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EV calculation equation (Math geniuses please help)

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  1. deezy5821 deezy5821 is offline

    Lawrenceville, GA
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    Jul 22nd, 2011 (7/22/2011 10:46pm)

    Ive been reading and realized I really need to get into the math part of the game if I want to take my game to the next level. I'm not sure how to calculate EV in spots where I'm not risking my all in life. Lets say the blinds are 150/300 50 ante and I raise in the HJ with 67s and get 3bet on the button and I'm assuming hes doing this with 25% of hands how do i figure out if a 4bet is +EV against his 5bet all in range assuming it would be 3.5% of his range against this given player?
     
  2. Riverhorse Riverhorse is offline

    Gardner, KS
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    Jul 22nd, 2011 (7/22/2011 10:53pm) in reply to deezy5821

    if you assume his 5 bet shove range is 3.5% of his total range then what percentage of the time do you think your your 67s is ahead?
  3. deezy5821 deezy5821 is offline

    Lawrenceville, GA
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    Jul 22nd, 2011 (7/22/2011 11:04pm) in reply to Riverhorse

    Thats not what I'm trying to figure out I'm trying to figure out how EV the situation is of times I get him to fold with a 4bet vs times I lose chips against his 5bet all in
     
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  4. Frank Hough Frank Hough is offline

    Rochester, MN
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    Jul 22nd, 2011 (7/22/2011 11:23pm) in reply to deezy5821

     
    Originally Posted by deezy5821 View Post

    Ive been reading and realized I really need to get into the math part of the game if I want to take my game to the next level. I'm not sure how to calculate EV in spots where I'm not risking my all in life. Lets say the blinds are 150/300 50 ante and I raise in the HJ with 67s and get 3bet on the button and I'm assuming hes doing this with 25% of hands how do i figure out if a 4bet is +EV against his 5bet all in range assuming it would be 3.5% of his range against this given player?

    If the 25% figure for the 3 bet and the 3.5% figure for the 5 bet are actually correct, and you assume he never flats your 4 bet, then it will be correct to 4 bet for the equity every time. The first thing to notice is that if he 3 bets 25% and only 5 bets 3.5% and never flats your 4 bet then he would have to be folding to your 4 bet (25 - 3.5) / 25. So he is folding to the 4 bet 21.5 / 25 times, so I am guessing your numbers probably aren't quite right; a 25% 3 betting range is very hi unless you are hu. If your numbers are right then he's folding 21.5 / 25 times, multiply both by 4, he is folding 86% of the time, so you will always have great fold equity. If it was a closer decision then you need to look at the size of your 4 bet relative to what you are winning if he folds and compare it to the % of time he's folding, just like your looking at pot odds. Hope this helps.
  5. ManchVegasPwn ManchVegasPwn is offline

    Manchester, NH
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    Jul 23rd, 2011 (7/23/2011 1:07am) in reply to Frank Hough

    doubt the structure on merge is deep enough to be looking for spots to 4b/f... I'm assuming you're playing on there
     1
  6. double_kyan double_kyan is offline

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    Jul 23rd, 2011 (7/23/2011 8:13am) in reply to ManchVegasPwn

     
    Originally Posted by ManchVegasPwn View Post

    doubt the structure on merge is deep enough to be looking for spots to 4b/f... I'm assuming you're playing on there

    i'm strictly merge right now and i was just thinking these thoughts as far as stack size / structure go on merge
     1
  7. Frank Hough Frank Hough is offline

    Rochester, MN
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    Jul 24th, 2011 (7/24/2011 11:57pm) in reply to double_kyan

    I want to take a few minutes to clarify how to calculate the break even point for re-stealing and then also discuss how we know what ranges of hands our opponents are likely to have if we know what percentage of hands they have in a particular spot.
    First of all, to clarify my response to the original question, I want to discuss the break even point for re-stealing. For simplicity sake lets assume we are heads up on the sb for blinds of 50/100. We open to 300 total, the bb 3 bets us to 900 total, and we consider a 4 bet bluff to 2700 knowing that if our opponent does not fold we will lose the hand. When we are considering the 4 bet to 2700 it is important to realize that there would be 1200 in the pot (300 + 900) and we are risking 2400 (2700 - 300) to try and win 1200. Therefore for this to be a profitable 4 bet bluff we would need our opponent to fold 2400 / (1200 + 2400) times. So we need our opponent to fold 24/36 or 2/3 times.
    Also consider that if the 4 bet would be an all-in for us then we would have some expected equity in the hand if the opponent decided to call. So instead of 4 betting and giving up when our opponent doesn't fold, lets say it's the same situation, we open to 300, get 3 bet to 900, and we are considering 4 betting all in for 4000 (I changed this from 2700 because our opponent would probably snap call our all-in if we went to 2700, he's getting 2:1). Lets say we have something like low to middle suited connectors or 1 gappers so we can assume we are about a 30/70 underdog to his calling range. Let's say that we expect him to call 40% of the time. Notice we have invested 300, there is 1200 in the pot, and our 4 bet costs us 3700 more. So if he doesn't call then we earn 1200 and if he does then we have 30% value of the 8000 chip pot. In this case our EV calculation for the push is 0.60 * 1200 + 0.40 * 0.30 * 8000 = 1680, meaning we have 1680 expected value from the shove that costs us 3700 to make, and therefore we are losing an average of 2020 chips every time we make this play.
    I also want to talk about how we know what our opponents ranges of hands are based on the percentage of hands they have in a given spot. I cannot emphasize enough how important this is for everyone to understand.
    Each specific non-pair combination makes up 8/52*4/51 = 0.012066 or 1.2% of a range. Each specific pair makes up 4/52*3/51 = 0.004525 or 0.45% of a range. This can easily be proved since there are 78 possible combinations of unpaired hands and 13 possible pairs. The proof is 78*0.012066 + 13*0.004525 = 1 or 100%.
    This is how we can estimate hand ranges. Lets use the example in the original post about him folding everything besides 3.5% of his range to the 5 bet. If we have a large sample size, so we can assume 3.5% is an accurate percentage of hands, then we know the only hands he can have are going to be something close to AA, KK, QQ, JJ, TT and AK. We can easily estimate this because each paired hand makes up 0.45% of the range and each non-pair makes up 1.2% of the range. There are 5 hands which make up 0.45% each and 1 which makes up 1.2% so we figure 5*0.45 + 1*1.2 = 3.45. So we know that if our opponent was only playing AA, KK, QQ, JJ, TT, and AK then his range, with a reliable sample size, would be 3.45%. You can do this yourself by multiplying 0.45% for each pair in someone's range and 1.2% for each non-pair in their range and determine what types of hands your opponent has if you have something like PokerTracker which compiles your opponents statistics for you. By the way, if you want figure in only suited hands, like if your opponent will open with suited 67 but not 67 off, then that specific hand being suited takes up 1.2% * 12/51 = 0.282% of the range.
    I hope this is helpful to some people, and I will check the thread periodically if anyone wants to post a reply with questions or whatever.
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