# Questions about EV concept and calculations

• Bronze
Joined: 08.06.2010
I seem to be making some conceptual mistake here, please let me know if there is some calculation mistake I'm making too along with mistaking the concept.

Assumptions:

Ranges are perfectly polarized.

Its the river, CO bets and its HU with BU and the CO has the BU covered so BU can only call or fold.

Pot \$100
CO bets \$50

Ratios:

FE=50/150=33%

BU should defend 67% of his range.

When the BU calls,

50/200=25%, he must win atleast 25% of the times so the CO can have 25% of his betting hands as bluffs and 75% should be value.

Assuming perfectly polarized ranges, all CO's bluffs lose and all his value hands win. So his range basically 100% equity and 0% equity hands, its river anyway so possible, the value:bluff is 3:1.

EV for CO

Case 1:
CO bets and BU folds

CO wins \$100
this happens a total of 33% of the times.
EV1=100x0.33=\$33

Case 2:
CO bets and BU calls and loses

CO wins \$150
this happens 0.67x0.75=0.5025 so 50.25% of the times.

EV2=150x0.5025=\$75.38

Case 3:
CO bets and BU calls and wins

CO loses \$50
this happens 0.67x0.25=0.1675 so 16.75% of the times

EV3=(-50)(0.1675)=-8.38

EV=EV1+EV2+EV3
=33+75.38-8.38
=\$100

Shouldn't this EV be \$0?

Isn't that why all the balancing and stuff happened?

What am I missing?

EV for BU

Case1:
BU folds he loses \$0, this happens 33% of the times.

EV1=0x0.33=\$0

Case 2:
BU calls and loses \$50, this again happens the same 0.67x0.75=0.5025
EV2=0.5025x(-50)=-25.13

Case 3:

BU calls and wins \$150, this happens 0.67x0.25=0.1675
EV3=0.1675x150=25.13

EV=EV1+EV2+EV3
=0-25.13+25.13
=\$0

So for the BU his EV is \$0 but for CO his EV is \$100.

So basically does that mean no matter what, in the long run this is a winning situation for the CO and at best a breakeven situation for the BU?

I thought they would win and lose the same amount. Like if CO has EV of +100, BU should have EV of -100, you know, zero sum game and such.
• 3 replies
• Bronze
Joined: 08.06.2010
If I take another scenario where the BU calls a lot more than needed.

Say he calls 80% of the times now instead of 67% that he should.

CO has a perfectly polorized range so his 100% equity hands always win and his 0% equity hands always lose. The CO doesn't adjust his strategy.

EV for CO

Case 1:

Again BU folds, CO wins \$100. This happens only 20% of the times now.

EV1=\$20

Case 2:

BU calls and loses, CO wins \$150

EV2=150(0.80)0.75)=\$90

I'm assuming the CO still wins only 75% of the times since he didn't change his strategy and he will still win 75% of the times and lose 25% of the times.

Similarly,

Case 3:

BU calls and wins, CO loses 50

EV3=(-50)(0.80)(0.25)
=-\$10

The freaking EV is again +20+90-10=\$100

I calculated the EV for BU as well in this scenario and same thing he got EV of \$0.

So does BU's calling frequency not matter if the CO doesn't change his strategy? do they still win the same? I assumed that now that the BU was calling more than needed he would definitely lose more EV as its not optimal anymore?

If the CO was to change his strategy against this guy I suspect he would, lets see, change the value:bluff ratio or his bet size.

Changes bet size:

He starts to bet \$75 instead of \$50.

EV for CO

I'm gonna keep the cases same. Case 1: BU folds, Case 2: BU calls and loses, Case 3: BU calls and wins

Case 1:
EV=0.20x100=\$20

Case 2:
EV=0.80x0.75x175=\$105

Case 3:
EV=0.80x0.25x(-75)=-\$15

EV=EV1+EV2+EV3=20+105-15=\$110

Viola, CO starts to win more. I did the same calculations for calculating EV of BU, got his EV of -\$10.

So I guess this is how CO can deviate from his strategy and start to exploit BU and increase his EV.

I'm sure same type of calculations for a different change in strategy as in changing the value:bluff ratio can also increase CO's EV.

So let me get this right? CO's EV remains the same no matter what strategy BU uses and CO can improve or reduce his EV by changing his strategy as the BU changes his? Cause vs same BU player a bet size of \$20 instead of \$75 or \$50 led to CO's EV becoming \$88 which is worse than the EV of\$100 that he had had he not changed his strategy at all after the BU changed his.
• Bronze
Joined: 15.06.2009
To OP:

In EV calc for CO, don't include value bets. He is supposed to be BE on his bluffs. The calculation for BU is prolly correct, he is is supposed to be BE on his bluff catching.
• Bronze
Joined: 15.06.2009
To maheepsangari:

Same thing.

If both play according to GTO, then either one can change their strategy (but not both) without shit happening. But the one that does become exploitable in the obvious way.