How About This Game Theory Problem

[RobNottsUk]

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As mentioned, a Ueber-Dominating pair of 7's is not going to gain much value in practical terms, as a set is very unlikely when you most need to win, so 72o will be a superior hand, under non-Push conditions. Obviously, folding a pair 7's will be easier than 8's as you will face 72o far less often! :lol:

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You must play 77. It's going to cost you $200 if 72 wins. You must stop 72 from winning.

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Agreed when you're pushing. The comment about 7's losing value was for "non-Push" conditions, normal practical play.

[RobNottsUk]

Now that's interesting! I do agree, that a tool to crunch the numbers is useful. I'll list the "pushing range". Also the Pokerstove 'odds' for 72o against the anticipated pushing range.

The reason to ask verbal questions, is to try and get to heart of it, and learn from the question some understanding that may be applicable in other situations.

So we have from David's quote of Maths of Poker :

AA.22
Axs
KQs..K7s
QJ..Q8s
JTs..J9s
T9s..T8s
98s..87s
AKo..A7o
KQo..KTo
QJo..QTo
JTo

Added : 72s, 72o ; Spence Suggests 97s

Calling Hands are stronger, as per Gap Concept

AA..55
AKs..A8s
KQs..KJs
AKo..ATo
KQo

Added: A9o


So why isn't K7o a Push?

As I understand it, because 72o is not a call, Dominating 72o has no special value.

But, becayse the BB may have 72o, then we lose approx. an additional $2.61 every time we fold. That means raggy hands holding a 7 or a 2, are safer folds, than non 7 hands (reduced chances of running into 72o).

That explains why A9o becomes a call. It argues against 97s becoming a Push. Does a hand like K9o, cross the threshold from marginal loss into 'crying' Push land?

It is actually still pretty unlikely that the BB will hold 72, about 1.3% by previous calc.

Now if the BB was shorter stacked, and 72o became a calling hand, that might not affect things much really, because Push hands with 7 or 2, would be Dominated more often than they Dominate 72.

Probably I've missed some candiate hand or something, please point it out!