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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?

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You are only partially right the fact that chasing depends on weather or not he bets big on turn. I just want to point out that if he always bets big on turn and you already got your flush you will get a lot more money out of the hand ( even though you had less chance to get it with only 1 card) In poker language - vs agressive players you have better implied odds so you might still want to call if he gives good odds on the flop –  Daniel Jul 25 at 9:15

2 Answers 2

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.

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+1 Jim, interesting perspective thanks. I guess the accuracy of this approach depends on his fold percentage to your all in. –  Mew Jul 22 at 8:41
    
@Mew to a certain degree, yes. But there is also value in buying both streets. Think of it this way - if you think that getting bad odds after the turn is very likely, then should your flop analysis be based on 1 card or 2 cards to come? You would have to conclude that using 2 cards is inaccurate and you might find yourself folding after the flop. But that doesn't seem like the right play either. So this play is as much as the possibility of the opponent folding as much as it is about making sure that you get two-shots at your draw, not just one. –  Jim Beam Jul 22 at 18:11
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true but if your opponent will never fold, then you are not getting correct pot odds even if you do guarantee seeing both the turn and the river. –  Mew Jul 22 at 18:15
    
You won't get correct pot odds on 100% of your bet, but you will on the amount that you're already calling. Also, some of the bad odds is mitigated by the fold equity of your opponent. To be certain, it IS an unusual play, but I can see the line behind it - having two cards to come (not just one) is the best thing for your draw. –  Jim Beam Jul 22 at 18:30

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).

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