110% var 225 vs 105% var 100

1) .25, 7/5 ddb (110% ev)



Everything falls on Baby quads with kicker or the Royal.
34 suited is now a viable hold.

2) $1, 8/5 ddb (105%)



Quad Aces, baby quads with kicker, or the Royal

I have the $ not the time. (Only 4hrs)
Which would you do?

Since both had variance in the stratosphere, I chose the higher ev one. (I had to get lucky for either if just 4hrs)

At 500 hands per hr, I should avg 4 quads in 4hrs.
Only got 1 quad and a straight flush.

But it was a dealt SF!


Lost $500 trying :(

Late, but here's the arithmetic for next time, taking the title's variances as per-hand variance in units of the bet. Four hours at 500 hands an hour is 2,000 hands.

Option 1, $1.25 a hand at 110%, variance 225: expectation +$250, standard deviation sqrt(2000 x 225) x $1.25 = $838. Chance of finishing $500 or more down: about 19%.
Option 2, $5 a hand at 105%, variance 100: expectation +$500, standard deviation sqrt(2000 x 100) x $5 = $2,236. Chance of finishing $500 or more down: about 33%.

So the dollar game had twice the expectation and three times the swing, and a $500 loss was a one-in-three outcome there against one-in-five on the quarters. Which one to play comes down to whether you want the EV or the smaller swing; with the bankroll you described, the expectation per hour on the dollar game is $125 against $62.50, and the quads you expected (about 4.7 in 2,000 hands) is the right count, you just drew the one.

If I was looking to launder large Black Jack wins in a VP machine, I'd try the $5 denom and rack up those W-2G's. I'd still expect to be down a few Royals ($20K each) before I ever hit one though.

I think I'd do better finding a virtual Black Jack machine that allows $1,000 bets or a terminal craps table that allows $1,000 PL bets.

Quote: alejandrobg

Late, but here's the arithmetic for next time, taking the title's variances as per-hand variance in units of the bet. Four hours at 500 hands an hour is 2,000 hands.

Option 1, $1.25 a hand at 110%, variance 225: expectation +$250, standard deviation sqrt(2000 x 225) x $1.25 = $838. Chance of finishing $500 or more down: about 19%.
Option 2, $5 a hand at 105%, variance 100: expectation +$500, standard deviation sqrt(2000 x 100) x $5 = $2,236. Chance of finishing $500 or more down: about 33%.

So the dollar game had twice the expectation and three times the swing, and a $500 loss was a one-in-three outcome there against one-in-five on the quarters. Which one to play comes down to whether you want the EV or the smaller swing; with the bankroll you described, the expectation per hour on the dollar game is $125 against $62.50, and the quads you expected (about 4.7 in 2,000 hands) is the right count, you just drew the one.
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Thx for the calcs!

Double the ev for triple the variance? Pass!

Quote: 100xOdds

Since both had variance in the stratosphere, I chose the higher ev one. (I had to get lucky for either if just 4hrs)

At 500 hands per hr, I should avg 4 quads in 4hrs.
Only got 1 quad and a straight flush.

But it was a dealt SF!


Lost $500 trying :(
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Not related to my Op but thought I'd put this here because SF holding just 2 cards:


My kingdom for the Ace! (Don't think I've ever had a reverse sequential before)

Minimum handpay instead of $32k :(

Option 1, playing $1.25 a hand for 2000 hands:

expectation=+$250;
variance=2000x225x1.25^2=703,125.

Option 2, playing $5 a hand for 2000 hands.

expectation=+$500,
variance=2000x100x5^2=5,000,000.


So, the variance of the latter is 5000000/703125=7.1111 times of the former.

To keep the wager amount the same, we can do a third option:

Option 3, playing $1.25x4 a hand for 2000 hands:

expectation=+$1000,
variance=2000x225x1.25^2x4^2=11,250,000.

Therefore, the variance ration becomes 5/11.250=0.444. This means the second option actually is better, variancewise.