Most of my life I just work things out myself. But here I'd like someone to verify my understanding. I have a hand below (0.02/0.05), where essentially, I expect my villian to always have a king (top pair). I turn a flush draw, giving me 20% chance to win. He bets .40c into a 0.87c pot. Let's just call the pot 80c for the sake of simplicity. So I get 3/1 on my money to call where 20% of the time I make a flush. Now I see this is a bad price, but my thinking is this. To get me the correct call to see this flush draw, the pot would have needed to be 1.20 (roughly). In that case, if he bet .40c into a 1.20 pot, I would need to pay 40c to see a 1.60pot. That would make my 20% chance of hitting the flop, a break-even call. So the way that I see it, is that I would need to make 80c (1.60 (which is the actual pot I would have needed it to be) minus the actual pot of 80), on the river when I do hit, to make this a break-even play. If I think I can make more money than this, then this would be a +EV call. In my head that's how I would work it out. Can anyone confirm thats correct?


PokerStars, Hold'em No Limit - $0.02/$0.05 - 5 players


ginom22 (UTG): $4.36 (87 bb)
HERO (CO): $5.11 (102 bb)
VILLIAN (BU): $5.43 (109 bb)
UrfinWoods (SB): $5.00 (100 bb)
ANENTAXTOS (BB): $2.91 (58 bb)

Pre-Flop: ($0.07) Hero (HERO) is CO with A♦ 5♦
1 fold, HERO (CO) raises to $0.15, VILLIAN (BU) calls $0.15, 2 players fold

Flop: ($0.37) Q♣ 2♥ K♦ (2 players)
HERO (CO) bets $0.25, VILLIAN (BU) calls $0.25

Turn: ($0.87) 2♦ (2 players)
HERO (CO) checks, VILLIAN (BU) bets $0.40, HERO (CO) calls $0.40

River: ($1.67) 3♦ (2 players)
HERO (CO) bets $1.25, VILLIAN (BU) calls $1.25

Total pot: $4.17 (Rake: $0.17)

What your describing is called “implied odds”... you do have to be a little careful, because you might not always get paid on the next street. You probably want some estimator of how often you get paid if you’re using it to make a calculation, but yes this is a solid concept.

I didn’t check your math, but if we say you think you always get called for 1.25 on the river when you hit,

Then you are calling 40 cents to win (87+40+125) so the equity you need is 40/(80+87+125) which is about 14% equity to continue.

It's also pretty likely that your Ax is good on the river. AQ/AK/QQ-AA would have likely 3-bet preflop, 2x is unlikely as well and you'll beat KQ and any other Kx. Mainly you'll lose to JT if you end up behind but you should factor the overcard into your equity.

I wrote an Implied Odds calculator in Excel that deals with these type hands.

For OP’s case, if you assume the 20% Hit chance will always win and villain will always call if hero bets, then a future bet of only 0.33 is required for break-even (not accounting for rake).

EV = 0.20*(0.87 + 0.40 + 0.33) – 0.80*0.40 = 0

The first term is for hero hitting and winning the pot and river bet with villain always calling. The second term is hero losing the 0.40 turn call when he doesn't hit.

To be more realistic, if a hit means a win 85% of the time and villain will call a bet 70% of the time, than a bet of 1.03 is required for break-even. Hero will fold if he doesn’t hit.

EV =0.2*0.3*(0.87+0.4)+0.2*(0.7*(0.85*(0.87+0.4+1.03)-0.15*(0.4+1.03)))-0.8*(0.4)

= 0

The first term is when hero hits and bets and villain folds

The second term is for hero hitting and betting , villain calling and hero winning 85% of the time and losing 15%.

The third term is for hero not hitting on the river and folding thus losing his turn call of 0.40.

An easy way to look at it is he gave you 3 bets to your risk of 1 which means you are 1 bet short of the 4 that you need to break even. So when you make your flush you’ll need to extract that last bet from him and in this case 1 bet equals 40c.

If he had of bet the pot then he’s giving you 2 bets to your risk of 1 therefore you’d need to extract those last two remaining bets on the river to complete your breakeven 4:1. In that case 2 bets would mean $1.60

I can confirm that is not correct.

If you needed 20% equity, and were getting 3:1, then you would just need another 1:1, which in this case is 40 cents. Note, you will need to make this on the river 100% of the time, but we can also settle for making 80 cents 50% of the time, or some combination of amounts some percentage of the time that total 40 cents in expected value or more.

But if villain has a king, we can win with three aces and nine diamonds. Let's say villain has KJ of spades. So that is 12 outs, we know 8 cards, so there are 44 left, we like 32:12 or 2.7:1 against. So we would have a 27% chance of hitting the river. Of course we should discount our ace outs for sure, and probably our flush outs, since a full house is already possible, so maybe your 20% estimate wasn't so bad after all.

I don't understand you. If he bets $.40 making imagining the pot was $1.20 (instead of the $.80). And we pay $.40 to try and win. Well that means, 4 times we will lose $.40, so a gross loss of $1.60. And one time we will win $1.20. I am not winning $1.60 if I wager $.40c (I am betting $.40 that I will win $1.20, so in the times I lose I lose my $.40c, and times I win, I am winning that $1.20). So if this was the case, I would be decreasing my stack by .40c each time. So I do think quite strongly that I do need to win $.80 each time, and not $.40.

Right so I've found the math. If villian bet $.40 into a $.80 pot, and we are a 4:1 dog, which we are (%20 to make a flush), then the correct size pot we would need to call to break even is as follows:

$.40 (the raise) * 4 (the ratio, of 4:1). So the pot would need to be $1.60 to make the call. So since the pot is $0.87 currently, it means we lack $0.73c that we would need to make up on the river if we do hit.

Except you are forgetting about your opponents bet. There is 80 cents in the pot, and 40 cents your opponents bet. So you only need to make 40 cents on the river (sticking to your original simplification).


On the turn you are risking 40 cents to win $1.20. 80 cents in the pot, and 40 cents in your opponents bet. The pot will be $1.60 after you call. Your equity is 20% so your share of that is 32 cents. A losing proposition if you were all in, but you still have a street to play, so you need to make eight cents per run, or 40 cents on the times that you hit (you are hitting 20% of the time, so .40 *.2 = 0.08).


Perhaps it is easier in ratio form.

You are getting 3:1. But you are a 4:1 dog. You need to be getting 4:1. That 1 is 40 cents.

I get it, yeah I missed the fact he already put another $.40 in the pot on the turn.

So if the current pot was actually $1.20, and he bet $.40, then the pot would be $1.60. In this scenario:

4 times I call $.40c and lose = $1.60
1 time I call $.40c and win $1.60

As the existing pot is $1.20 (not $.80c, as I forgot to factor in he already put $.40 in the pot on the turn), this means the current total pot is $.40 short for me to call and break even. So on the river, if I can make anything more than $.40c then this is a +EV play (excluding rake). Good. I'm glad I understand it now. My logic was there, but my brain just forgot to add his existing bet to the pot, like you say. Thanks for your help.

So if he had of bet the 80c pot now how much do you need to get on the river when you hit?

Note: If you’re answer isn’t $1.60 then your working out is wrong