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 Post subject: heads up sng cEV vs $EV
PostPosted: Sat Feb 01, 2014 7:57 am 
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Joined: Thu May 23, 2013 11:35 pm
Posts: 23
does cEV = $EV in a heads up sng?

this site says it does but offers no proof (or even an argument):
http://www.tournamentterminator.com/tou ... tegy-sage/

"The ratio between the number of chips and the theoretical claim in price money is now linear as in cash games."

this site says they are different
http://www.husng.com/content/22-flawed- ... usng-poker

"While I will concede there are sometimes very small differences where a stack of t1000 might not be worth exactly twice as much as a stack of t500 in a HUSNG,..."

I ran a coin flip simulation with stack sizes of 2. And indeed you have 25% chance to win if you have a stack size of 1. (The math is not obvious to me)

Thoughts?


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PostPosted: Sat Feb 01, 2014 3:22 pm 
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Joined: Wed Dec 04, 2013 12:40 am
Posts: 49
You ran a simulation based on the ICM hypothesis, but that's not how we play.
Change it to make position matter for example and it will alter the results :P


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PostPosted: Mon Feb 03, 2014 5:01 pm 
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Joined: Sun Mar 10, 2013 10:31 am
Posts: 139
May be its your mistake in coding.
Code:

#include <cstdlib>
#include <iostream>
#include <ctime>

using namespace std;

int main(){
      
   int deals_first_win = 0;
   int deals_second_win = 0;
   int tourney_first_win = 0;
   int tourney_second_win = 0;
   int iterations = 10000;

   srand(time(0));

   cout<<"start simulation\n";

   for (int iteration=0; iteration<iterations; iteration++){

      int stack_1 = 1;
      int stack_2 = 2;

      cout<<"Simulates tournament #"<<iteration<<"\r";

      while ( (stack_1 > 0)&&(stack_2 > 0) ){

         int winner = rand()%2;

         if (winner == 0){
            stack_1++;
            stack_2--;
            deals_first_win++;
         } else {
            stack_2++;
            stack_1--;
            deals_second_win++;
         }
      }
      if (stack_1 == 0) tourney_second_win++;
      if (stack_2 == 0) tourney_first_win++;
   }
   
   cout<<"tournament simulated: "<<iterations<<endl;
   cout<<"Tournament win by first: "<<tourney_first_win<<endl;
   cout<<"Tournament win by second: "<<tourney_second_win<<endl;
   cout<<endl;
   cout<<"Deals win by first: "<<deals_first_win<<endl;
   cout<<"Deals win by second: "<<deals_second_win<<endl;
   cout<<endl;
   cout<<"tournaments wining first ratio: "<<(double)tourney_first_win/(double)iterations<<endl;

   getchar();
   return 0;
}


For stack sizes 1 and 2 chips:
Image

For stack sizes 10 and 20 chips the same image
Image

p.s. is there spoiler tag?


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PostPosted: Mon Feb 03, 2014 10:35 pm 
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Joined: Wed Dec 04, 2013 12:40 am
Posts: 49
Didn't see the mistake, not 25% with stack sizes 1 and 2 but one third indeed.

When all hands are instant all-in, ICM predictions will be verified.
And even when you chose a random value of exchanged chips for larger stacks.

If you try to introduce asymetric advantages, you will induce variations.
It means that you consider that your $Stack depends not only on your cStack (but on position too for example)

If you believe there are asymetric advantages in HU, then $EV != cEV


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PostPosted: Tue Feb 04, 2014 7:45 am 
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Joined: Thu May 23, 2013 11:35 pm
Posts: 23
perhaps I was unclear in my first post.

I meant that if starting stacks were 2 and you have 1 ( meaning your opponent has 3) then your win % is 25%, which confirms that cEV = $EV.

I have a hard time convincing myself that position matters.
Lets say you're in BB, opponent shoves all in. you work out that calling gives you +0.1 BB. folding gives you -1BB obviously. Lets say you also know that in SB you expect to win 1.3BB (1.3BB-1BB > 0.1BB therefore folding is better??). Does this mean you should fold as BB? I don't know, because after your SB hand, you have to play another BB hand.

edit: Actually it's impossible to win 1.3BB as SB because BB can simply always fold and only lose 1BB per hand. therefore my example never works.

Can you think of another example?


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PostPosted: Tue Feb 04, 2014 9:49 am 
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Joined: Wed Dec 04, 2013 12:40 am
Posts: 49
Ok for 25% then.

Don't think about the EV you have once you look your cards and chose your move (strategic) but before (the hand utility).
It could be something like +0.01 bb for SB in a Nash Equilibrium for a given stack size.
This small +EV is computed knowing the strategies of both players.
You have to consider a Nash Equilibrium strategies if you want to study the general case because it gives you a guaranteed minimum EV against any opponent.
Nash Equilibrium are considered as reference strategies that provide a base EV.

In SNG this small +EV for SB means that the probability distribution of hand's end stacks size when playing the equilibrium (both players) is ponderated in a manner SB has (a little bit) more chances to grow.
You can put this in a simulation by modifying your coin flip probability according to the EV for each situation of a SNG at a known level (position / stack distribution).
You'll see your $EV != cEV

When you talk about the EV of pushing/calling, don't forget that the chosen moves for SB and BB depends on their cards, you can't look at the EVs ignoring the cards to decide what to do!


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