Mathematical Expectation in tourneys vs. cash games
 

Dear Forum Members,

I finished reading The Theory of Poker by David Sklansky and have applied his idea of Mathematica Expectations in play, but I find that the "correct" plays based on pot odds and draw odds can't really be adapted to tournament play that effectively because they require a large number of reoccurring episodes to meet the Mathematical Expectation, and tourneys are too short; even if everything happens according to mathematical expectation over the many many tourneys that one plays, the short segments of each tourney is rather random and the ME cannot really be counted upon. Has anyone else found the same problem and have solutions to it??? And will you please share your secrets...

A friend reminded me that in tourneys, survival is most important because you can't win if you bust out; so in all-in situations, ME should be used differently because a 3 to 1 chance of winning means you'll lose 2 time out of 3. But other than all-in situations, how should ME be adjusted for tourney play because of the aforementioned reasons of limited time, limited chips, limited episodes?

Thank you in advance for your comments! [img]/images/graemlins/smile.gif[/img]

Re: Mathematical Expectation in tourneys vs. cash games
 

I don't believe you should be adjusting your ME very much at all unless you're deep in the tournament and surviving a few more hands has a high likelihood of moving you up significantly in the prize money.

In TPFAP, Sklansky does discuss foregoing some +EV plays earlier in a tournament IF you are significantly better than your opponents because you can turn down a slightly EV play knowing your bad opponents will give you much greater EV chances in the near future. The misuse of this advice is one of the most common excuses I hear for playing too weakly in a tournament. Early in a tournament you should be attempting to build a stack so you can be effective later in the tournament when it really counts.

While this may result in your busting out more frequently, it should also result in you having a larger stack late in the tournament more frequently. There are some interesting implications to consider from a $/hr perspective as well. When tournament payouts were more top-heavy, it definitely made sense to play for the win or go home early. With the modern tournament structures starting to smooth out to pay more places and higher percentages to lower places than before it's possible there is more to be said for trying to sneak into the money.

So IMO, if you have a +EV play you should make it and live with the results, foregoing only the really small edges unless you've got some short stacks about to get busted by the blinds. Tournaments are very high variance - that's just the nature of the beast.

Disclaimer #1: I'm assuming we're talking about decent sized tournaments here, not a S&G.
Disclaimer #2: I am a much better cash game player than a tournament player. These are just my thoughts.

Re: Mathematical Expectation in tourneys vs. cash games
 

Thanks Pov, you sound like a lawyer [img]/images/graemlins/laugh.gif[/img] with the disclaimers.

I see where you're coming from; I've also gotten similar replies from others elsewhere and in other forums, but non-the-less, I appreciate your time and advice very much. Please add to it if you come up with more.

Re: Mathematical Expectation in tourneys vs. cash games
 

We're fond of saying that "it's all one long poker game" when talking about expectation and long term vs. short term luck.

But what you seem to be saying is that for a tournament player, it's not all one long poker game and that it's really about the short duration of a single tournament. That each tournament resets the luck continuum somehow.

I guess this is true, if this is your very last tournament ever. Period.

But the same can be said for a ring game player who is playing his very last game ever. Period.

How are discrete ring game poker sessions different than discrete tournament sessions? I just don't see how the zero-sum nature of a tournament is fundamentally different - from a statistical standpoint - than a ring game.

I may be missing the issues you are raising in your post.

Regards,

T

Re: Mathematical Expectation in tourneys vs. cash games
 

SheridanCat makes a good point. People say in a ring game it's different because you can just buy back in. This is of course true, but in a tournament you can essentially do the same thing, it's just you buy into the next tournament. The long run, as incredibly long as it is, is even longer in tournament play. This is probably why we hear so many stories about even the very well known tournament players being broke and getting staked so often.

Re: Mathematical Expectation in tourneys vs. cash games
 

In a ring game each hand you play is indepentant, like one toss of a coin, maybe thousand of independant hands per year.

In a tournament the hands are not independent but are all just part of the tournament. Each tournament is just one toss of a coin. Even if you played one tournament a day that would only be 365 tosses of the coin per year, unlike the thousands of tosses of ring games. (I just made this up off the top of my head as an idea to throw in to the discussion.)

Re: Mathematical Expectation in tourneys vs. cash games
 

Just because its only 1 tourney doesn't make correct play incorrect.

But the fear of being busted out means bluffing opportunities against the over-cautious.

If you can win a pot with no showdown, it doesn't matter what cards you have.

Re: Mathematical Expectation in tourneys vs. cash games
 

[ QUOTE ]
In a ring game each hand you play is indepentant, like one toss of a coin, maybe thousand of independant hands per year.

In a tournament the hands are not independent but are all just part of the tournament. Each tournament is just one toss of a coin. Even if you played one tournament a day that would only be 365 tosses of the coin per year, unlike the thousands of tosses of ring games. (I just made this up off the top of my head as an idea to throw in to the discussion.)

[/ QUOTE ]

Hmm, I don't think so.

The cards have no memory. The cards received and played on one hand do not influence the cards received on another hand. In a tournament, you could say you are carrying over your chip stack and the advantages that gives you - and that will reset at each new tournament. However, the same can be said for, say, a NL ring game session.

Of course, there is image and style that carry over, but those are going to carry over whether you are playing ring or tournament.

Nope, still not convinced of any meaningful different in expectation outside the edge cases that Pov pointed out previously.

Regards,

T

Re: Mathematical Expectation in tourneys vs. cash games
 

While the mathematical expectation of any particular hand may or may not be the same in a tournament v. a cash game (I don't know the math that well, but I suspect the structure of the tournament would affect hand values), the decision about how to play the hand should not be made on mathematical expectation alone.

Even in cash games other factors are always considered, but there are even more things to think about in a tournament: relative stack sizes, reads on opponents, table image, number of players left in the tournament, payout structure of the tournament, blind size, time before next blind increase, whether you are playing to win or be "in the money", etc. (some of these are relevant in cash games too, of course).

Since the goal is to win the tournament (or at least be in the money), your decisions should be directed toward achieving that goal, not maximizing the long term mathematical expectation of the cards you are holding.

Depending upon the circumstances, the correct tournament strategy with a hand like KTo when it is folded to you in middle position when you are on the bubble could be to fold, raise 3-6x the big blind, or go all in. Early in a tournament, the correct stategy would usually be to fold.

Whatever mathematical expectation KTo has on a particular hand is less important than (1) how valuable it would be to steal the blinds, (2) how likely you are to be able to steal them, and (3) what are the best/worst things that could happen on this hand (i.e., could you get knocked out of the tournament or could you knock someone else out?).

Also, remember that in a tournament you can benefit by not playing a hand (e.g., when someone gets eliminated), which is another major difference from cash game play.

I'm not sure if I'm explaining this clearly (and I have to stop typing now), but maximizing your expecation for a tournament is not as simple as tyring to play so that you maximize the expectation of each individual hand in tournament.

Re: Mathematical Expectation in tourneys vs. cash games
 

In a ring game each hand has only one winner -- thats the end of it -- like one coin toss.

In a tournament there is only one winner -- the whole tournament is the game -- like one coin toss is one game. All the hands you played in the tournament all add up to produce your result -- winner or looser.