In the early stages of a $100 tournament, I faced the following situation:

Cutoff raise to 2.5x, we defend BB with Ad7c (BB ante in play). SPR is about 8.

Flop is TdTh2d.  Villain cbet 1/2 pot, I called.  .

Turn was 7s, we both checked.

River was 2s, I checked and called a 60% pot bet.  Villain showed 66.

My thoughts:

Most Villains in these tournaments cbet too much and play honestly on turn.  Therefore, I like to float, even out of position, on any board that is not a huge range disadvantage for me.  I have plenty of Tx in my defend range, so this board is certainly not a ‘bad’ one for me.  The BDNFD was a nice bonus, but I am defending here with all of my Ax.  My plan was to give up on turn unimproved, and to bet pot or a little more on river.  This is how most of the player pool plays Tx.

When the turn gave me a pair, I changed plans.  I’d still fold to a bet on turn, assuming any kind of decent size (though maybe I should check raise semi bluff?).  When the river was another 2, I thought I had enough showdown value to call a bet.  I was lucky in that Villain’s pair was smaller than mine, as she probably plays all pairs this way.  Checking the math, it is essentially a break even call if Villain bets all pairs on river for this sizing.  Of course she could have some of her own slow played Tx, or she could have some total air like QJo that she is bluffing with.

What does PIO think?  With no constraints, it bets flop only 28% of the time as Villain.  It check raises 34% of the time as hero, including my exact hand; it fold all other A7o.  I think we can agree this isn’t how this street gets played in $100 buy ins.

I then forced PIO to bet flop, which I think is how most Villains play (before I saw this, I would have assumed we can bet range here).  When we forced Villain to bet, PIO check raised 45% of the time, and called only 2% of the time.  It still check raised Ad7x.

I ran a 3d simulation where I did not allow hero to check raise.  Notice this is how much of the player pool plays; if they are slow playing their Tx, that just doesn’t leave much in terms of check raising.  Now hero defends about 48% of hands.  Interestingly, this hand is a mix between fold and call.  I’d have thought this was a slam dunk call (we might be ahead, our ace might be live, we have BDFD), but PIO thinks this is just a break even call.  It does assume Villain will play the turn correctly, which I assume not to be the case.

On the turn, PIO is straight calling a bet (that never came) when it makes a pair of 7s. Its bluffs are mostly 98, and Ax of diamonds.  It obviously thinks my hand is too good to turn into a bluff, though I am not sure that is the case.  I have very little showdown value here versus a value heavy betting range.

On the river, it actually bets my hand about 1/2 the time; although I feel confident this is a better bluff catcher.  I don’t think I am ever being called by worse, as, remember, my line looks a lot like Tx to most Villains.  PIO does bet Villains actual hand, and all pairs, except it does check back some 33, 44.  It checks all Ax, turns Kx into a bluff.

One more thing; If I had missed the turn and went to bluff river:  I gave PIO 3/4 pot, 1.5 pot, and all in (5x pot).  It used 3/4 pot 18%, 1.5 pot 28% and bombed it 3.5%.  It does not turn Ax into a bluff, it prefers hands like J9 etc.  Ax blocks Villains better Ax, while hands like J9 block JT,T9.  I don’t think I’d ever use the all in option, but it is kinda cool with the hands it uses; T7s and 22, which of course make sense, they beat Tx.  

Sorry if this was too long, but I liked the hand, both in reality, and from a PIO point of view.