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Examining tournament EV

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  • Examining tournament EV

    Hi guys,

    Ive read this article http://www.pokerschoolonline.com/art...#order=popular and i dont understand some things.

    ''A decent guess is that this extra chance is worth about $500. That means 10,000 chips will be worth about $140 on average after the bubble - not counting the $300 every player will get after the bubble no matter what.

    You have 32,000 left which is 3.2 times 10,000. So your chips are worth about 3.2*$140 = $448.

    Therefore:

    Your total EV = [guaranteed prize for making it to the money] + [worth of your stack]
    = $300 + $448 = $748

    That means you will win about $750 on average if you fold''

    Question:
    -Why wont you guess like 600-800$ or something?
    -Where does that 140$ come from ?

    ''So your EV if you call and win = $1,400.

    The total EV of a call (factoring in the potential of winning and losing the pot) is the EV if you win multiplied with the probability to win plus the EV if you lose multiplied with the probability you lose.

    Here it is written as a formula:

    EV call = equity * [EV call and win] + (1-equity) * [EV call and lose]
    = (65% * $1400) + (35% * 0)
    = (65% * $1400)
    = $910

    Question:
    -Where does that 1400$ come from ?
    -Is ''Ev call and win'' and ''Ev call and lose'' is that the range of your opponent where you might against with?

    I hope that someone understand this,because I think it's a very usefull tool to play profitable at the bubble.

    Cheers!

  • #2
    I'm a little busy now, but I'll answer your questions later unless someone else gets in first.
    Bracelet Winner

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    • #3
      My head is hurting a little and it took me a while to understand all this math, although I think it's based on ICM (Independent Chip Model, google it). It took me a while to work out where the $140 in the first part came from. :/

      In case it's not clear, when you buy-in for $200 and get your chips, you have $200 of equity in the tournament, because you put $200 in to the prize pool. This equity is represented by your chips as a proportion of the total number in play. (If you had 50% of the chips in play, then you "own" 50% of the prize pool.)

      Imagine it's a heads up game. Both you and villain have 10,000 chips, and both paid $200 for them. That means that you have 50% of the chips in play, so "own" 50% of the prize pool (which totals $400). Your 10,000 chips give you $200 of equity in the tournament. If you lost half your stack, so you were down to 5000 chips, you'd only have 25% of the chips in play, so your tournament equity would be reduced to 25% of the prize pool. You'd now only have $100 of equity.

      Where does that 140$ come from ?
      Everyone that survives the bubble is guaranteed to cash for $300. All the min-cashes added together make up 30% of the total prize pool, which means that you're only playing for the remaining 70% of the prize pool. Since the buy-in was $200 for 10k chips, but 30% of the prizes have already been accounted for, 10k chips are now only worth 70% of the buy-in. 70% of $200 is $140.
      So if you had exactly 10,000 chips when the bubble bursts, you'd "own" $300 (guaranteed mincash) + $140 of chip equity for a total of $440 tournament equity.

      Why wont you guess like 600-800$ or something?
      I think the $500 mentioned on the page is based on the prize structure of the tourney. If you were the shortest stack, then it's very likely that you'll just mincash for $300, but if you're a bit further up the leaderboard, you might be in line for closer to $500.

      Where does that 1400$ come from ?
      If you call all in and win the pot, you'll have 70,000 chips.
      10,000 chips was what you got for your $200 buy-in, so 70,000 chips will mean you have 7 * $200 = $1400 of equity.

      Is ''Ev call and win'' and ''Ev call and lose'' is that the range of your opponent where you might against with?

      It's not the range, no, although you're on the right lines. It's the expected value when you calculate how often you'll win or lose when you call against a range.

      In the example on the page, villain is shoving 50% of hands (a very wide range!). Against a 50% range, 99 will win the hand about 65% of the time and lose 35% of the time. It's clearly a good call if you're going to win the hand as often as 65% of the time.

      I used Equilab to get the following stats:

      Equity Win Tie
      Hero 64.34% 63.96% 0.38% { 99 }
      Vill 35.66% 35.28% 0.38% { 22+, A2s+, K2s+, Q2s+, J4s+, T6s+, 96s+, 86s+, 76s, 65s, A2o+, K5o+, Q7o+, J7o+, T8o+, 98o }

      If villain was shoving a narrower (stronger) range, then 99 would have less equity than 65%. If villain was shoving the top 12% of hands, then 99 would be roughly flipping against that range, so it's a much closer decision when considering a call.

      The EV calculation is quite simple really. If we estimate that 99 will win 65% of the time, then 65% of the time, we increase our stack to 70000 (and our equity to $1400, as above), and 35% of the time, we lose all our chips and all our equity.
      So the total EV for calling is 65% of $1400 - 35% of 0, which is $910.

      No one is expected to be able to do this sort of math during a hand, but with experience you'll get a feel for when to make big laydowns or hero calls. One thing I sometimes do when near the bubble is look at my position on the leaderboard and then see where I'd be if I had a double up or if I lost half my stack or something like that. If that double up would mean I would win a much bigger prize, then I'm more likely to make a big call. Other times, I might notice that a double up won't radically alter my leaderboard position, and I might be better just folding and hope others go broke before I do, so that I can make a certain min-cash. Most serious tourney players will tend to make big gambles, because they recognise that the big money is at the top of the leaderboard. They aren't interested in min-cashing. They'd rather take a big flip and try and make the final table, or go bust trying.

      Hope this helps!
      Last edited by ArtySmokesPS; Sat May 04, 2013, 01:21 AM.
      Bracelet Winner

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