What is the real +-EV of a video poker game

My understanding is that the EV of a game is determined through a computer playing over 6 trillion hands. Would it not be a more accurate "real" EV if 6000 hands were played a million times and the results averaged? Why 6000 hands? I believe that playing 600 hands per hour over 10 hours would be more than the average player will play, but there are some that can do it. I probably play 300 hands per hour for 6 hours. Can anyone out there do that and let me know what the results are?

Quote: packerbackerrich

My understanding is that the EV of a game is determined through a computer playing over 6 trillion hands.

False.

Results can be obtained through combinatorics as well as simulations.

I know of no game where 6T hands are used for a simulation of anything. I've simulated up to 2B for some games, but that was only to get the result correct to 0.01% for some games of high volatility. 100M is more than adequate for almost every game.

Quote:

Would it not be a more accurate "real" EV if 6000 hands were played a million times and the results averaged?

Simulations don't depend on sessions. So, the simulated results will be the same if it's 6T hands or 6K x 1B or 6M x 1M hands. (What trillion are you talking about? I use the one that has 12 zeros.)

Quote:

Can anyone out there do that and let me know what the results are?

You didn't mention the game. But, I'm sure the results are already available at the Wizard's other site.

--Dorothy

I would be playing 9/6 JoB or 8/5 BP and this is why 6 trillion hands:
There are 32 possible choices regarding which cards to keep from your initial 5 card poker hand. Choice number one is to keep all 5 cards. (You have a pat hand.) There are 5 possible ways that you can keep 4 cards and discard the fifth card. There are 10 possible ways that you can keep 3 cards and replace the other two. There are 10 more combinations of keeping two cards and drawing three. There are 5 ways you can keep 1 card and draw 4. Finally, you can toss the whole hand and draw 5 new cards. If you add all of these combinations together, the total comes to 32 different possible strategies for your poker hand.
We can add all of these partial results together to get some idea of how many poker hands the computer has to generate/evaluate just to find the optimal strategy for ONE particular poker hand.
Stand Pat: COMBIN(5,0) x COMBIN(47,0) = 1
Draw 1: COMBIN(5,1) x COMBIN(47,1) = 235
Draw 2: COMBIN(5,2) x COMBIN(47,2) = 10,810
Draw 3: COMBIN(5,3) x COMBIN(47,3) = 162,150
Draw 4: COMBIN(5,4) x COMBIN(47,4) = 891,825
Draw 5: COMBIN(5,5) x COMBIN(47,5) = 1,533,939
Total = 2,598,960 poker hands to generate/evaluate just to find the optimal strategy for any given poker hand.
This can be carried one step further. Suppose you want to evaluate the expected return/value for playing Video Poker. There are COMBIN(52,5) = 2,598,960 possible initial poker hands that you could be dealt. Your computer program would have to generate all 2,598,960 of these possible initial hands and then carry out the above 2,598,960 evaluations on each of these initial hands. If your computer can generate/evaluate these final results at 1,000,000 per second, it will take 2 1/2 months to get an answer. Of course, next week the casino can change the payoff table and it will take another 6+ trillion poker hand evaluations before you will find out if you can win in the long run even if you use optimal strategy.

People who analyze JOB run a cycle. My code can run a cycle in about 5 seconds.

See this ...

Click me

--Dorothy

I guess I've not made my question as coherent as I could. Playing $.25, I want to know what the win/loss of a million sessions of six thousand hands of 9/6 JoB is. Saying a game has a +-EV of 99.54 isn't accurately reflecting a 6000 hand session. I'm just wondering what the true cost is. I'm arbitrarily using a million sessions to hopefully get close to what will really happen. I guess you could say that I'm looking for the short-term monetary results using perfect strategy. I've got to believe from my experience that it will be a couple hundred in the negative. Anyway, thanks for trying to help me. Rich

Quote: packerbackerrich

I guess I've not made my question as coherent as I could. Playing $.25, I want to know what the win/loss of a million sessions of six thousand hands of 9/6 JoB is. Saying a game has a +-EV of 99.54 isn't accurately reflecting a 6000 hand session. I'm just wondering what the true cost is. I'm arbitrarily using a million sessions to hopefully get close to what will really happen. I guess you could say that I'm looking for the short-term monetary results using perfect strategy. I've got to believe from my experience that it will be a couple hundred in the negative. Anyway, thanks for trying to help me. Rich

Short term = long term.

Expected loss = (house edge)x(total wagers).

In your case you are wagering $1.25 per hand (max play is 5 hands at $0.25 per hand). Playing 6000 hands gives $7500 in total wagers. The house edge with perfect strategy is 0.46%. So

Expected loss for you = (0.46%)x($7500) = $34.50.

The fact that you will almost never experience this result for any fixed set of 6000 hands doesn't change a thing. Also, because a fair amount of this expected loss is tied up with the very rare "royal flush," in general you will experience higher losses per 6000 hands unless you hit the royal.

--Dorothy

Thanks Dorothy. I'll probably never get my answer, but I'll still have fun chasing the royal. I hope that all your days are fun as well....Rich

Quote: packerbackerrich

Thanks Dorothy. I'll probably never get my answer, but I'll still have fun chasing the royal. I hope that all your days are fun as well....Rich

I understand why you might think that 6000 hands played out 1 million times would be different than just playing 6B hands, because it feels like you might not get a Royal if you are only playing 6000 hands, so that will make your return lower than the 99.54 or whatever. But deciding that one session is over and another has begun isn't going to make it more or less likely that a Royal is going to come. You might get no Royals in some sessions, pulling your return down, but in others you'll get one or maybe two, making those sessions much stronger. If you just average 6000 hands as one unit, and do it 1M times, it's going to be the same as 6B hands divided by 1 million. But someone here could probably do it for you.