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parappa
11-18-2004, 07:04 AM
Hi--

Blackjack, .5% house advantage.

Does making 600 $5 bets have a higher or lower variance than making 1000 $3 bets where you are playing three hands at a time?

Kenser
11-18-2004, 12:18 PM
If I remember, the numbers for playing 3 hands are approx. 57% of the 1 hand bet. In your example for 3 hands the proper bet size would be $2.85. So $3 on 3 hands would have a higher variance than the single $5.

parappa
11-18-2004, 01:13 PM
Thanks very much.

mannika
11-18-2004, 01:46 PM
If the total amount being wagered is the same (in this case it is), the higher variance option will be the one with the least trials, or the greater amount being bet.

Think of the extreme. If you were to only make one $3000 bet, compared to 10 $300 bets, which would have the higher variance? The one $3000 bet obviously would.

So making 1000 $3 bets is the lower variance option.

parappa
11-19-2004, 09:18 AM
Hmm. That seems to contradict the previous response...I was going to disagree with you mentioning the covariance of playing 3 at once, but you have sidestepped that by treating it as one $3 bet.

Now I"m confused.

Kenser
11-19-2004, 02:11 PM
I just know to get the same amount of risk and profit potential on 1 hand compared to multiple hands(this takes into account splits/double downs) you place 73% of your 1 hand wager on 2 hands and 57% on 3 hands. 57% of $5 is $2.85 for your example. Of course you could not bet this odd amount. These figures give you the same risk on 1,2 or 3 hands. The number of rounds has nothing to do with it. If you play more rounds with a higher risk, your variance will increase.

Kenser
11-19-2004, 02:40 PM
I suggest you post the question @ one of the many free blackjack boards. Many people there will give you an answer and are more versed than myself. The 2 that I suggest are advantageplayer.com and bj21.com.

parappa
11-19-2004, 07:01 PM
[ QUOTE ]
I just know to get the same amount of risk and profit potential on 1 hand compared to multiple hands(this takes into account splits/double downs) you place 73% of your 1 hand wager on 2 hands and 57% on 3 hands. 57% of $5 is $2.85 for your example. Of course you could not bet this odd amount. These figures give you the same risk on 1,2 or 3 hands. The number of rounds has nothing to do with it. If you play more rounds with a higher risk, your variance will increase.

[/ QUOTE ]

Oh, I've got it. So what you're saying is that 3 bets of $2.85 each produces the same variance as one bet of $5. But $2.85*3=8.55/bet. Since $1*3<$2.85*3, Mannika's answer is obviously correct for the question I asked, and your answer is the variance-levelling bet size.

Thanks to both.

Reef
11-19-2004, 09:31 PM
lower the bet size, lower the variance. With $2 bets and a $200 initial deposit (with a $200 bonus), the odds of getting lower than $200 after wagering 2k are practically Nil. Run a search for Homer's post on it