I haven't seen this addressed anywhere so....

I was watching an HU poker video last night, made by 2 high stakes crushers, and they said, 

"if we min open every button, the BB has to defend more than 50% or we auto profit - even if we were to open fold the flop when called." 

I've heard this before and never really liked it, but i just accepted it as true due to all the high stakes video makers repeating the idea.  

Anyway, last night i got to thinking about it and I think its wrong, here's why.

If we take a simple game as an example. Stacks are $100 with $0.5/$1 blinds.  No ante, no rake, no rebuys/top ups. Player A is always the SB and opens 100%.  Player B is always the BB and folds 50% and 3bets 50% of the time.  Player A always folds to the 3bet.  If the conventional wisdom above is correct, my game should produce no profit for either player, however, lets look at what happens to stack sizes.

Stacks start at $100 each.

Hand #1  Player A  min raises.  Player B folds.   Player A Stack = $101.  Player B stack $99

Hand #2  Player A  min raises.  Player B 3bets.   Player A folds.   Player A Stack = $99.  Player B stack $101

Hand #3  Player A  min raises.  Player B folds.   Player A Stack = $100.  Player B stack $100

Hand #4  Player A  min raises.  Player B 3bets.   Player A folds.   Player A Stack = $98.  Player B stack $102

Hand #5  Player A  min raises.  Player B folds.   Player A Stack = $99.  Player B stack $101

Hand #6  Player A  min raises.  Player B 3bets.   Player A folds.   Player A Stack = $97.  Player B stack $103

Hand #7  Player A  min raises.  Player B folds.   Player A Stack = $98.  Player B stack $102

Hand #8  Player A  min raises.  Player B 3bets.   Player A folds.   Player A Stack = $96.  Player B stack $104

 and so on...So, Player A's stack erodes away, at the amazing rate of -50bb/100!!  He profits $1 for each win, while losing $2 on each loss.  This is a huge loss and much different that what the conventional wisdom is suggesting.

I think what's happened here is the +EV nature of a bet laying $1.50 to win $1.50 ( player A's situation with a button min open) if called less than 50%, has been interpreted as PROFIT, which is clearly not case.  The profit/expense of his play is +$1/-$2 or -$0.5, which is significantly different than the EV.  

The issue is that Profit is the difference b/w Income - Expenses.  When the above button min opening is employed as a strategy, the blinds are an expense which need to be accounted for in the profit equation.  They are a real cost in this strategy and have a huge impact on the overall Profit of the STRATEGY, while irrelevant to the EV of the open raise.

EV as it is used here relates to the immediate ROI of a bet, but is not equal to the Profit of the strategy as it does not account for the expense of the blinds. 

Therefore, equating EV (how it is used here) with Profit is a fallacy, and using only EV to justify a game strategy becomes faulty.  The implications of this are that it is ok to play tighter than 50% out of the blinds in this game, as we are not getting exploited as conventional wisdom supposes.

( NOTE: in some situations EV = Profit, but not here)