Thoughts on VP$IP as a function of M during a MTT

[trojanrabbit]

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Wow. Did you really overcome the hand ranking and overcall limitations you mentioned a few months ago? If so, kudos, that's quite an accomplishment.

(still waiting on Amazon for my book)

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No problems with hand rankings, but overcalls are still ignored. I have studied the overcall problem and it only has a minor effect, especially for an M of 4+.

I can understand the frustration with Amazon. They've sold out 3 times. This last time after they announced immediate availability they sold out in 12 hours. I guess that's good and bad news.

As far as an example, here's the equilibrium solution for pushing with an M of 6, with no antes:

<font class="small">Code:</font><hr /><pre>
Position No Antes
Small Blind 22+,A2+,K2+,Q6o+,Q2s+,J8o+,J3s+,T7o+,T4s+,97o+,95s +,87o,85s+,76o,74s+,64s+,53s+,43s (59.9%)
Button 22+,A2+,KTo+,K5s+,QTo+,Q8s+,JTo,J8s+,T7s+,97s+,86s +,76s (32.7%)
Cut-Off 22+,A4o+,A2s+,KTo+,K9s+,QJo,Q9s+,JTo,J8s+,T8s+,98s (27.0%)
Hijack 22+,A9o+,A2s+,KJo+,K9s+,QJo,Q9s+,J8s+,T8s+,98s (20.7%)
3-off 22+,ATo+,A7s+,A5s,KJo+,K9s+,Q9s+,J9s+,T9s (16.7%)
4-off 33+,AJo+,A8s+,KQo,K9s+,Q9s+,J9s+,T9s (13.9%)
5-off 55+,AJo+,A9s+,KQo,K9s+,QTs+,JTs,T9s (12.1%)
6-off 66+,AJo+,A9s+,KTs+,QTs+,JTs (10.1%)
7-off 77+,AQo+,ATs+,KTs+,QTs+,JTs (8.4%)
</pre><hr />
For those nit-picky game theorists, this does consider mixed strategies and these are the hands that are pushed at least 50% of the time.

Kill Everyone lists out the solutions for the other stack sizes and also does it with and without antes for comparison. I also list what the equilibrium calling ranges are as well for each case. And... there is some nice discussion about it including some shortcuts for helping you memorize approximate solutions for use at the table.

Hope that's enough of a teaser. [img]/images/graemlins/wink.gif[/img]

Tysen