M=4, Is the best move to go all in when UTG?

[sirio11]

I would like to challege the forum to solve this problem using some math, assume no ante, and a 10 handed table with stacks greater than M=8 all of them; and most of the players are good and most likely understand desperation short stacks moves.

The options are,

a) going all in with a random hand UTG or
b) wait one more round,

and the variable I want you to involve is the likekihood to be called by the table if you go all in.
Obviously if the likelihood is 0% you should go all in, and if it's 100% you shouldn't do it with a random hand, should you?

[Exitonly]

1000/2000 blinds

hero: 12k
9 other guys: 25k+

<font class="small">Code:</font><hr /><pre>
Pos. Calling Range Call % Equity

UTG+1 TT+,AJs+,AQo+ 5% 72%
UTG+2 TT+,AJs+,AQo+ 5% 72%
MP1 99+,AJs+,AQo+ 5.4% 72%
MP2 99+,AJs+,AQo+ 5.4% 72%
MP3 99+,AJs+,AQo+ 5.4% 72%
CO 77+,AJs+,AJo+ 7.2% 71%
BT 77+,AJs+,AJo+ 7.2% 71%
SB 66+,ATs+,KQs,AJo+ 8.3% 71%
BB 66+,ATs+,KQs,AJo+ 8.3% 71%
---------------------------------------------------------
55% 71.5%
</pre><hr />


so 55% of the time you win 3k and your stack is 15k
and 45% of the time you win 28.5% of 25k (total pot), or 7125.

so .55 * 15 + .45 * 7125 = 11450 stack on average.

Compared to a 12k stack when you fold.


But that doesn't account for you having to post 25% of your stack the next two hands. but i'm not convinceed that's bad.

I got tired halfway through this, but i guess i'll post what little work i did.