Theoretical question

Hectorjelly

You are a consistent 10ptbb winner at whatever stakes you play. Someone who fancies you in the IT department of the poker site decides to give you a helping hand. You get an extra Ace every 100 hands you play. What effect, if any, should this have on your winrate?

Some starting maths,

Every card you get has a 1/13 chance of being an ace. The chance of getting an ace in a single hand is 13%. So in 100 hands you should get 13 aces. You will now get 14!

Jesus Wept

Wouldn't make much difference to me I don't think.... most ace hands are fairly useless. It would make a big difference to the chief though, he came out with this gem the other night...

'Ace-rag is a beaut-if-ful hand'

DeVore

I'm not clear on the logic behind the extra ace... 13 out of 100 hands have a natural ace => in 1538 hands you will get 200 hands with an ace. Are you then saying that 2 of those 200 hands will get one card replaced randomly with an Ace and (since its 50/50 that it replaces the natural ace), one of them will be turned into AA??

Then the difficulty is valuing hands like AK and AQ. Also it will screw with your pairs (imagine KK turning into AK? 44 turning into A4?) and suited connectors (89s turning into A8o?)

I dont have the numbers to calculate anything exact so I'll go with my gut and guess that it will barely make a difference and I wouldnt be completely surprised if it had a negative impact.

DeV.

ps: if Oscar comes in with some funneh comment about A6s ignore him.

Hectorjelly

For every 100 hands you get you should get 13 aces. Now you get 14. That extra distribution is taken evenly from all the other cards. So you are a tiny bit less likely to get a 2 or a king or whatever.

I havent done any maths or thought about it for more than a few minutes, but I would bet my entire bankroll that it would have a positive effect.

Since the bet would be impossible to make, ill say why.

AA and KK normally account for something like 1/3 of a winning players profit. AA is by far the most profitable hand. Under the changed circumstances you are going to get aces more often than before, and your increase will be 12 times greater than the decrease in kings. (as the ace is shared by all other cards).

Hands like 89s are basically neutral. If you play well and run ok you will show a small profit with them. So the affect on them (which will be small anyway) is meaningless.

DeVore

Fair enough but I doubt the overall benefit will be more then marginal, and you havent factored in the damage done to pairs (which must account for a good chunk of the remaining income... I mean, who doesnt like sets )

Overall its not a big extra edge.

DeV.

kincsem

One hand in a hundred gets an ace where previously there was a random card. My guess is the ace sweetens the hand where the other hole card was JQKA (four hands JQKA from thirteen 23456789TJQKA).

Assuming you win a standard one ninth of hands dealt at a nine hand table, then in 100 hands you win 100/9 or 11.11, plus I guess an extra .31 (four from thirteen), for a total of 11.42 where previously you got 11.11. That is slightly under a 3% increase. Of course the AA; AK; AQ; AJ might not hold up.

The_Daddy_H

kincsem wrote:

One hand in a hundred gets an ace where previously there was a random card. My guess is the ace sweetens the hand where the other hole card was JQKA (four hands JQKA from thirteen 23456789TJQKA).

Assuming you win a standard one ninth of hands dealt at a nine hand table, then in 100 hands you win 100/9 or 11.11, plus I guess an extra .31 (four from thirteen), for a total of 11.42 where previously you got 11.11. That is slightly under a 3% increase. Of course the AA; AK; AQ; AJ might not hold up.

Im not sure if this is quite right. It assumes a linear increase in the distribution of both your "earning" starting hands and the amount won from each.

I think you bascially have to see what your PT numbers are for each hand, calculated the new probabilities for each hand occurrence and then your new PT/100. Maybe subtract from sets and other pocket pairs, perhaps just a minor adjustment.

Van Dice

It obviously increases your winrate, last post by T D H is spot on imo, the actual increase depends on your winrate with each specific hand, ie how you fare with A4o, etc etc, then adjust for increased frequency of Ax and decreased frequencies of all other hands.
Plus side issues like your image gets looser, tons of variables.
Also PM details + photos of IT employee in question thx

Mellor

Hectorjelly wrote:

Every card you get has a 1/13 chance of being an ace. The chance of getting an ace in a single hand is 13%. So in 100 hands you should get 13 aces. You will now get 14!

I just thought i point out a little mistake.
Every card you get has a 1/13 chance of being an ace. For every hand its not 13%, its just over 15%
So with the bonus ace it becomes 16 %, its not much of a difference but its less of a bonus than before. But there is no chance that its negitive. Its defo a benefit.

Mellor

From a rough sum, You wil ages aces 1 in 206/207 times instead od 221
So you will get aces an extra time in every 2500 hands.

This is only aces and doesn't account for the extra AK etc hands.

Instead of being 1/13 for an ace, its 1.065/13