for poor players. Let’s assume that the English guy won the first hand! Now he started out with $0.01 EV and by taking out the man with $40,000 he must have more than doubled his EV – he probably added more than $0.01 to everyone else’s EV too!

Anyway this may not have helped you but here in the UK it is nearly 2am and I need to stop thinking about this so goodnight.


PS Wotmog theory is, as of today, a google whack.

[Jdanz]

How did Richas not get more response?

just looking at other players EV rather than your own was a great inuitive leap.

The rest of the post is just gravy. I mean clearly he's wrong about how much it matters to you about which guy you knocked out, but it's pretty clear proof that there are distinctly non-linear relationships between chips/EV/skill.

[0evg0]

WTF

[Jdanz]

Why the bump? i know everyone has seen it, but i think we have a lot more to talk about.

[Piers]

I think you conjecture is intuitively obvious, and almost certainly correct for reasons that others have no doubt stated.

However I think the key point is quantifying the effect. For instance is the effect so small that you should not change your strategy on account of it?

Computer simulation is a good way of getting a feel for things. I did some tests a while back although I assumed equal skill, maybe I will go back and rework them.

The other important question is what is our great player going to do if he gets knocked out of the tournament? Is there a great $500/$1000 NLH game to get back to? Are there several $10000 buy in comp starting online in the next few hours. In other words what exactly is your objective.

I think the question is dangerous, in the sense that a casual reader might get the impression your conjecture applies to them in the tournaments they typically enter. I think the TCEV<>$EV is the most abused concept in tournament poker.

[Jax_Grinder]

I think you have supplied insufficient information to formulate a response to your hypothesis. How many seats (in addition to this one) does our hero have in the tourney? 3? 4?

[Richas]

<i>I think you have supplied insufficient information to formulate a response to your hypothesis. How many seats (in addition to this one) does our hero have in the tourney? 3? 4? <i>

It was not my hypothesis - I blame some Malmuth guy whose book of poker essays I am ploughing through for some light relief from Harrington doing my head in with hand scenarios.

My assumption is that it is a closed tournament - 1 seat per participant, no rebuys nadir.