Dipsy
Joined: Aug 31, 2010
• Posts: 13
September 1st, 2010 at 1:56:05 AM permalink
Hi, I've found some +EV games that have different return and standard deviation. How do I tell which one is better?

for example one game's EV is ~112% with approx 81 standard deviation.
the other is 100.10% with 0.75 standard deviation.
and compare these two games with FPDW of 100.76% and a standard deviation of 5.08

which one is a better game? Is it as simple as the advantage devided by the standard deviation?

or
.1200/81.0=0.001481
.0010/0.75=0.001333
.0076/5.08=0.001496

So the FPDW is still a better game here?
ahiromu
Joined: Jan 15, 2010
• Posts: 2102
September 1st, 2010 at 3:27:03 AM permalink
I don't know the correct statistical math to figure this out, but I think it would be good to explain your bankroll situation. If you have a very large bankroll compared to the money played then it should be obvious to play the high return, high standard deviation game. It only gets interesting when you are at a significant risk of busting out -- which you probably already knew but yeah just throw out numbers.
Its - Possessive; It's - "It is" / "It has"; There - Location; Their - Possessive; They're - "They are"
teddys
Joined: Nov 14, 2009
• Posts: 5450
September 1st, 2010 at 4:35:28 AM permalink
What are the games, if you don't mind me asking?

Edit: What the Wizard says makes sense. If you pay the 100.10 percent game perfectly forever at the right proportion, eventually you'll turn your \$100 into a million bucks. (Granted, it will take a while).

What I want to know is what game has a 0.56 variance? That's less than blackjack!
"Dice, verily, are armed with goads and driving-hooks, deceiving and tormenting, causing grievous woe." -Rig Veda 10.34.4
Wizard
Joined: Oct 14, 2009
• Posts: 23604
September 1st, 2010 at 7:25:53 AM permalink
The Kelly Criterion would suggest maximizing advantage/variance. Remember that variance=(standard devation)^2. In your example, that is highest with the 0.1% advantage game.
It's not whether you win or lose; it's whether or not you had a good bet.
Joined: Nov 30, 2009
• Posts: 555
September 1st, 2010 at 8:48:47 AM permalink
Quote: Dipsy

Hi, I've found some +EV games that have different return and standard deviation. How do I tell which one is better?

for example one game's EV is ~112% with approx 81 standard deviation.
the other is 100.10% with 0.75 standard deviation.
and compare these two games with FPDW of 100.76% and a standard deviation of 5.08

which one is a better game? Is it as simple as the advantage devided by the standard deviation?

or
.1200/81.0=0.001481
.0010/0.75=0.001333
.0076/5.08=0.001496

So the FPDW is still a better game here?

I assume this is purely theoretical. Most games have a negative EV. I assume the preference is more based on risk tolerance. I would throw up at an 81 std deviation event. So on a volatility adjusted basis, I would choose 100.1% at .75 std deviation over a 5 or 81 std deviation event.
mkl654321
Joined: Aug 8, 2010
• Posts: 3412
September 1st, 2010 at 9:42:59 AM permalink
Imagine a video poker game where the ONLY payoff was for a royal flush. Let's say that the payoff is \$40,000 for a 5-coin bet at .25 denomination. Let's also say, just for grins, that it's 25,000/1 to hit a royal if you play to maximize your chances of hitting one (throwing away all five cards from 99996 or 34567SF, for example). The 32,000-to-1 payoff would obviously mean that the game is highly positive EV (around +30%), but the variance would be MASSIVE. It would be very easy to go twenty grand or more in the hole before you hit. So, who should play this game? Millionaires? Anybody?

The conundrum is that the EV of every single play is about 75 cents, but anyone with a sufficient bankroll to play such a game would probably be dissatisfied with only earning \$450/hour!!!
The fact that a believer is happier than a skeptic is no more to the point than the fact that a drunken man is happier than a sober one. The happiness of credulity is a cheap and dangerous quality.---George Bernard Shaw
teddys
Joined: Nov 14, 2009
• Posts: 5450
September 1st, 2010 at 10:10:15 AM permalink
Quote: mkl654321

Imagine a video poker game where the ONLY payoff was for a royal flush. Let's say that the payoff is \$40,000 for a 5-coin bet at .25 denomination. Let's also say, just for grins, that it's 25,000/1 to hit a royal if you play to maximize your chances of hitting one (throwing away all five cards from 99996 or 34567SF, for example). The 32,000-to-1 payoff would obviously mean that the game is highly positive EV (around +30%), but the variance would be MASSIVE. It would be very easy to go twenty grand or more in the hole before you hit. So, who should play this game? Millionaires? Anybody?

The conundrum is that the EV of every single play is about 75 cents, but anyone with a sufficient bankroll to play such a game would probably be dissatisfied with only earning \$450/hour!!!

Hmmm...interesting. I think another reason nobody would play this game is because it would be boring as hell! No payouts for anything besides the RF?
-------------------
Richard Brodie of Microsoft played 3-coin \$100 FPDW at Caesars. That's a 0.76% advantage with a variance of 25 or so. Not as scary as your example but still pretty hairy. I think he went in the hole about \$120,000 and then hit the ducks twice (\$60,000 each) and the royal twice (\$240,000 each). Then they kicked him out.
"Dice, verily, are armed with goads and driving-hooks, deceiving and tormenting, causing grievous woe." -Rig Veda 10.34.4
Dipsy
Joined: Aug 31, 2010
• Posts: 13
September 2nd, 2010 at 3:18:42 AM permalink
Quote: mkl654321

Imagine a video poker game where the ONLY payoff was for a royal flush. Let's say that the payoff is \$40,000 for a 5-coin bet at .25 denomination. Let's also say, just for grins, that it's 25,000/1 to hit a royal if you play to maximize your chances of hitting one (throwing away all five cards from 99996 or 34567SF, for example). The 32,000-to-1 payoff would obviously mean that the game is highly positive EV (around +30%), but the variance would be MASSIVE. It would be very easy to go twenty grand or more in the hole before you hit. So, who should play this game? Millionaires? Anybody?

The conundrum is that the EV of every single play is about 75 cents, but anyone with a sufficient bankroll to play such a game would probably be dissatisfied with only earning \$450/hour!!!

you guessed it very close. The actual game pays 11000:1 for RF and 2500:1 for 4 deuces for one coin. Its a deuces wild game.
Dipsy
Joined: Aug 31, 2010
• Posts: 13
September 2nd, 2010 at 3:28:09 AM permalink
Quote: teddys

What are the games, if you don't mind me asking?

Edit: What the Wizard says makes sense. If you pay the 100.10 percent game perfectly forever at the right proportion, eventually you'll turn your \$100 into a million bucks. (Granted, it will take a while).

What I want to know is what game has a 0.56 variance? That's less than blackjack!

That's pai gow poker that pays 1.05 instead of 0.95.

The EV is calculated by Wizard's probability of each outcome times the return. i.e.

Possible Outcomes in Pai Gow Poker
Player wins both
28.61%
Tie
41.48%
Banker wins both
29.91%

28.61%*2.05+41.48%*1+29.91%*0 =1.001305

However i'm not sure if this is how Wizard computed the EV of the game. Moreover, the game uses Flamingo's house way. I'm not sure if that increases or decreases the EV if i use the house way button. Their house way seems less sophisticated than Trump Plaza's tho.

I'm happy to share where the game is if the calculations above can be confirmed.It's from an online casino btw.
Caffiend
Joined: Aug 3, 2010
• Posts: 27
September 2nd, 2010 at 2:33:50 PM permalink
Quote: Dipsy

The EV is calculated by Wizard's probability of each outcome times the return. i.e.

Possible Outcomes in Pai Gow Poker
Player wins both
28.61%
Tie
41.48%
Banker wins both
29.91%

28.61%*2.05+41.48%*1+29.91%*0 =1.001305

Forgive me for seeming dense, but doesn't that exclude your own wager? Any game where you lose 0 on losses would have a hell of a player advantage!