vinnie
Legend
Silver Level
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:
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.
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
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.