Awhile ago I wanted to roughly estimate what hand range I had a 50% chance of seeing over X hands. I believe that is as TIGHT and as patient as you could possibly be in a tournament... The exception is if you have a crazy ability to read or see opponents hole cards AND/OR know exactly what they will do facing an all in. If so you might be more patient and when they don't have a hand they can call an all in with, just move in. In reality though I doubt that is true for anyone. You may try being slightly more patient simply because there may be equity in folding your way up the money AND you might get a "walk" OR a free flop in the big blind and that may be enough to keep you alive just a few hands more, but don't get too carried away.
Edit: There are other reasons you can be more patient that I didn't consider. However, you probably shouldn't be too much tighter.
1)As the blinds go up there is a greater reward for waiting
2)As you get more short stacked you are more likely to get called by MULTIPLE callers which greatly enhances your equity if you have a premiumhand like AA or KK.
3)As you get shorter you also increase chances of there being additional dead money in the pot from multiplayers all in. So if player A flops a flush draw and player B flops top pair and bets all in, than you may beat top pair but lose to a flush, but because there is additional betting you always have the chance that someone scares away a hand.
4)By being more patient you may not actually get a chance to really maintain chips with a double up but you will last significantly longer by being more patient and fold your way up the money a little bit.
5)The assumption was that if you can wait half of the hands you have left, you will win about double your stack and a little extra which will allow you to continue to wait without blinding down enough to fall behind. You have to be able to do something to get ahead and build your stack. However, because of the blinds increasing, the half way point will be OVER half what you started with. So if you have 40 hands left and you on average wait until a top 1/20 hand you actually will have significantly more than half on average BECAUSE of the nature of the increasing blinds.
6)Based upon knowledge of opponents, there may be more profitable situations that come up than just a raw hands calculation. If a maniac goes all in with the top 50% of hands from middle position every time on your blinds, you only really need a top 20% hand to call to be profitable. So you may need to adapt to situation. However, if you understand this as a baseline you can still adapt.
end of edit.
So here is the table. There may be some alternate pushing ranges based upon similar hand percentages that may be more optimal depending upon opponent's likely calling ranges that perhaps includes more ace rag hands and fewer suited connectors or something... Then there may be better "calling off" hands that are less likely to be dominated. I am not sure of the exact specifics but this gives a good guideline for how patient you can be. Anything more patient than this is probably too tight as you are an underdog to pick up a hand and even if you do you may not have enough chips anyways.
The odds of seeing a particular hand is equal to 1-the odds you will see a hand^number of hands you will see.
hands left 50% chance of being best YOU will see.
1 This is the only hand, thus ANY two cards.
2 22+, A2s+, A7+, K2s+, Q3s+, J4s+, K7+, T6s+, 96s+, 86s+, 74s+, 63s+, 53s+, Q8+, J8+, T6+, 97+, 85+, 75+
3 44+, A8+, K9+, QT+, JT+, T9, A2s+, K4s+, Q7s+, J8s+, T7s+, 97s+, 86s+, 76s, 65s
4 55+, AT+, KT+, QJ, A2s+, K7s+, QTs, JTs, Q9s, J9s, T8s+, 98s
5 66+, AT+, A4s+ (minus A6s), K9s+, Q9s+, KJ+, JTs, T9s, QJ
6 77+, AT+, A8s+, K9s+, QTs+, KJ+, JTs
7 77+, AJ+, A8s+, KTs+, QTs+, KQ, JTs
8 88+, AJ+, A9s+, KTs+, QJs+, KQ
9 88+, AJ+, ATs+, KTs+, QJs+
10 88+, AQ+, ATs+, KTs+, QJs+
11 88+, AQ+, ATs+, KJs+,
12 99+, AQ+, ATs+, KQs,
13 99+, AQ+, ATs+, KQs,
14 99+, AK, ATs+, KQs,
15 99+, AK, AJs+, KQs,
16 TT+, AK, AJs+, KQs,
17 AK, TT+, AJs+
18 AK, TT+, AJs+
19 TT+, Aqs+, AK
20 TT+, Aqs+
21 TT+, Aqs+
22 TT+, Aqs+
23 TT+, Aqs+
24 TT+, Aqs+
25 TT+, Aqs+
26 JJ+, Aqs+
27 JJ+, Aqs+
28 JJ+, Aqs+
29 JJ+, Aqs+
30 JJ+, Aks
31 JJ+, Aks
32 JJ+, Aks
33 JJ+, Aks
34 JJ+, Aks
35 JJ+
36 JJ+
37 JJ+
38 JJ+
39 JJ+
40 JJ+
41 JJ+
42 JJ+
43 JJ+
44 JJ+
45 JJ+
46 JJ+
47 JJ+
48 JJ+
49 JJ+
50 QQ+
51 QQ+
52 QQ+
53 QQ+
54 QQ+
55 QQ+
56 QQ+
57 QQ+
58 QQ+
59 QQ+
60 QQ+
61 QQ+
62 QQ+
63 QQ+
64 QQ+
65 QQ+
66 QQ+
67 QQ+
68 QQ+
69 QQ+
70 KK+
71 KK+
72 KK+
73 KK+
74 KK+
75 KK+
76 KK+
77 KK+
78 KK+
79 KK+
80 KK+
81 KK+
82 KK+
83 KK+
84 KK+
85 KK+
86 KK+
87 KK+
88 KK+
89 KK+
90 KK+
91 KK+
92 KK+
93 KK+
94 KK+
95 KK+
96 KK+
97 KK+
98 KK+
99 KK+
100 KK+
101 KK+
102 KK+
103 KK+
104 KK+
105 KK+
106 KK+
107 KK+
108 KK+
109 KK+
110 KK+
111 KK+
112 KK+
113 KK+
114 KK+
115 KK+
116 KK+
117 KK+
118 KK+
119 KK+
120 KK+
121 KK+
122 KK+
123 KK+
124 KK+
125 KK+
126 KK+
127 KK+
128 KK+
129 KK+
130 KK+
131 KK+
132 KK+
133 KK+
134 KK+
135 KK+
136 KK+
137 KK+
138 KK+
139 KK+
140 AA+
In the future, I am going to convert this data to a "probability that hand will be best IF you get it" as well by position. In other words by looking at the average table position and chance your hand is best preflop, you will be able to take that range and adjust by position to the equivilent hand strength. Since folding around to the button increases your chances of having the best hand, a hand like 99 may actually be stronger than TT from under the gun because the odds your 99 is best is much greater since you only have to worry about 2 opponents. This information will allow one to adapt a more thorough strategy that maximizes your chances of having the best hand, allowing you to construct a strategy based upon that.
Personally I would raise in with 1.5times the hands I am willing to call off with, maybe even 2 or 2.5 times the amount depending upon opponents and other factors...
Missing variables:
What some people will usually do is calculate "hands left" based upon current blinds. For example if the blinds are 300/600 30 ante and the cost is 270+300+600=1170 per rotation, that with 5850 in chips left you have 5850/1170=5 rotations *9 hands per rotation = 45 hands left. That is entirely wrong. What matters is
1)How many uncontested chips you intend on being able to get without all in risk at current levels.
2)How fast the blinds rise
3)How fast people play.
Ultimately that determines how many TRUE hands you have left adjusting for the blinds. I usually estimate about 15 hands per 12 minutes or 12.5 per 10 minutes. As such you play X hands and then you pay the NEXT level of blinds. With a spreadsheet you can map it all out and estimate the TRUE number of hand left and construct a strategy.
Depending on how many blinds you have and what a "standard" raise is, you can determine how many bets you can get in. I typically would 4bet with 1/3rd the hands I raised with and was 3bet, so if a "4bet" is all in you can raise with 3 times the amount.
Also, I typically am trying to make a push without it being an over push so I may switch between a limp and 3bet limp raise all in push and a raise and 4bet all in depending upon what is most likely to be the reasonable move. I also can adjust my raise size so that I am better positioned to push facing a 3x my bet raise or so.
THAT is how you can prolong the inevitable all in for some time while also raising with a number of hands that's well structured to withstand reraise without being exploitable. ALSO, some situational steals may be necessary but anything that buys you time can be useful. Of course if table conditions are reckless I am not going to raise with NEARLY as high as 3 times the percentage as I am willing to get all in. In other conditions I may raise with 4-5 times the percentage I am willing to push with.
Then there is positional adjustments, if it folds to me I am much more willing to raise in late position than early position and my all ins should be structured as such. AK on the button after several folds is a monster. AK under the gun when facing a reraise is probably a coinflip at best and probably you get the worst of it overall.
I don't have time to get into anything else, but that establishes a baseline. Sorry, you cannot wait for aces, and kings, and thus must have a strategy to accumulate chips. That's where "nutball" poker comes in.
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