The General Theme of the +EV Decision

[spoonitnow]

I'm going to take a moment before my morning sessions and make poker (and the math involved) really easy. In poker, we're usually concerned with finding two numbers and then comparing them. The first number is a risk-to-reward ratio, and the second number is our chance of winning. Different scenarios will have us calculating these two numbers in different ways. I'm going to give a few basic scenarios, let people reply, and then come back with some more questions.

1. A lone Villain bets into you on the river and if you call you'll have a 25% chance to win. Should you call?
2. On the river you're out of position against a lone Villain. If you bet pot and Villain calls, you'll have a 25% chance to win. Should you bet pot?
3. You have a 12-out draw on the flop and a lone Villain shoves the flop. Should you call?

[krimson]

1) If the bet is less than 1/2 pot.
2) If villain folds at least 25% of the time.
3) If villain's shove is less than 4,5 times the pot (assuming villain has no redraws, 12 outs = 45% chance to win).

[Robb]

2) If villain folds at least 25% of the time.

If villain folds/doesn't raise at least 25% of the time.

Edit: if villain raises, here, the math changes. I'm late for class, so I'll rethink this later.

[Fnord]

1. A lone Villain bets into you on the river and if you call you'll have a 25% chance to win. Should you call?

You still might call with slightly less than pot odds to do so in order to keep your opponent's bluffing frequency in line. Basically trading a small -EV mistake to protect our equity in future pots.

Actually trading small -EV mistakes to protect from bigger mistakes or to induce/exploit bigger mistakes is a pretty common big bet poker theme.

[Fnord]

...that said, I think it's one of the reasons some fish like big bet poker over limit poker. They can justify small mistakes via some concept of image or implied odds when in reality they're often spiraling down the road of cascading errors (small mistakes that lead to even bigger ones.)

[spoonitnow]

...that said, I think it's one of the reasons some fish like big bet poker over limit poker. They can justify small mistakes via some concept of image or implied odds when in reality they're often spiraling down the road of cascading errors (small mistakes that lead to even bigger ones.)

All of that is definitely true but I'm drawing some newbies into a trap to help them with future analysis (which I'm sure you see).

[Rage2100]

I've not worked any stuff like this out for a while, but these are my answers.

1: As long as Villain bets less than 1/2 the pot.

2: As long as Villain calls less than 2/3 of the time.

3: As long as the shove is no more than 83.33% of the pot.

[Erpel]

1. A lone Villain bets into you on the river and if you call you'll have a 25% chance to win. Should you call?

If the bet is less than 1/2 pot it is immediately profitable to call. If the bet is 1/2 pot or more it is not immediately profitable to call. In both cases it is well worth considering if any size of raise has a chance of causing the villain to fold. If he bets 1/2 pot and we raise to 1.5 pot he needs to fold 37.5% of the time for raising to be as profitable as calling if we reduce our chance to win if called to 0%. Any higher chance for the villain to fold or any chance to win if called above 0% makes it more profitable. Generally, I would also think that the size of the bet should modify my assessment of my chance to win. Similarly, my chance to win if I raise and he calls will definitely be modified downwards as he will mostly call with the very hands that beat me.

2. On the river you're out of position against a lone Villain. If you bet pot and Villain calls, you'll have a 25% chance to win. Should you bet pot?

To differ a bit from the previous replies I'll go out on a limb here and just say no - you shouldn't bet pot. A pot sized bet is causing hands that you beat to fold causing your chance to win to fall to 25% against the hands that call. If you instead bet 1/3 pot (or some other size) weaker hands will be likely to call and stronger hands will be more likely to raise which can make you profitable when called and safe to fold if raised. Without dreaming up numbers and doing the maths I'll consider it probable that a PSB is not the bet size with the best EV.

3. You have a 12-out draw on the flop and a lone Villain shoves the flop. Should you call?

If you have reason to believe that all 12 outs are clean - almost always. The odd chance that the villain is open shoving with something that you beat unimproved or something that you can beat if you improve to a simple pair or through a runner-runner makes it profitable to do so.
However, the villain open shoving on the flop makes it somewhat likely that he is drawing to the same kind of hand you are - a better flush (straight flush?) or a higher straight - which would tend to make your 12 outs not entirely clean. You really need to have at least the A of whatever suit you are going for, as well as the gutshot being to an A-high straight - and even then an A-high straight can be a split pot.
That said - not disputing krimson's calculation in his reply but considering the above I'd feel comfortable calling at least up to a pot sized shove with any 12-out combodraw, up to any size shove if I have the A of my suit and drawing to the royal flush of my suit holding a blocker for a lower straight flush (either Q, J or T of my suit)

[spoonitnow]

In my OP I noted that the two numbers we are usually worried about when deciding if most poker decisions are +EV are our risk-to-reward ratio and our chance of winning. Then I gave these three questions:

1. A lone Villain bets into you on the river and if you call you'll have a 25% chance to win. Should you call?
2. On the river you're out of position against a lone Villain. If you bet pot and Villain calls, you'll have a 25% chance to win. Should you bet pot?
3. You have a 12-out draw on the flop and a lone Villain shoves the flop. Should you call?

Some of you picked up on something, and some of you didn't: in all three of these questions given, you need more information to find an answer. I'm going to list the basic ideas in each and go on to something else.

1. If you are getting 3:1 pot odds (Villain bet half the pot) then you break even. If you're getting worse, you can't call profitably.
2. Here we don't know how often our opponent is folding or how often we win a showdown if we check, so we can't determine if betting is +EV.
3. Like the first question, you don't know your pot odds. Of similar importance though, we don't know the composition of our opponent's range, which could swing things a little either direction also.

Fairly often we see hands posted for suggestions with little or none of the poster's own analysis, and if you can't do this analysis away from the tables, you certainly can't do it while you are playing. I started off with these three questions to show why things like calculating your pot odds and putting your opponent on a range are so important: they give you the proper information to base your decisions on.

What I'm trying to encourage with this post is the following:

• The active accumulation of information (ie: consistently putting Villains on ranges instead of playing like a robot)
• Evaluation of decisions based on that information (ie: considering all of the relevant information, not just okay I have [insert hand here] so I call)
• Becoming engaged analytically away from the tables as well

Now what does this have to do with +EV decisions? The ability to identify them and act when the time comes.

[Ragnar4]

I'm going to take a moment before my morning sessions and make poker (and the math involved) really easy. In poker, we're usually concerned with finding two numbers and then comparing them. The first number is a risk-to-reward ratio, and the second number is our chance of winning. Different scenarios will have us calculating these two numbers in different ways. I'm going to give a few basic scenarios, let people reply, and then come back with some more questions.

1. A lone Villain bets into you on the river and if you call you'll have a 25% chance to win. Should you call?

---Depends on whether or not your getting better than 3-1 to call. Villan has to bet 49.99% of current pot for this call to be profitable.

2. On the river you're out of position against a lone Villain. If you bet pot and Villain calls, you'll have a 25% chance to win. Should you bet pot?

---If that's the only way you can win, yes. When you bet pot and your opponent calls and you win, you win 3 pots, when you lose, you lose one pot. So (100*.75)-(300*.25) = 75 - 75 which = zero. So if your villan folds even 1% of the time you make money over time. This is odd, I expected a different number here... my math is probably off.

3. You have a 12-out draw on the flop and a lone Villain shoves the flop. Should you call?

---Yes, because you have just about 50% equity, and all the money in the pot already is juice when you consider his shove to be 1-1 to your call after it all works out.

12/47 + (35/47 * 12/46) is your chance of making your draw

that's about 45% equity
so if your call represents more than 45% of the pot, it's EV-

we break even at 45%
his shove is 45%
the pot is 10%

so if the pot is less than 4.5 times our remaining stack we should call

[dranger7070]

1.) You should call if ur getting 4:1 on your money or better.
2.) Not sure honestly. I think it could go either way. You could bet pot, but you're making it so only better hands call/raise and worse hands fold. On the other hand, if your opponent folds 1/3 of the time you break even (i think) so like i said 50/50 for me.
3.) Depends on if you feel like gambling. You're about a 50% to win so if you feel like risking your stack on a coin flip call, if not, fold.

[kb coolman]

Now what does this have to do with +EV decisions? The ability to identify them and act when the time comes.

This is the best post ever, Spoon. Thanks for taking the time to set it up and break it down.

[Monty3038]

I'm going to take a moment before my morning sessions and make poker (and the math involved) really easy. In poker, we're usually concerned with finding two numbers and then comparing them. The first number is a risk-to-reward ratio, and the second number is our chance of winning. Different scenarios will have us calculating these two numbers in different ways. I'm going to give a few basic scenarios, let people reply, and then come back with some more questions.

1. A lone Villain bets into you on the river and if you call you'll have a 25% chance to win. Should you call?
2. On the river you're out of position against a lone Villain. If you bet pot and Villain calls, you'll have a 25% chance to win. Should you bet pot?
3. You have a 12-out draw on the flop and a lone Villain shoves the flop. Should you call?

I haven't read any of the responses yet, and I really want to learn, lately I've felt like I'm not making ANY progress... so here is my shot at it.

1. A lone Villain bets into you on the river and if you call you'll have a 25% chance to win. Should you call? Let's see, 25 Chance to win, means you will win 1 out of 4 times. So if you win 4x the bet when you do win, it is an even break, if you will win 5x the bet or more, you should call... correct?

2. On the river you're out of position against a lone Villain. If you bet pot and Villain calls, you'll have a 25% chance to win. Should you bet pot?
No. You can't bet enough by betting pot to get the correct pot odds of 5:1, correct? (see above answer)

3. You have a 12-out draw on the flop and a lone Villain shoves the flop. Should you call?[/quote] With 12 outs and 2 cards to come, you are about a 48% chance to win, making it pretty much a coin flip, personally I call, but often I'm not the brightest... it is probably the wrong answer on this one.

[Monty3038]

I haven't read any of the responses yet, and I really want to learn, lately I've felt like I'm not making ANY progress... so here is my shot at it.

1. A lone Villain bets into you on the river and if you call you'll have a 25% chance to win. Should you call? Let's see, 25 Chance to win, means you will win 1 out of 4 times. So if you win 4x the bet when you do win, it is an even break, if you will win 5x the bet or more, you should call... correct?

2. On the river you're out of position against a lone Villain. If you bet pot and Villain calls, you'll have a 25% chance to win. Should you bet pot?
No. You can't bet enough by betting pot to get the correct pot odds of 5:1, correct? (see above answer)

3. You have a 12-out draw on the flop and a lone Villain shoves the flop. Should you call?

With 12 outs and 2 cards to come, you are about a 48% chance to win, making it pretty much a coin flip, personally I call, but often I'm not the brightest... it is probably the wrong answer on this one. [/quote]

There seems to be some major disconnect in my math. I don't understand the 3:1 vs 5:1 on the first one, I am apparently running the numbers backwards... so it would seem the 25% chance is not one out of four times, but one out of three.. which to me would be 33% chance... see this is where I get so confused on this crap. I know I'm making it hard than it is, but for some reason the % just doesn't translate properly into 1 out of x so that I can come up with a comparison to pot odds... x:1

Back to square one...

And I'm also ticked because I started my answer for #3 with you don't know his range, then thought better of it because the 12 outs seemed like you were going just based on outs vs amount to call...

God I think I need to start over. No wonder I can't get past break even.

[killerkebab]

Monty, 25% is 1 out of 4, or 3 to 1 AGAINST happening... you see the numbers?

In the first case it implies that if we ran it 4 times we're likely to hit once. In the second case it implies that we'll miss three goes before we hit one.

1 in x chance = (x-1):1

[spoonitnow]

Quoting myself from another thread:

Tommy picks a marble from the bag. The odds against him picking a blue marble are 5:2 = 2.5:1. The chance of him picking a blue marble are 2/7 = 1/3.5 = 0.286 = 28.6%. In this example, we see that 2.5:1 = 1/3.5.

[PlayToWin]

God I think I need to start over.

Hey Monty - Check out this link. I thought it was well written.

http://entertainment.howstuffworks.c...poker-odds.htm

GL at the tables.