Hi,

Scenario:
We are on the turn and in position. The pot is 100 and villain bets 75 into us, giving us 2.3:1, or 30%. Our hand only gives us 15%, meaning we need >=15% "implied odds" to make the call.

Question:
Which of the below formulae is correct? And if neither, what would be the correct formula? Thank you!

=pot(175)*(odds required(30%)-current odds(15%))=implied odds needed(26.25)

or, is this in fact correct?

=(pot(175)+call amount(75))*(odds required(30%)-current odds(15%))=implied odds needed(37.5)

Any help is appreciated!

If you are assured of winning if you hit your outs and villain will call your bet with a large enough stack, the future bet you need for a +EV call is:

F$=C$*(CO – PO)

where

C$ is the amount you have to call (75)
PO is the pot odds = Pot/C$ (175/75 =2.33)
CO = Card Odds = (1-eq)/eq (85/15= 5.67)

Then F$ =75*(5.67-2.33)= 250

The required implied odds is then (Pot+F$)/C$ = (175+250)/75 = 5.5 to 1.

As a check,

EV= 0.15*425 - 0.85*75 = 0

Since you won’t always win if you hit and you might not always get a call, the F$ value is a lower bound, and perhaps can be at least doubled. For example, if you replace the 15% equity with a 25% chance of hitting your outs and a 60% chance of winning if you do hit (0.60 *0.25=.15), then you need a future bet of 750 for implied odds of 12.3 to 1.

I'm with you on this.

I don't understand how this works out our implied odds. I agree that we hit the river 1 in 5.5 times w/ 15% equity, but what I need to know is how much I need to make up ("make up" being defined as getting called worse on river (we always win when called)) on river to give me the correct implied odds, as I need 30% and only have 15%.

I'm a bit slow sometimes, so making it as "simple" as possible for me may help

Thank you!

For implied odds, you only call a bet on the current street if the total amount you could win on a future street has positive EV assuming if you hit your outs you will bet an amount F$ and if you don’t hit you will fold.To determine what are the required implied odds, you have to find the minimum bet to make if you do hit and win.

The corresponding EV equation is


EV = eq*(P$+ F$) – (1-eq)*C$

Where
eq is your equity (win %)
P$ is pot after villain bets on current street
C$ is amount you have to call.

Setting EV to 0 and solving for F$, we have

F$= C$*(1-eq)/eq –P$ = C$*Card Odds – C$*(P$/C$)

F$=C$(Card Odds-Pot Odds)

The corresponding implied odds =(P$+F$)/C$

Note the conditions assumed in this formulation. If you hit your outs, you will make a bet of F$, villain will call and you will win the hand. Therefore the denominator of the odds equation, the risk amount, is only the call amount for the current street. The F$ you may bet in the future is not at risk since we assumed a hit implies a win and if you do not hit, you don’t make the future bet.

I then showed how the result can change if you hit your outs but don’t win – the reverse implied odds case. This was obtained by employing a relatively complicated model which is the main focus of a draft article/blog I'm writing.