M, Q, D

[dfwdevil]

What I'm concerned with in a tourney, when it comes to an all-in decision that will potentially send me to the rail, is this: is it worth taking a 60% the best of it here for my whole stack? If I go all-in as a 60-40 favorite four times, and someone has me covered each time, my chances of going to the rail are a whopping 87%. If I go all-in as an 80-20 favorite five times, then 68% of the time, I'm gone. Bye bye.

Obviously you can't win tourneys by avoiding good situations, but the question I'm posing is whether you can avoid some of them. Consider that the punishment for going all-in and losing before the money is always the same. Doom. Tournament death, unless you're in a rebuy. So the "risk" portion of the equation never changes, but the "reward" does. A successful all-in in the opening stages of a tourney will net you a few thousand chips at most; whereas a successful all-in in the later stages can position you for the final table; and a successful all-in at the final table can mean a lot of money indeed.

That is to say, those later all-ins are substantively better bets. You stand more to gain, for the same amount of risk. Put another way, if you're going to risk your tourney life, prefer to do it for big pots, preferably the kind of pots that can make or break you. It's better to burn out than to fade away, or, as Sam Farha would say, "in order to live, you've got to be willing to die."

Anyway, D is a way of expressing this. It's nothing new. Just the ratio of a) the average final-table stack to b) the size of your expected net from the current pot. If the average stack at the FT is going to be 1,000,000 chips, and you find yourself playing a pot which if you win will net you 20,000 chips, your D is 1,000,000 / 20,000 = 50. A relatively high D which would seem to indicate, don't risk it here, unless your M is low.

Which brings me to my question. Assuming you have a high M (ie, are large stacked relative to the blinds), how important is the hypothetical D? Do you submit to the skewing of chip values enforced by the tourney structure, such that you are frequently folding 60-40s even when you can see your opponent's cards, or do you play straight EV poker and not consider the value of the chips vis a vis what you will realistically need to do well, given the top-heavy tournament structures common nowadays?

Thanks

[jay_shark]

If a tournament had 32 participants , then the probability you place in first may be slightly better than 1/32 . If your ROI is 100% then the probability you place 1st may be around 2/32 or 1/16 .

So you need to double up 5 times to win the tournament .
x^5=1/16 and so x ~57.5% . So there is some evidence to support calling 60/40 gambles even if you're an exceptional player .

[Dromar]

[ QUOTE ]
If a tournament had 32 participants , then the probability you place in first may be slightly better than 1/32 . If your ROI is 100% then the probability you place 1st may be around 2/32 or 1/16 .

So you need to double up 5 times to win the tournament .
x^5=1/16 and so x ~57.5% . So there is some evidence to support calling 60/40 gambles even if you're an exceptional player .

[/ QUOTE ]

Extremely well put.

[geo8o2]

depends on the buy-in level 2 i would think. i'd gladly take a 60/40 for sure at a high buy-in early in the tourney. i probably won't get much better than that.

[Woolygimp]

You're an idiot for playing tournaments in the first place, because it's very unlikely that anybody can beat them, especially those that are live even if they are exceptional due to 30-40% of the prize pool being effectively raked due to state/federal tax, and 10% rake.

[drzen]

[ QUOTE ]
What I'm concerned with in a tourney, when it comes to an all-in decision that will potentially send me to the rail, is this: is it worth taking a 60% the best of it here for my whole stack?

[/ QUOTE ]

Yes. Glad I could help with that.

[pzhon]

[ QUOTE ]
You're an idiot for playing tournaments in the first place, because it's very unlikely that anybody can beat them, especially those that are live even if they are exceptional due to 30-40% of the prize pool being effectively raked due to state/federal tax, and 10% rake.

[/ QUOTE ]
In this past thread, you stated "Cash games have always been the sole point of focus for me" and you asked whether it made sense to play tournaments despite the rake and taxes. The majority of responses said yes, and many of us explained why, e.g., Gonso said, "A lot of people are getting rediculous ROI's that far outweigh these costs, which are overstated as is." Now, you call us idiots. That doesn't make sense, and it doesn't help the OP here.

[Woolygimp]

I've played thousands of multi-table SNG's and my share of tournaments before going to nothing but cash games, and there is absolutely no way that someone has a 100% ROI. It's just not possible.

Theoretically, if someone had a 100% ROI it's not from getting it all in as a 60/40, or even as an 80/20.

[pzhon]

[ QUOTE ]
What I'm concerned with in a tourney, when it comes to an all-in decision that will potentially send me to the rail, is this: is it worth taking a 60% the best of it here for my whole stack? If I go all-in as a 60-40 favorite four times, and someone has me covered each time, my chances of going to the rail are a whopping 87%.

[/ QUOTE ]
So, what? If you fold those opportunities, what do you think your chances are of winning the tournament? If you have less than 1/16 of the chips, you didn't start with a high chance of winning. The par chance of doubling up 4 times is about 6%, so surviving 13% should sound great to you.

There is no reward for surviving the hand. Instead of measuring the probability of busting out by the hand number, it is better to measure the probability of busting out by the chip count. What is your probability of doubling up if you take the risk, or don't?

As has been discussed in previous threads, that's not the end of the story. Someone who expects to double up 55% of the time eventually should not be indifferent to taking a 55-45 gamble for all of his chips now, since he gets extra time to apply his skill advantage. He might be better off taking a 53-47 gamble now, even if he could double up 55% of the time by waiting.

"...if you knowingly pass up a 60:40 opportunity, you're not a top player." -- Greg Raymer

[ QUOTE ]
Consider that the punishment for going all-in and losing before the money is always the same. Doom. Tournament death, unless you're in a rebuy. So the "risk" portion of the equation never changes, but the "reward" does. A successful all-in in the opening stages of a tourney will net you a few thousand chips at most;

[/ QUOTE ]
That is a very bad way to look at it. To analyze X versus a risk (Y or Z), you are completely ignoring the value of X (the option of folding). The correct risk versus reward is to say that the risk is X-Y, and the reward is Z-X.

When you have chips which represent an expected value of $100, twice as many chips might represent an expected value of $190. In this case, you risk $100 to gain $90, so it is clearly worth it as a 3:2 favorite. Getting $190 60% of the time is worth an average of $114.

[ QUOTE ]
as Sam Farha would say, "in order to live, you've got to be willing to die."

[/ QUOTE ]
That quote is normally attributed to Amir Vahedi. I think Farha tends to say things like, "You have to gamble to win," which is different.

[ QUOTE ]
Anyway, D is a way of expressing this. It's nothing new. Just the ratio of a) the average final-table stack to b) the size of your expected net from the current pot. If the average stack at the FT is going to be 1,000,000 chips, and you find yourself playing a pot which if you win will net you 20,000 chips, your D is 1,000,000 / 20,000 = 50. A relatively high D which would seem to indicate, don't risk it here, unless your M is low.

[/ QUOTE ]
No, if anything, a high D indicates the opposite, as it means you will probably need to double up repeatedly to cash. That you are unable to coast to a share of the prize money means that you have to risk busting out, and a 60-40 opportunity (even if the dead money is negligible, which is rare) is much better than normal.

The size of your stack affects your expected winnings. You are making the common mistake of underemphasizing accumulating chips.

[pzhon]

[ QUOTE ]
I've played thousands of multi-table SNG's and my share of tournaments before going to nothing but cash games, and there is absolutely no way that someone has a 100% ROI. It's just not possible.


[/ QUOTE ]
In smaller tournaments, such as most multitable SNGs, it isn't possible. In larger tournaments, such as the WSOP main event you asked about, it is not just possible, but much higher values are possible. See the MTT FAQ, which says that a skilled player should be able to cash 20%, 100% over par, in a slow tournament with deep stacks. ROI is generally higher than that premium because skilled players do better once in the money. However, it takes thousands of tournaments to get a good estimate of the ROI when they are large, since you need to play enough tournaments to win several times.

I'm not sure how you became so convinced of the opposite of the consensus on the previous thread. Is there any reason to trust your feelings over the MTT FAQ and the consensus of those who have actually played a lot of real MTTs, not just SNGs?

[ QUOTE ]

Theoretically, if someone had a 100% ROI it's not from getting it all in as a 60/40, or even as an 80/20.

[/ QUOTE ]
What, if anything, was that supposed to mean? As a mathematician, I assure you that it is quite possible to have a ROI of 100% or more in model tournaments where you repeatedly put your life on the line as a 60:40 favorite. Your statement just looks false.

If you mean that it is more common to have advantages in smaller pots, so what? If you have a skill advantage, you should be more willing to take a fast gamble than a slow one. A fast gamble gives you more time to accumulate chips.