All-in equity with rake taken into account

    • GreenPiece
      GreenPiece
      Bronze
      Joined: 03.06.2010 Posts: 5,962
      Hi everyone!

      Been searching google for the subject, got links to other forums and this one as well but didn't find the answer to the question.

      It's better be shown with the example. Let us take the very first level of HU HT SNGs on PStars as their rake is the highest among all stakes for this type of tournaments at this site, it is 4%. So we have the very first hand with 500 in chips (25 ES) and the opponent goes all-in. If we don't have rake we could probably call him with 50% equity but if we do it with 4% rake for say 100 times in a row at this very situation we end up losing. So we need to adjust our ranges for our hands to have 52%+ equity vs the opponent's. Is this logic flawless?

      Let's take it a bit deeper. Say we're 250 in chips (1000 chips to gather to win the tournament) and our opponent goes all-in again (12.5 ES). We can't say for sure we need exactly 52% to be break even as the tournament is not over after we win. It is taking more time for us to win passing the opportunity playing another tournament thus affecting our hourly winrate... And not only this.

      We can wait for better opportunities being 25bb deep passing some marginal (taking rake into account) +EV situations for better ones throughout the game. The logic behind this is that we don't want to risk the whole tournament before we are really forced to do so, we want to convert our small edges into chips without investing all the chips. When we're 12bb deep we don't have that many opportunities as with 25bb, we can't easily convert small edges (minraising, cbetting etc.) without risking the whole stack so we probably want to lower our requirements for all-in equity even with 4% rake.

      In this thread people suggest to set edge in SNG Wizard to 0, maybe slightly in plus, like 0.1. What does it mean in terms of the original question? It means that if SNG Wizard suggest to call all-in with 50% (ok, maybe 50.1% or 50.2%) equity being 25bb deep (playing of course tournament with 4% rake) then hero should take the opportunity. They say all the calculating errors when putting the opponent on certain range, seeing more plus EV opportunities ahead and so on - all these factors compensate each other and we can neglect the edge. It seems wrong to me but maybe it is right.

      Any thoughts are highly appreciated and welcome!

      Another good thread on the topic can be easily found with search query "HUSNG Theory - Rake, tournament equity and hourly rate" (can't post links to external forums here). I think I'm getting what the author wants to say but I'd like to see ideas of other people as well.
  • 3 replies
    • VorpalF2F
      VorpalF2F
      Super Moderator
      Super Moderator
      Joined: 02.09.2010 Posts: 8,979
      Originally posted by GreenPiece
      It's better be shown with the example. Let us take the very first level of HU HT SNGs on PStars as their rake is the highest among all stakes for this type of tournaments at this site, it is 4%. So we have the very first hand with 500 in chips (25 ES) and the opponent goes all-in. If we don't have rake we could probably call him with 50% equity but if we do it with 4% rake for say 100 times in a row at this very situation we end up losing.[1] So we need to adjust our ranges for our hands to have 52%+ equity vs the opponent's. Is this logic flawless?[2]

      Let's take it a bit deeper. Say we're 250 in chips (1000 chips to gather to win the tournament) and our opponent goes all-in again (12.5 ES). We can't say for sure we need exactly 52% to be break even as the tournament is not over after we win. It is taking more time for us to win passing the opportunity playing another tournament thus affecting our hourly winrate... And not only this.

      We can wait for better opportunities being 25bb deep passing some marginal (taking rake into account) +EV situations for better ones throughout the game. The logic behind this is that we don't want to risk the whole tournament before we are really forced to do so, we want to convert our small edges into chips without investing all the chips. When we're 12bb deep we don't have that many opportunities as with 25bb, we can't easily convert small edges (minraising, cbetting etc.) without risking the whole stack so we probably want to lower our requirements for all-in equity even with 4% rake.
      [1]To CALL a shove you need an edge. Let's say for example that villain shoves with the top 60% of all hands. If you are calling vs that range, you want to be calling with a range that wins more than 52% of the time, which is a tighter range. The open shover has some fold equity, so he can be a bit wider.
      [2]The logic is OK as far as I can tell, except as noted above. I would run these things through Holdem Resources calculator to find out what the real numbers are.

      To boil it down:
      If you call with the same range as the pusher, you will lose in the long run as you point out.

      Relative stack sizes matter too.
      If you ever get more than 2/3 of the chips, you can shove any two (I think) because villain needs now to win two AIs in a row to win, you only need to win one.

      I don't play the HU HTs any more. It felt too much like gambling, and I was a bit too tight, and didn't call *enough* pushes.

      Cheers,
      --VS

      Cheers,
      --VS
    • GreenPiece
      GreenPiece
      Bronze
      Joined: 03.06.2010 Posts: 5,962
      Thank you for your reply! Useful thoughts are always welcome :)

      Originally posted by VorpalF2F
      The open shover has some fold equity, so he can be a bit wider.
      Do you mean that if both players use Nash equilibrium then actually the shover widens his range and the caller tightens? I mean that it seems theoretically ok but in practice (especially at lower stakes) very few people if any at all adjust their ranges because of rake concern.

      Originally posted by VorpalF2F
      Relative stack sizes matter too.
      If you ever get more than 2/3 of the chips, you can shove any two (I think) because villain needs now to win two AIs in a row to win, you only need to win one.
      So if to bring it to numbers, if SNG Wizard shows that your expectation in the situation when you have 3/4 of the chips is -1 chip then would you make this move? Would you make slightly negative move because of chip advantage? And if yes then to what extent and is there some math behind it?

      I understand that you do not play these tournaments anymore so you may have no ready answers but please share anything you feel appropriate.
    • VorpalF2F
      VorpalF2F
      Super Moderator
      Super Moderator
      Joined: 02.09.2010 Posts: 8,979
      If you have a look at this chart:
      http://www.holdemresources.net/h/poker-theory/hune.html
      You will see that the caller's range is tighter than the pusher's range.
      Be sure to read the links "Using the Nash Charts" and "About the Solution" -- good info in there.

      The chart may be outdated -- I don't think people push 20BB stacks any more, Especially with 22-55 -- or do they?

      Trying to rely on Nash when your opponent is unaware that the concept even exists is a recipe for disaster. In that case, you MUST play exploitively. Or am I wrong about that?

      What is YOUR image? Will your shove get a fold? If so, shove wider.
      Will opponent typically defend wide against you ? If so, tighten up.

      I never used SnG Wizard -- when I wanted the Nash equilibrium for a particular hand I used the Web Calculator from the same site.

      Here is an example from a HUHT Note that SB is shoving 66%, and BB is calling 50.8% What is REALLY interesting to me is that if you reverse the stack sizes, the ranges don't changes.

      If you increase SB's lead to 780:220 BOTH ranges widen.

      The above site is parent for HoldemResources Calculator (the link takes you to PokerStrategy.com's download page for it).

      I don't know that rake is considered at all.
      The question is: To improve your win rate, do you push (or call) tighter or wider?
      To answer THAT you need to know your opponent, I think.

      Cheers,
      --VS