High Stakes Poker - Gold vs Antonius (Contains spoilers)

[RichEO]

Surely the more times it is run the closer to the actual win percentages for each player to win the pot will be achieved. However when they run it more than once on HSP the turn and river cards are not shuffled back into the deck therefore on each running the percentages for the next running are not the same as they were on the original flop. Therefore I dont think there is a conclusive answer as to whether its a positive or negative running it more than once other than to say it cuts down on variance.

Not shuffling the outs back in means that whoever is drawing has less chance. It obviously doesn't affect the chance if they miss the 1st time, but the times when they hit on the 1st or 2nd card decreases their chances on the other cards where it shouldn't.

[Longy]

I haven't done the maths but i would bet a reasonable amount that running this n (where n is any number) times doesn't effect our EV. Surely this is common sense, ev is an expression of our long term expectation and therefore each trial simply has the same ev ,admittedly the 2nd trial is effected by the first but as we don't know what the outcome of the first trial is, these probability balance one another.

I mean do you think some like Patrik Antononius (sp?) wouldn't be aware of such a fact and therefore would delibritley choose a number which benefitted his EV, instead of having a bit of "It doesn't matter" attitude about how many times they ran it.

*Curses that he is thrown away his probability and statistics uni notes*

[totalise]

no it doesn't affect the EV of the hand, but there are advantages/disadvantages to running it twice, or rather, being known as a person that will run it more then once.

if you are a nit, its good to do it, and if you are a good loose aggressive player, its a bad idea to do it, because people sometimes get more inclined to call if they know they are gonna get to see more cards.

[Longy]

Running once, Gold's chance of winning is 22.7%

So he wins 0.227p where p is the pot size.

Running 3 times:

Gold's chance of winning all 3 is 0.0084
winning 2 out of 3 is 0.1109
winning 1 out of 3 is 0.2272

So overall:

0.0084p + 2/3 0.1109p + 1/3 0.2272p = 0.0084p + 0.0739p + 0.0757 = 0.158p

Running it 3 times puts Gold at winning 16% on average instead of 23% !!!

I think I got it right, and well I think that's quite a big difference.

Obviously if you're drawing you get less outs as you continue so your chances are shot at. Better for the made hand to run it more times - for example (to the extreme though..!) Gold has 10 outs in this hand. If they ran it 20 times, Antonious would be certain to win 10 of those as there aren't enough outs for Gold to win more than 10, he has won 50% for certain, he now has good chances of winning the other 10 too!

Hmmm i don't think this is right. Given that we don't shuffle cards back in the deck i get Gold's chance of winning 1 of the 3 trials at 42.4%.

52 cards 8 already known so 44 left in the pack. Gold has 10 good cards, Patrik 34.

I drew a tree diagram (the old maths teacher in me lol) and he can win on either the 1st,2nd or 3rd trial. So all branches of the tree will have the same probability just different denominatiors and numerators. It comes out to be (10/44) * (34/43) * (33/42) = .141 and then multiply that by 3. Give us 42.4% (rounded).

Winning 2 i get a similar number 11.6%

Winning 3 i get .9%

So (.424 * 1/3)p + (.116 *2/3)p + 0.09p= 22.7% voila.

Any queries and question stay behind please.

Caveat i probably made an arse of this like my degree, sigh.

[Rupert]

EV doesn't change, just variance.  The run it 20 example pretty much proves that your actual monies received just tends towards your expected value.  It just lowers variance since you run the situation for multiple smaller pots.  Flipping 2 coins for $5 each has lower variance than flipping 1 coin for $10.

[The_duke]

Running once, Gold's chance of winning is 22.7%

So he wins 0.227p where p is the pot size.

Running 3 times:

Gold's chance of winning all 3 is 0.0084
winning 2 out of 3 is 0.1109
winning 1 out of 3 is 0.2272

So overall:

0.0084p + 2/3 0.1109p + 1/3 0.2272p = 0.0084p + 0.0739p + 0.0757 = 0.158p

Running it 3 times puts Gold at winning 16% on average instead of 23% !!!

I think I got it right, and well I think that's quite a big difference.

Obviously if you're drawing you get less outs as you continue so your chances are shot at. Better for the made hand to run it more times - for example (to the extreme though..!) Gold has 10 outs in this hand. If they ran it 20 times, Antonious would be certain to win 10 of those as there aren't enough outs for Gold to win more than 10, he has won 50% for certain, he now has good chances of winning the other 10 too!

Hmmm i don't think this is right. Given that we don't shuffle cards back in the deck i get Gold's chance of winning 1 of the 3 trials at 42.4%.

52 cards 8 already known so 44 left in the pack. Gold has 10 good cards, Patrik 34.

I drew a tree diagram (the old maths teacher in me lol) and he can win on either the 1st,2nd or 3rd trial. So all branches of the tree will have the same probability just different denominatiors and numerators. It comes out to be (10/44) * (34/43) * (33/42) = .141 and then multiply that by 3. Give us 42.4% (rounded).

Winning 2 i get a similar number 11.6%

Winning 3 i get .9%

So (.424 * 1/3)p + (.116 *2/3)p + 0.09p= 22.7% voila.

Any queries and question stay behind please.

Caveat i probably made an arse of this like my degree, sigh.

You two have just got to get out more 

[Moskvich]

I haven't done the maths, but I can't see that it would change the EV. If you did take it to the extreme, and ran it 44 times with no burn cards, you'd obviously end up with your EV from the pot, and eliminate variance altogether (apart from the effect of the first burn card). The more times you run it, the closer you get to that extreme.

[RichEO]

I give up.

Still not sure

[AlexMartin]

The only way i see it affecting EV and not just reducing variance is the fact that cards are not reshuffled into the deck. Nice lessons RicheO and Longy (esp tree diagram  bit .

Its very interesting that after running it a certain no. of times Antonius is GAURANTEED to at least break even. Remind me of that when im playing next year...

[Woodsey]

Do all the maths you want but I doubt even these guys will play enough $750k pots in a lifetime to be able to even out variance at that level by whatever means.

[totalise]

The only way i see it affecting EV and not just reducing variance is the fact that cards are not reshuffled into the deck. Nice lessons RicheO and Longy (esp tree diagram  bit .

Its very interesting that after running it a certain no. of times Antonius is GAURANTEED to at least break even. Remind me of that when im playing next year...

whats interesting about that?  if he runs out all the cards in the deck hes GUARANTEED to get 73% of the pot

it doesn't affect EV. Period. Think about what the E in EV stands for.

[RichEO]

Alex[/url] Martin link=topic=28916.msg592181#msg592181 date=1195174373]
The only way i see it affecting EV and not just reducing variance is the fact that cards are not reshuffled into the deck. Nice lessons RicheO and Longy (esp tree diagram  bit .

Its very interesting that after running it a certain no. of times Antonius is GAURANTEED to at least break even. Remind me of that when im playing next year...

whats interesting about that?  if he runs out all the cards in the deck hes GUARANTEED to get 73% of the pot

it doesn't affect EV. Period. Think about what the E in EV stands for.

Electron?

[The Sweeney]

is there any advantage in running it 2/3 times?

Not EV wise but it does reduce varience which is an advantage of sorts.

In general terms, I think you're pretty much spot on with this statement.

Referring to Rich's mathematical analysis as it relates to this specific hand, I find an Antonius percentage gain of .42 and .86 for running it twice/three times respectively.  Where he finds a 7% swing against Gold I don't know, although, if 'wishing' is factored in.....
In respect of Mr. Shoelace's subject heading of 'contains spoilers', too bloody right!  Said spoilers are a and a from where I'm sitting!


PS.....I think it's vari'a'nce   

[AlexMartin]

Alex[/url] Martin link=topic=28916.msg592181#msg592181 date=1195174373]
The only way i see it affecting EV and not just reducing variance is the fact that cards are not reshuffled into the deck. Nice lessons RicheO and Longy (esp tree diagram  bit .

Its very interesting that after running it a certain no. of times Antonius is GAURANTEED to at least break even. Remind me of that when im playing next year...

whats interesting about that?  if he runs out all the cards in the deck hes GUARANTEED to get 73% of the pot

it doesn't affect EV. Period. Think about what the E in EV stands for.

Lol, obv. I think ur missing my point.

[julian]

is this series on the telly now?
prey tell where & when tyvm