Originally Posted by crow27
be more of a gut feeling


Gotcha! See, that's the thing with all of these questions. I have no "gut feeling" because I rarely play tournaments (and when I do play tournaments, they tend to be games other than NLHE). All of these questions have a mathematical answer.
And secondly, SnG's *are* tournaments. They're just smaller, and easier to model mathematically. However, the concepts in both are the same (chips have diminishing utility, ect.).
So here are the answers, and hopefully a decent explanation. Kinda surprised this thread got this many responses.
Question #1:
The correct answer is A, B, and D. Its just a matter of pot odds. When there are only two players left in the tournament, chip have exactly their value. Therefore, no ICM modeling is needed to calculate the value of your chips, and you can use simple pot odds to make your decision. Therefore, since we know villain's shoving range, we can calculate which hands we can call with using pokerstove:
Villain's Shoving Range:{ 22+, A2s+, KQs, A2o+, KQo }
46.2% { 33 } which is greater than 45%, its a call.
59.1% { 88 } pocket 8's are a fist pump call with 59% equity.
35.8% { 76o } not surprisingly, the low rags are a fold.
47.9% { A9o } and A9o is also an obvious call.
Question #2:
The answer to question #2 is B, we want villain to fold. Here's why:
Preflop, there are 300 chips in the pot, that if villain folds, we get risk free. And if villain calls, then we have a ~60% chance of winning 900 chips. However, in tournament situations, especially near the bubble, chips have what's called diminishing utility. The second 1000 chips you have isn't worth as much as the first 1000, and the third 1000 is worth even less. Even if you have 99.9999% of the chips in a tournament, you can still only win 50% of the tournament prize pool (or whatever first place pays).
ICM takes this into account, and using an
ICM calculator, we can model our tournament equity given our chip count & our opponent's chip counts:
If villain folds, we will have 1100 chips, and our equity will be 10.8%.
If villain calls, we have a 68% chance of having 1700 chips, and 15.3% equity.
The other 32% of the time, we will have 0% equity, because we're out.
So we just do the math to see which value is greater:
0.68*0.153 = 0.104 or 10.4%, which is less than 10.8%. So therefore, on average, villain folding will show a greater profit than him calling.
Question #3:
Rebuy tournaments are really interesting in that during the rebuy period it often becomes correct to put money in as a slight underdog. When you lose all your chips in a normal tournament, you cannot win them back. However, in a rebuy, those chips stay on the table, and you often get a chance to win them back over the next hour or two of play.
Also, having more chips at your table makes it more likely for you to have more chips than other players in the tournament. Consider the following two table tournament. At table 1, no one rebuys. At table two, each person makes 3 buy ins total. At the end of the rebuy period, the two tables have the following total chip counts:
Table 1  13500
Table 2  40500
Obviously, players at table 2 have an advantage, and once the tables are combined, the players at the final table from table 2 will likely be bigger stacked.
Therefore, it becomes correct during the rebuy period to put your money in as a slight underdog, especially if you feel the player you are against is very poor, because a slight underdog is offset by the ability to win those chips back & to get more chips at your table.
Therefore, we should call with hands A, C, and D. However, getting money in as a 2:1 dog with 27o is almost never correct, and is certainly incorrect in the rebuy period. Hand D (QTo) is only a ~43% underdog to A9. The others are actual favorites.
Question #4:
The answer to this question is B, 63%. If we had no cards at all, and villain folded 74% of the time, we would show a profit. However, its surprising how little the 38.6% equity QJs has matters to this analysis. But once again, the diminishing utility of tournament chips near the bubble of a tournament almost always makes avoiding showdown the correct play.
This is yet another math problem using the ICM calculator.
If we fold, our tournament equity is 19.3%. So the average equity yielded by shoving must be greater than 19.3%.
If we shove, and villain folds, we have 23.7% equity.
If we shove, and villain calls, on average, we will have 12.5% equity (38.6% of the time we will have 32.4% equity, the rest we will be out).
Therefore we can create the following equation, and solve for F, which is fold percentage:
0.193 = F*0.237 + (1F)*0.125
F = ~60.7%
(Apparently I did the math wrong the first time, when I got 63%. But still pretty close.)
Either way, the important thing to note here is how important fold equity is around the bubble of a SnG. Blind stealing & accumulating chips without seeing showdowns is superbly important. And the trick is, many good SnG & tournament players know this, and so they will fold far more than the range I listed above. However, if villain does call with the AT+, KJ+, 66+ range, then getting 61% folds is very unlikely to happen.
Conversely, in a cash game, we would calculate this with actual pot odds:
2300 = F*3100 + (1F)*(5100*0.386), and F = 29%. Crazy how much things change in a tournament!
Hope its been helpful.