some more hints:

Work the problem backwards and from the beginning forwards.

Work with the assumption that you know all 18+2 (x) hole cards at a full table all the time--decide how much lower than 18 you'd need to still win (the whole tournament) 100% of the time. From there, start getting creative and think it through, what does the function look like as x decreases?

One problem I had to overcome is how to deal with a succession of tables where you are stuck with people who raise preflop on every hand, and other assorted maniacs.
This is why my initial lower boundary was 99.997% or so...

Problems arise if you have much fewer than 5000 entries, or if the blind structure wasn't in wsop format.

Doyle Brunson strikes me as the person most likely to agree with my answer (Todd and Matusow too). I think Ivey would too but with less certainty. Though I've only spoken to Negreanu for about 1-2 hours I don't have a clue what he'd think... (to his credit!)

I think the 10-20 best poker thinkers would have to think it through for about 10-60 minutes to get from asserting a 99.997% to 99.999999999% chance of winning.

I had to think about 20 minutes to convince myself that 100% was more reasonable than one in a sexillion or smaller chance of failure.

There's a bag of tricks, some entirely respect the spirit and intention of the question, others are borderline, that solve for that highly unlikely situation where you face, for instance, a psychotic, heads up/two remaining, who gets AA twenty times in a row and goes all in preflop every time, even in the SB (you have to assume that you start with a stack 20-40 times bigger than his, which is very reasonable--yes, this alludes to another part of solving the puzzle).

Yes, it's only fair that the above is within the realm of 'the real world' ...

Your chances of facing an average lucky player heads up are higher than facing a pro after normalizing the data.

Worst case, I'm wrong and there's an infinitesmal chance you couldn't win all the time (something like ten to the minus 23rd to 40th power, I'm guessing).

***

It would somewhat difficult to convince me that you could perform at 100% probability in the subsequent year's WSOP (ME) after winning.

To achieve it 3-5 years in a row ... probably they'll catch on to your bag of tricks. Probabilities decline non-linearly.

I can't tell you the bag of tricks, it wouldn't work any longer if I did... Sometimes wanting is better than having, and here, pondering is better than knowing.

Excluding the above bag of tricks (for simplification), it would be unsurprising to state that optimal play in this situation cannot be explicated by me--similar to but vastly simpler than optimal normal poker play.

It's intractable but solvable.

Sometimes we're better off not having DS tell us the answers, this is an example of a great question to occupy us in the event we become a castaway or end up in prison.

I've excluded a major basic hint that would make many of the previous posters realize that they missed something fundamental, because I think you'd enjoy figuring it out for yourself.

I'm here to make this more enjoyable for you, I hope this helps.

"Chances of winning are one in 2000."

I overlooked this sentence while triple checking my answers.

My answer is that you still have over a 98% chance of winning, higher if you have the time before the tournament to think matters through.

As for the variation where we do not know ahead of time that future hand(s) provides extra info--it's some number that I'm uninterested in calculating and I'm probably not competent to provide.

Okay, now I get it.

The answer to the second question is that your chances of winning are marginally or even negligbly increased.

The lesson is to illustrate the value of persistent sources of information, mostly from those within range of BSB play.

The best example was chosen, you are BB exploiting the SB who acts before you (things change at the final table).

You have four players to focus on, if you can pick up info/tells on other players, that's just gravy.

I wish to copyright the oxymoronic terms:

coefficient of omniscience (from knowing 4 of 25 cards)

or

partial omniscience...

and

thread ending answer, or T.E.A. [QED]

ha ha...

I disagree. If you get a "McManus" on your right and no one gets high carded away and the table doesn't break, you're going to have to play good old-fashioned poker with only the small edge of knowing 2 cards that won't come. It's very possible that you will bust out on day 1 even with that edge.

I don't know what the odds of getting a "McManus" in the hot seat are, but they're definitely non-zero.

Do I see his cards just once, or can I go back and check for suits in the middle of a hand?

...
You should seek professional assistance. Possibly a neurologist to see if there's something wrong with your short-term memory capabilities.

It was a [censored] joke...

Knowing it will happen everytime. Somewhere between 20% and 80%. Remember that you never worry about the obviousness of your plays. And that this is a seven day tournament. You should very quickly be the biggest stack at your table and should have no trouble grinding up at a faster rate than the blinds, which go up very slowly. There would be almost no situation where you would go all in before the river.

My answer to the other question is about 2%. Off the top of my head.

Sorry, but I disagree...mainly about NOT going all in before the river. What odds are appropriate for going all in? In my mind, if you're significantly +EV you should take the "gamble", especially 3:1 or higher odds (pot odds permitting, of course). It's silly to avoid going all in as a favorite against the victim, since you can easily gain lost chips back at a later time by continuing to play the better odds (giving your additional information). As long as you are the bigger stack and there is no fear of being put out, you should be willing to "gamble" (at better than proper odds...simply "adequate" odds aren't good enough since you could wait until an even better opportunity) since getting an even bigger stack allows you to gamble more...and more...and more...and keep building up your stack.

Seems simple really.

When he says all-in, I'm pretty sure he means you are all-in and covered by another player. If no other players have you covered, you can't really be all-in.

You're not going to get very far with this type of argument. Besides being condescending, it also fails because there are a number of people here who are very smart and not convinced by your purported brilliance. I am sure someone in this thread besides you got double 800s on the GRE, and I am sure there are many others who have very high IQs.

It helps if you're smart, but it's more important to know what you're talking about.

" You obviously don't know much about math. Donk goes all in to your right with 23o. You hold AA. You obviously (wrong) call. You have only a 86.2% chance to win. You can't always wait until you have the absolute nuts to put your money in, this would most likely (wrong) result in your whole stack being eaten away."

I was directing the comment purely in answer to the insult by soontobepro and I had no other reason to mention those facts. It should be obvious that such comments are bound to get people upset, so I wrote like a vulcan (no condescending content, if you look carefully). Sorry to divide by zero for offending you.

24 hours after my previous post were spent reviewing the poker literature in light of my discoveries, and the subsequent 24 hours brought me discoveries that are not mentioned in poker literature, but I would imagine Bill and Jerrod could write about it in the future. The magnitude of these two periods resulted in 100 and 10000 fold increases in my comprehension, I say this only to suggest that there's a treasure in this ingenious yet simple puzzle.

The hands and thus the EVs should be viewed as a continuum, their functions should involve future and past hands, of course to a lesser degree.

One way to think of the problem after you find f(h)=100% where h is the number of exposed hands (more useful than for values less than 100%) is how drastically your play changes, (imagine that someone will shoot you in the head if you bust out, so how do you play? As I had mentioned earlier, the puzzle yields so much more to you at 100% than at 95% or less) it's counterintuitive for a few reasons:

though we know what characteristics exponential functions have, we are not familiar with the hand dimension (which DS takes us into) thus a visualization might help (it did with me);

there are two characteristics that expand our thinking, persistence and amnesia; in synthesizing how we must change our play, we should keep those ideas in mind; e.g., think of Gold for a recent persistence example, and Juanda for a good amnesia example (poker journalism has not uncovered what his edge consists of outside of Negreanu's comment about his fantastic preflop play);

It so happens that the scenario 1 (again, choose the value of h that gives YOU 100%) edge is far greater than any edge a current pro has today, examine why this is the case and you will make more discoveries. Yes, the edge is ridiculous at the final table, but that is due to our observational limitations.

The reason I had problems remembering that I should have a 2000:1 chance to win is due to the iterative aspects of the puzzle. Once you realize how the edge compares to real life edges, you learn too much to be able to play that badly.

Are the few days up yet?

yes, i would say 15% better. Given there are 10 players at the table. You get the 10% edge plus you can gather even more chips and add some more edge when you have a larger chip stack. The player will go out early probably though due to this and 10,000 chips isnt all that much to increase your EV significantly in the main event.

There's just no way 20-80% is the right answer for the first scenario.

Have the brilliant lurkers figured it out yet?

Mr. Ivey? Are you there?

P.S. Have any of the previous posters on this thread scored two 800s on the older GRE analytical and quantitative sections and if so, can you do it with time to spare? if so, how much?

I would lay 20000:1 that there weren't any in this thread. I don't want to start a flame war, I just want to ascertain the 'truthiness*' of a previous statement.

*really just veracity, yay, colbertnation.com

If you know that you are going to continue to see cards I would guess your chances aree > 90%. If you dont know you will be able to keep seeing your opponents cards (which you think you would figure out after hand 200), then your chances of winning are 62.456%.

I like this thread a lot.




Lets make an assumption.

1. We do have enough (infinite) time. (a big enough (infinite) stack).


This implies the following => We get dealt enough (infenetly many) hands. Because we have enough time and play enough hands we will be playing heads up against the guy on our right enough times. Against him we will put our money in when we are 100% certain to win the hand, otherwise we can fold, because our stack is big enough.

Apparently we are going to win the tournament every single time, it will just take forever.

In the real world, of course, we do have a limited stack. We cannot wait forever. Various things might go wrong:

"Never" means as much as we dont have enough time (blinds eating our stack) to wait long eough.

1. The guy to our right never plays a hand.
2. We never get headsup with him.
3. whenever we get headsup with him we are never 100% ahead.

Because of that we will have to adjust towards these circumstances to still play optimal. That would mean:

1. Playing hands with others as well.
2. Bluffing our opponent although we are not ahead.

Basicly we should also make plays which dont guarantee us to win the pot 100% of te time but also some plays where we get our money is as a slighter overdog.

How big of an overdog we need to be to take a gamble depends on how much time we have. If we have infinite time we should only take 100% shots. With a crap-shoot structure we might need to take 60% shots. At the WSOP I think we have a lot of time, so I think our winnign chances are very close to 100%. Maybe 99.99%. One in 10 thousand times we would be extremly unlucky. (well our opponent might still not be playing so the chances to win are less like 99.9%)

Solved.

First of all, if you read the end of the puzzle it says that you are not aware that you will continuously see your opponents cards... THIS MAKES ALL THE DIFFERENCE IN THE WORLD. If you did know that you were going to see the cards every hand, you would still be way under 100% to win the entire tournament...

If you did not know that you were going to keep seeing your opponents cards you would have to pretty much play like you normally would with an extreme advantage in the hand if the player to your right calls... There can still be other players in the pot though and you wouldnt know to wait until you had isolated the player to your right... Therefore you would still be in danger from the 3rd party and still in slight danger from the player to your right (because of outdraws)...

Hell, you wouldnt be 99.9% to win the tournament if you could see EVERYONEs cards at the table. ANd that is SAD but TRUE.

This being poker, the edge is always approaching, but never reaching 100% with length of tournament. If you could see EVERYONE's cards all the time, adn you play perfect poker, your edge is still not 100%.

eg/

you are AA in SB, villain has 34o in BB. It is folded to you and you decide to risk one small bet (limp in) in hopes of possibly winning more chips if your opponent decides to bluff or spikes Bottom Pair.

Now the flop is 4 5 T rainbow, and you bet, just enough so that he doesnt get his odds to call. However, small enough that he will call thinking about his implied odds(which he does not really have since you will know when he hits or not).

But, BB is agressive with his draws and decides to put his tournament on the line and pushed all in on his draw. My arguement is you should FOLD here to increase your EV. Yes odds cleary state you should call this hand mathematically. But knowing your odds while seeing the cards of others has a GREATER EV than the EV you get from making this call. therefore this call is not one worth making(unless your raise left you with a very very small amount of chips (maybe < 8 BB left).

WTF? seemorenuts, have you ever played poker? do you understand how the game works? how anyone that is presumably smart could think it was ever possible to have a 100% edge (or even an 80% edge) without the ability to control all cards dealt on the board is beyond me.

Depends on player to right's style.

Locksmith - plays AA & KK (wins last longer bets often)

There's value first few laps of button, but after that...

Maniac - plays any 2, in unopened pots

lots of value, you'll know exactly when to call, when to fold, and when to wield the Hammer!

So how to average out those differences? It's bit like the value estimation of "raising for value" in NLHET&P.

David,

sorry about hijacking the thread, but this reminded me of a question which may have some similarities to this:

I'm curious about what edge you figure you have over the field of the WSOP Main Event?

Would it perhaps be sensible to express this in the form of what odds you would take a bet on whether or not you could make it into the money? I.e. what are the odds that you could beat the 90% or whatever it is that ends up outside of the money, if you were playing for solely the purpose of making the money?

If so, what odds would you set for a bet on this for a relatively insignificant sum of money? (Say, for 1% of bankroll or net worth.)

What if the bet was for 25% of your bankroll on your side -- what odds would you need to accept that bet? (If at all?)

Hi Latefordinner,

lol, yes, I have played poker for a little while.

My first MTT was just after reading HOH 1&2 and I came 4th/77 for a four figure cash.

My first three MTTs in the US got me another two four figure cashes, something like coming 4th/158 and 2nd/179 for $100 and $200 entry fees.

I mostly play MTTs bankrolled by friends who know how smart I am (viz. all of the above listed ones). Hey, do you want to bankroll me? Anyone? lol...

As for this puzzle, here's the approximate timing of how I solved it for scenario 1:

200-300 milliseconds: Prob. => 50-80% to win tournament
1 second: at least 90% " " "
3 seconds: at least 95% " " "
8 seconds: at least 99.9995%" " "
20 seconds, while typing post: 100% chance of winning tourn

20 minutes: rechecking whether 100% made more sense than 99.99999999999999%. 100% was my conclusion.

The subsequent 24-48 hours taught me the most about poker, I just stared at the ceiling thinking about the answer's ramifications. I was very, very happy.

So yeah, it's kind of fun when people think I'm nuts.

Try this at the WSOP, ask Bill Chen and Jerrod, Ivey, the Brusons, Ferguson, Juanda, Lederer, Negreanu, Forrest, Bloch, Cunningham, Miller if he's there..., Reese and Harman what they think the chances are of winning in scenario #1.

Get back to me on that... lol.

Read my posts more carefully and follow my instructions, then you might get it... honest. Have fun.

This is a tough question... I think if you play smart enough (steal his blinds in blind wars ect... dont force yourself all in before the river) I think your chance of winning the tournament is around 5%...