Understanding Pot Size [Related] Raises: And Why BetOnline Has It Wrong

vinnie

vinnie

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Warning: Math ahead, and details.

Tonight, while playing in the freeroll, I noticed that BetOnline's "1/2 Pot" and "2/3 Pot" betting amounts were incorrect in raising situations. This isn't shocking. It's not even the first time that I have found a site doing it wrong. Getting the numbers correct requires understanding what the purpose of Pot Size Related Bets and Raises is.

We size our bets in relation to the size of a pot in order to offer the most committed player specific odds.

Note: This has nothing to do with No-Limit or Pot-Limit aside from the fact that Pot-Limit gives us a hard cap on the worst specific odds we can offer to the most committed player.

Let's get a sample game. I'm playing heads up $1/$2. I raise to $6 and my opponent calls. The pot, on the flop is $12. If my opponent checks to me, I can bet the following amounts:
  • $12 (Full Pot) :: Opponent offered $24:$12 or 2:1
  • $9 (3/4 Pot) :: Opponent offered $21:$9 or 7:3
  • $8 (2/3 Pot) :: Opponent offered $20:$8 or 5:2
  • $6 (1/2 Pot) :: Opponent offered $18:$6 or 3:1
  • $4 (1/3 Pot) :: Opponent offered $16:$4 or 4:1
I can bet other amounts. But these give you an idea. A quick way to calculate the odds you are offering is to take the fraction of the pot, add the numerator and denominator, and then the numerator is the other side. An example. If you bet 3/8 the pot you would be offering odds of (3+8):3 or 11:3.

Alright, still with me? We bet fractions of the pot to offer specific odds. This gets a little tricky when it comes to raising. If my opponent leads into me for $6, I have to raise $30 to give him odds of 2:1. If I raise to $30, he has to call $24 and there is ($12+$6+$30) or $48 in the middle. $30 is way more than the $18 that the pot size looks like.

A pot sized raise needs to be an amount equal to the pot after you call ABOVE the amount you need to call. The amount needed to call is $6. The pot will be $24 after I call. I need to raise to $6+$24 or $30. BetOnline does this correctly. If you hit the pot button, it will get you the correct pot size.

It is the next step that it gets wrong. Figuring out a 1/2 pot bet, when there is no raise, is easy. It's half the amount of a pot-sized bet. If the pot is $12, a half pot bet is $6. Does this same logic work if facing a raise?

$12 pot and the other player leads for $6. A pot sized raise is $30. Is a half-pot raise $15? (BTW: This is how BetOnline calculates it, so you probably already know the answer.)

If raising to $15 offers 3:1 pot odds to the last person to bet, call, or raise (the most committed player), then it is half-pot. But, the other player only needs to call $9 and the pot is ($12+$6+$15) $33. They are getting 11:3, approx 3.7:1. Those aren't the right odds! The same thing happens when BetOnline goes to calculate a 2/3 pot bet. It would say that pot is $30, so $20 is 2/3 pot. 2/3 pot should be 5:2 but we get ($12+$6+$20) $38 to $14 or 19:7 which is ~5.4:2...

We aren't offering the odds we are promised that we should be offering! So, how do we fix that? We start by calculating what a pot-sized RAISE would be. Here we know it is $24. We raise $24 on top of the $6 to make $30. And, then we take the fraction of that!

Let's see it in action. Same $12 pot and the opponent leads for $6. After we call the raise, the pot would be $24. Half of that is $12. So, we raise $12 on top of the $6 to $18. Now our opponent is being offered ($12+$6+$18) or $36 to the $12 he needs to call, which is 3:1. How about 2/3 pot? Same thing. 2/3 of the $24 raise is $16. So, we raise $16 on top of the $6 to $22. Opponent needs to call $16. That means he is being offered ($12+$6+$22) $40 to $16, which is 5:2!

I know this seems like a minor implementation detail, but it's not. It goes to the heart of what Pot Size Related Bets and Raises are supposed to do. They are supposed to set a specific price for that last person (still in the hand) to act before you. Of course, other players might be getting a worse price (if they checked and there is a bet and a raise, they have to call more for the amount out there). And, if someone calls behind you without raising, then the person will actually get a better price when it arrives back at him. Still, you set a price for that player, and it should be the right price.

If you are clicking the button, and it's not raising enough, you're not setting the price you intended to.

Ignoring the fact that the site does this wrong, this is still important to know and realize. If you really think about the price you want to lay someone, you can use this knowledge to help figure out your bet size to maximize the difficulties of your opponent's decision. You can bet an amount that almost offers him the correct price.
 
darthdimsky

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Alright, still with me? We bet fractions of the pot to offer specific odds. This gets a little tricky when it comes to raising. If my opponent leads into me for $6, I have to raise $30 to give him odds of 2:1. If I raise to $30, he has to call $24 and there is ($12+$6+$30) or $48 in the middle. $30 is way more than the $18 that the pot size looks like.

A pot sized raise needs to be an amount equal to the pot after you call ABOVE the amount you need to call. The amount needed to call is $6. The pot will be $24 after I call. I need to raise to $6+$24 or $30. BetOnline does this correctly. If you hit the pot button, it will get you the correct pot size.

......
......

We aren't offering the odds we are promised that we should be offering! So, how do we fix that? We start by calculating what a pot-sized RAISE would be. Here we know it is $24. We raise $24 on top of the $6 to make $30. And, then we take the fraction of that!

Let's see it in action. Same $12 pot and the opponent leads for $6. After we call the raise, the pot would be $24. Half of that is $12. So, we raise $12 on top of the $6 to $18. Now our opponent is being offered ($12+$6+$18) or $36 to the $12 he needs to call, which is 3:1. How about 2/3 pot? Same thing. 2/3 of the $24 raise is $16. So, we raise $16 on top of the $6 to $22. Opponent needs to call $16. That means he is being offered ($12+$6+$22) $40 to $16, which is 5:2!

Sorry for resurrecting an old post I spent about an hour digesting the content in this one. :smile:

Vinnie, for the sake of my own mental math, nothing else, I've used this formula in a few instances and it seems to hold water. I've used these because these are the known variables at the time of our call

Pot sized raise:
Current pot + (lead x 2)

Examples:

Current Pot = 018 :: Lead = 06 :: Bet = 030 [018 + (06x2)]
Current Pot = 140 :: Lead = 60 :: Bet = 200 [140 + (60x2)]
Current Pot = 134 :: Lead = 54 :: Bet = 242 [134 + (54x2)]
 
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darthdimsky

darthdimsky

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K. Just realised that this only works if you want to offer 2:1 odds. Your recommendation, after re-reading the last para quoted, is simply the best way to go if you want to offer other ratios. Thanks for the informative read :)
 
vinnie

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Yeah, they have full pot-sized raises correctly done. So, if you want to offer 2:1, you can safely use their buttons. If you're looking at offering different, but specific odds, you aren't going to be successful with their 1/2 pot and 2/3 pot buttons (if there is a bet or raise in front of you).

In PLO, there are very few times when I am willing to offer better than 3:1 when I raise. Full pot (2:1) might be more than I think I can get, but I won't offer better than (3:1) except in very rare spots. If I am facing a bet, I can't rely on BOL's 1/2 pot button to give me the right amount for my minimum. Fortunately, I can figure the numbers right in my head pretty quick. I use the buttons for a quick sanity check to make sure I didn't make a mistake--which is how I caught this in the first place, because I was getting different numbers way more than usual.

It is still important to know what a pot-size-related bet or raise is supposed to do. That is, that it is designed to offer specific odds to a specific player or players. If you bet 1/3 pot, you are offering 4:1 odds to someone, intentionally or not. If you mean to bet 1/3 pot, but bet less than that, you're giving better odds than you wanted.
 
quick

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Great tips. I noticed this happens on other sites too. Seems like giving an "almost" good price on many draws would be 2/3s or slightly more of the current pot, but you're right you need to adjust it up to account for other players yet to act who may flat call your raise giving the next person to act better odds. Best to ramp up your bet higher than the almost good price when there's more than one person left to act.
 
vinnie

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Great tips. I noticed this happens on other sites too. Seems like giving an "almost" good price on many draws would be 2/3s or slightly more of the current pot, but you're right you need to adjust it up to account for other players yet to act who may flat call your raise giving the next person to act better odds. Best to ramp up your bet higher than the almost good price when there's more than one person left to act.

Well, I wasn't really talking about the risk of someone flatting your raise behind you. That's part of why my original post talks about heads up situations. That is a different consideration than the one about relating your bet-sizes to the size of the pot.
 
terryk

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amazing,this post got no interest first time around,thx for reserrecting it Dims,and as always great post,vinnie:stupido2:
 
vinnie

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I wasn't shocked, really, when it got no interest. It was an esoteric math-based post that focused on a problem that involved thinking of bet-sizing in a way that most players aren't really focused on. I thought about writing BOL to see if they would fix the issue, but decided against it. It benefits me when players bet less than they intended to. So, fixing it would only make certain spots tougher against players who aren't thinking carefully about their sizing.
 
terryk

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Well,as much as i enjoy the `fav snack while playing posts`:eek: i enjoy posts that make me think,more:),respect.
 
darthdimsky

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What I found very interesting was that despite no replies there were exactly 500 views when I posted last. So quite a few people had read it it seemed. It's gone up by 150+ more views since.
 
vinnie

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I did notice that, also, after I originally posted it. It got a bunch of views, a couple hundred, in the first week, but no one responded to it. I figured it was just not interesting to most people, or they had nothing to say about it. Not a big deal. I am sure a lot of my posts aren't interesting to many people here.
 
darthdimsky

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That's a very self effacing way of looking at it I think. I'm pretty sure it's because the amount of effort you put in is just so extensive that a casual comment would seem out of place.

I mean I found it intimidating when I started reading it. I had to step outside for a smoke when I had a eureka moment and started to really understand it. Even that one hour wasn't enough because I had completely missed the last para that contained your practical solution. It's just that advanced a concept for a novice - mid level player like me.
 
vinnie

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That could also be true. I also chose to put it in "Learning Poker" because I considered it something related to learning, but it is more complicated than the typical posts you find in this section. So, the audience that ran across it might have considered it beyond where they were at the moment, or at the very least, something that they didn't have anything to contribute to.

I was hoping that people found it useful or that it built their understanding. If 100 people found that it helped improve their thinking regarding how they sized their bets but none one responded to the thread, it would still be a good post in my mind.
 
darthdimsky

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Also the audience. Higher concentration of new players browsing this sub forum than usual say the ones in the leagues or the hand histories. I actually subbed to it first and archived it in a sub folder reserved for useful info. Didn't, at first, intend to reply to it until that eureka moment. :p
 
M

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Being a newbie to BetOnline and not having played in ages, this post really helps!! Thanks for that. I am not great at the math part but am studying to improve that part of my game. Going to implement your info at the site. Thanks so much!!!
 
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