when facing a bet on the river and determining the amount of times required to win the pot to make the call, why do we divide the call by the pot (incl. bet we're facing) plus the call?

why is it not call divided by pot (incl. the bet we're facing)? in other words, why risk / risk + reward and not risk / reward, in a river spot like this specifically? i'm just looking for an explanation or a breakdown so i can understand what's going on, thanks very much

You're not explaining the point you're making at all clearly in the slightest, but it sounds like you are describing identical situations. Make up a hand and tell us what we are calculating as opposed to what we think we should be calculating please

Edit - In fact, let me do that for you. Pot is $100, villain bets $50. Show your work

I have no point to make.

here's an example: OTR, we cover villain

OTR pot is 400, villain checks, hero bets 250, villain jams 750 ai.

500 to win 1400.

risk / risk + reward says break even equity is 26%. In other words, we need to call and win 26% of the time or more for the call to be profitable (yes?).

I am confused as to why in this spot do you add your call to the 1400 in the denominator.

thanks,

you are not adding your call to the denominator

there is 400 in the pot after the river

you bet 250, that makes it 650

he jams for 750, that makes it 1400

your call is not mentioned ever

the formula for breakeven equity is risk / risk + reward

we are risking 500 to win 1400

500 / 500 + 1400 gives 26%

to make the numbers easier, change it to an initial pot of 500, everything else is the same. You will need to call 500 to win 1500, with a final pot of 2000. Your pot odds are 1500/500 = 3 to 1.

If it is 3 to 1, that means you need to win 1 out of 4 times to break even (out of every 4 times, you win 1 and lose 3). 1 out of 4 equates to 25% - which can also be calculated as 500/ (500+1500).

So the short answer is that if you are calculating pot odds, you use the amount of the pot, not including your call - and if you want to calculate the percentage you need to win you include the post-call pot size. Whichever way you do it gives you exactly the same result, just expressed differently.

To state it another way, assume the pot is P before you call a bet of B. Then the total pot is P+B, which is the total amount you will collect if you win. Your “fair share” of that total pot is the percent you last contributed, which is B/(P+B) so that should be the relative frequency you collect.

One more way: The EV equation for calling a bet of B into a pot of P after villain bet is

EV = amount won – amount lost weighted by occurrence probabilities eq and 1-eq

= eq*P - (1-eq)*B

Set EV to 0 to find the minimum required equity:

eq*P - (1-eq)*B = 0

eq*p - B + eq*B = 0

eq *(P+B) = B

eq = B/(P+B)

If you decide to call you gonna put in your 500$ and the pot will become 1900$. The question now becomes, how frequently do you need to win to get back your 500$. If you multiply 0.263 by 1900$ you gonna get 500$, in other words, if you win exactly 26.3% of the time you are getting your 500$ back. If you win more frequently than 26.3% you make some profit And you already know the formula how to calculate 26%.

Now let's imagine we don't add our call to the 1400$, we'll end up with 500/1400, which is 35.7%. But if you win 35.7% of the time you are winning on average 0.357 * 1900$ (because the whole pot is 1900$) = 678$ which is a lot bigger than your 500$ call. This calculation doesn't make much sense.

i think this is where i stopped computing. the total pot when facing the raise is 1400. so since we end up with everything if we win, we have to use 1900.

yes i think this seals it home.

thank you, everyone

Pretty sure you are depicting the % times you collect vs the villains combo ratio that is good vs you and comparing the two percentages ?

Story problems are always fun .. eh? Maybe no for a lot of folks ..

.. determining the amount of times required to win the pot to make the call .. (OP's words) The answer to this is always once, what you're trying to determine/say is how often can I play this hand and be 'OK to call'. That is Pot Odds, win v loss(es). In the simple case your Pot Odds are 500 to 1500, or 1 win to 3 losses .. but you need to play 4 hands in order for that to happen, right? That's why you need to add the call to the pot .. you need to count 'all' the hands needed to break even, thus 4 in this case. And that converts to a 25% win percentage (1 out of 4)

Once you have Pot Odds you need to determine the strength of your hand at Showdown, Equity. If you feel that you will win more than 25% of the time, then this is a +EV call for you. Whenever your determined Equity is greater than your Pot Odds you should have long term success.

Pot Odds and Equity are not the same thing, they are factors that you compare when making poker decisions.


Player bets 200 into 100 (300 total) .. you have to win once (200) against 1.5 losses (300). That's not easy math, so double each number .. win twice against 3 losses, or a 'record' of 2-3, which is 40% Pot Odds (2 out of 5). I use this extreme example because it's a concept that a lot of Players don't grasp when their Aces get cracked .. and it's also why you need to study away from the table to be able to recognize and feel comfortable putting your chips in at 'any' time. In this example here, Even when AA Guy bets twice the pot (on the Flop) you may still be correct in calling if you have a massive draw that includes both straights and flushes.

In the long run you should be able to grasp certain 'classic' Equity spots (flush, straight, OESD, Set) and know what Pot Odds you need in order to continue in the hand.

I like easy math .. big number/smaller number .. (existing) Pot/call calculates your losses, then add in the one time you're going to win and move on from there to calculate a Pot Odds percentage and THEN compare to your determined Equity of calling (and winning). GL


PS .. I love the equations, they work. But in real life I like to help people think in simpler terms .. How many times can I 'afford' to lose for each time I win?