Pot odds for chasing a flush against unknown opponent

Question

Consider 2 scenarios, in which a flop has given you an approx. 33% chance of making an Ace high flush by the river. The pot size is currently 600 and there is 1 player remaining. It costs 200 to call.

Scenario 1.
Suppose you call and your opponent after the turn card (which doesn't make your flush) bets 200. The pot size is now 1000 and it costs 200 to call. With odds of 1:5 and a 20% chance of hitting the flush on the river it makes sense to call.

In this scenario, your initial call of 200 after the flop had a positive EV.

Scenario 2.
Again you call the bet of 200 after the flop, and again the turn card doesn't give you your flush. Now your opponent is a very aggressive player and bets 1000 chips, bringing the pot size to 1800. This gives you odds of 1:1.8, which is definitely not enough to call on a 20% chance of making your flush on the river. You must fold.

Now in this scenario, it was only correct to call the initial bet of 200 on the basis that you will see 2 more cards. However against such an aggressive player, it can be shown mathematically that calling after the flop in this situation will yield a long term net loss, since 80% of the time you are going to fold on the turn, only seeing 1 card, not 2 which the pot odds were calculated for.

Summary:

The size of the pot required to justify chasing a flush after the flop depends on how likely your opponent is to let you see both the turn and the river. If you are against a new opponent and you do not know whether the opponent likes to bet big on the turn or just call or min bet, what pot size do you really need in order to chase your flush?

Answer 1

You remind me of a session I had with a poker coach. He had an interesting take on this same scenario and that's to go all-in on the flop - the call would be a "mistake". Your analysis is right on the odds, and yes, you would be frozen-out on odds if the opponent bet's 1000 into you.

The thinking was to avoid the exact scenario you're describing. The all-in on the flop gets you (1) the potential that your opponent will fold & you will win on the spot and (2) you're essentially "buying" both 4th and 5th street. You're effectively closing out the potential of being priced out after the turn and making sure that you get two shots at making your flush. Otherwise, you're basically only getting 1 shot at the flush (the turn) which truncates the odds you just calculated.

So, if the odds are there on the flop, make sure you get to see out the rest of the hand to 5th street. The only way to really do that is to shove on the flop.

Answer 2

Each out you have for your flush draw gives you roughly 2% equity for the turn and river

• 2.13% for Turn
• 2.17% for River
• 4.26% for Turn + River - This is most often used for all-in situations.

Pot Odds Chart

• 1/4 Pot | 16% Equity
• 1/3 Pot | 20% Equity
• 1/2 Pot | 25% Equity
• 2/3 Pot | 28.5% Equity
• 3/4 Pot | 30% Equity
• 1 x Pot | 33% Equity
• 2 x Pot | 40% Equity

There are some additional things to consider such as Implied odds and Reverse Implied odds.

Implied odds take into account additional betting after you make your hand or miss it (by potentially bluffing) in order to justify making a bad call.

Ex. You hit your flush on the turn, villain checks, hero bets, villain calls = extra money to make up for the bad call.

Reverse Implied odds are when you make your draw yet you still get beat by a better hand or bluffed out of the pot.

Ex. You hit your flush on the river, but it pairs the board, villain had trips but now has a full house (or bluffs the full house, not likely to work but if you and your opponents stack sizes are large compared to the pot it can be profitable for him.)

You have 9 outs with a flush draw if one of those outs doesn't give him a hand that beats your flush (such as a better flush, full house, etc.) and he doesn't catch a better hand on the river when you make your flush you'll have 19% equity which means the pot odds have to be at least 19% in order for this call to break even and less for it to be profitable PER STREET, provided there is no money to be gained from implied odds. If your opponent bets 1/3 pot (20% equity required) you are roughly breaking even. If he bets more you are unprofitable. If he bets less/checks you are profitable.

So to answer your question, The first scenario isn't profitable. He bets 200 into a 400 Pot = 1/2 Pot. He would have to bet 133 into a 400 Pot (1/3 Pot) for it to be break-even.

Second scenario isn't profitable either, however if we make it so the pot was 600 and he bets 200 it is break-even for the Turn card (200 is 1/3 Pot). After however you would need roughly 35% equity to break even (17 outs).

Answer 3

The answer is that you need immediate pot odds. There is absolutely NO basis to assume they are going to let up on the turn if a blank hits.

According to Skansky every time you make an opponent make a bad decision you benefit. Opponent gave you 3:1 and you called thinking you would get a free card on the river. Any good opponent is going to turn up the heat if a blank hits on the turn.

If opponent had nothing and really wanted you gone they would bet the pot.

That is a value bet if they had a pair or better and were protecting from the flush. A better bet is actuality 1/2 the pot as you probably would have chased that also getting 2:1 thinking you would get a free river.

Lets look at EV of villain
On the turn take down the pot with a pot sized bet
(this assume you will fold to a pot sized bet)
EV 800

Bet 1/2 the pot and get a call on the flop - pot is now 1600
If a blank hits bet 1/2 the pot again and take it down on the turn
EV = -400 + (1 - 9/43)1600 = 865
865 > 800 If villain had a single of the suit and took your outs to 8 then 902

By only betting 1/3 the pot on the flop villain actually had a negative EV if the plan was to take down a blank on the turn 600 versus 590.

If your ace is good then you pick up 3 more outs. So I think you did the right thing to call getting 3:1. You are getting just short of 3:1 on the turn alone if the Ace is good (they only have a single pair and no ace).

Ace little is just not that strong. You only want to play it late and cheap in multiplayer pots. You are only going to make a flush by the river 1:16. And if you pair you ace you can easily get yourself in trouble. A lot of people will say mid suited connectors are better to play than ace little suited.

That was just poorly sized value bet by villain. It would be like top pair or trips that wanted to keep mid or bottom pair along on a board with no draws.