Effective odds are the real odds a player is getting from the pot when the player calls a bet with more than one card to come. David Sklansky, "The Theory of Poker" Chapter 06 Effective Odds, page 50.

Effective Odds seem easier (more logical) to calculate for Limit games - where the betting/raising amounts are defined in each round. In No-Limit games a player would be required to use predicative thinking to estimate the % of the pot an opponent would bet on following rounds to compute the Effective Odds.

If I understand Effective Odds correctly.... in NLHE if we have observed an opponent who raised pre-flop then betting 1/2 the pot on the flop, 3/4 on the turn/river then we can use this information to compute the Effective Odds when we are in a hand against him? Am I thinking through this properly? Does anyone have an example that they can post where they used Effective Odds to play a NL hand?

Thank you!

Only if that opponent always uses the same betsizes, which is not necessarily going to be true. Let's look at some action:

no limit holdem 100 big blinds deep three handed.

big blind: me
small blind: standard tag
button: the variable

button raises 3x, small blind folds, it's on me.

I continue with different ranges vs different opponents:

opponent 1) often makes large postflop bets; high effective odds to see showdown. I play relatively tight vs this opponent because the price to continue isn't good considering future action.

opponent 2) often makes small postflop bets; low effective odds to see showdown. I play relatively loose vs this opponent because the price to continue isn't that bad considering future action.

opponent 3) checks postflop very frequently, but makes large bets when choosing aggressive actions. I play relatively loose vs this opponent preflop, but I play relatively tight vs this opponent postflop when facing these big bets.

opponent 4) checks postflop very frequently, and makes small bets when choosing aggressive actions. I play very loose vs this opponent preflop because the effective odds are so low postflop. Bluffcatchers and weak draws in particular will perform much better vs this opponent than vs the others specifically because of the effective odds.

It's true that it's difficult to calculate your effective odds in NLHE. It is sometimes instructive to look at "best case" and "worst case" effective odds, since sometimes you can rule out calling or folding based simply on the extreme cases.

Otherwise, you're going to have to use your judgement regarding how much you think the player will bet.

Sklansky provides a Fixed Limit Example for us to think about Effective Odds. I'll use Sklansky's example to mock up a hand for review so that we can further discuss. Our hero (BB) is trying to determine if he should make a call ON THE FLOP when drawing to a flush. Our mission is to determine if Hero is getting the correct Effective Odds to make the call ON THE FLOP.

The Game:
Fixed Limit Hold'Em $10/$20 (this makes SB = $5 and BB = $10)
Pre-flop/Flop betting increment $10.
Turn/River betting increment $20
Player stacks are EQUAL, each has $200 (no-one will be all in this hand)

Pre-flop:
- Action folds around to the SB (cards unknown) who completes.
- BB has 8 J and checks option
- This means that two players will see the flop (SB/BB)
- Current Pot Size $20

Flop: A 2 7
- SB bets $10 on the flop
- Current Pot Size $30
- BB is deciding if he should call $10 to win $30 or 3-to-1 pot odds
- BB has 9 outs to make his flush.
... 19.6% to make the flush on the turn (1 card) in ratio form 4.1:1
... 35% to make the flush on the river (2 cards) in ratio form 1.9:1

Comparing the pot odds to the immediate odds when Hero (BB) only plans to see the turn (1 card) we have 3-to-1 pot odds against 4:1 chance of improving. Our calculations indicate that calling the flop is NOT a good call.

Comparing the pot odds to the immediate odds when Hero (BB) plans to see the turn/river (2 cards) we have 3-to-1 pot odds against 1.9:1 chance of improving. This calculation looks to indicate a good call on the flop BUT - it is not a correct comparison (we've used immediate odds) UNLESS the 2nd card is free (i.e. a player is all-in). In our scenario there are no players all-in, so we can expect that we will be faced with a decision on later rounds. Effective Odds will help our Hero (BB) determine if he should call the flop based on predictive thinking about the turn/river rounds.

Turn: Hypothetical - Hero (BB) is deciding if he should call the flop
- SB will potentially bet $20
- BB needs to think about what he will win or lose in the hand
... $10 call on flop + $20 call on turn = possible loss -$30
... $30 (current pot on flop) + $20 (opponents turn bet) = possible win $50
- Effective Odds are $50 to $30 or in ratio form 1.66-to-1
- Predicted pot size following turn action = $80

Comparing our Hero is getting 1.66 Effective (real) odds to against 1.9:1 chance (seeing 2 cards) of improving. Our calculations continue to indicate that calling the flop is NOT a good call.

River: Hypothetical - Hero (BB) is deciding if he should call the flop
- The hits the board giving our Hero (BB) a flush!
- Hero believes he will get paid off, that SB will call a bet on the river
- BB needs to think about what he will win
... $30 (current pot on flop) + $20 (opponents turn bet) + $20 (opponent calls Hero's river bet) = possible win $70
- Effective Odds are $70 to $30 or in ratio form 2.33-to-1

Comparing our Hero (remember, our opponent MUST call the river) is getting 2.33 Effective (real) odds to against 1.9:1 chance (seeing 2 cards) of improving. Our calculations indicate that calling the flop IS a GOOD call.

In summary: In this Fixed Limit Hold'Em example I believe that Sklansky's point is that a player is making a mistake when he only considers the immediate odds - the "right now" - when he needs to draw to improve his hand. A great player takes into account the $$ that he will be required to put in the pot on later rounds, the TOTAL amount he might win or lose, to make a good decision to call (or not) in earlier rounds.

If someone will confirm that I've understood and articulated this example from Sklansky's Theory of Poker (chapter 6) correctly - I'll attempt to perform the same kind of analysis on the 4 types of opponents that Bob148 mentioned in his reply.

Yeah that's the idea. I dislike the example though; does the small blind never bluff? I'm actually a bit excited about playing a Jack high flushdraw in position vs 97.5485% of opponents.

----

Let's look at two hands:

100bb no limit holdem

button raises 3x, small blind folds, I call in the big blind.

458r

I check, button bets 4 big blinds.

If I call, the pot will be 14.5 big blinds with 93bb behind.

100bb no limit holdem

button raises 3x, small blind folds, I call in the big blind.

458r

I check, button bets 10 big blinds.

If I call, the pot will be 26.5 big blinds with 87bb behind.

The respective stack to pot ratios:

hand 1: ~6.4:1

hand 2: ~3.3:1

Notice that just the difference of 6 big blinds for the flop bet and call cuts the spr in half.

Also note that the betting ranges for the respective betsizes will be different; it takes a much stronger hand to bet in the second example than the first.

The effect on the big blind's strategy is that the flop folding frequencies will be lower in the first hand and higher in the second hand. The larger betsize in the second hand also has the effect of strengthening the ranges that go to the turn; if I call the flop then I have many more hands that can call big bets on the turn and river in the second example. In this sense, the big flop bet has opened the door for me to lose my stack much more often in the second example.

The first hand exemplifies low risk:high reward.

The second hand exemplifies high risk:low reward.

relatively speaking, of course.

BB raises the flop and wins some percentage of the time right there, plus has odds to call any reraise. This makes the hand play entirely differently. Limit is a very nuanced form of poker with a different skill set, in my opinion. When trying to extrapolate to no-limit there will be lots of examples where the best strategy is totally different between the two games.

It is well known that one way of looking at future betting is through implied odds. I have developed a model that can evaluate this situation from an Implied Odds perspective for NLHE. It considers hero’s equity as equal to P(Hit an Out)*Pr(Win | Hit) assuming villain calls. Therefore it accounts for the possibility of reverse implied odds – the chance hero hits but loses, in this case possibly to a higher flush or maybe a full house. If hero doesn’t hit he will fold to a future villain bet and lose the current street call amount.

I used the following inputs.

Pot Before Villain Bet = 20
Villain Bet = 10 Hero Call = 10
Flush Hit Probability = 9/47 = 19.1%
Win Given Hit = 85%
Villain Call Probability Given Hero Hit = 70%

The following results were obtained:

EV of Current Street Call = -3.35 (clearly hero needs implied odds to make the call)

Required Future Bet (minimum) = 33.5 (=66.8 if villain folds 70% of the time)
Implied Odds: 6.4 to 1

The fact the model incorporates Reverse Implied Odds is something I haven’t seen much.

So the model actually includes hero making the flush but losing the amount he bets 15 percent of the time? That is neat!