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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%.
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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
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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;
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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.
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as Sam Farha would say, "in order to live, you've got to be willing to die."
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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.
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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.
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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.