## Poll

 Hanukkah 1 vote (33.33%) Christmas 1 vote (33.33%) Winter solstice No votes (0%) Kwanzaa 1 vote (33.33%) Festivus No votes (0%) Other (explain) No votes (0%) Chanukah is spelled with a C, Wiz! No votes (0%) I have a lot of grievances to air this year. No votes (0%) Where does it say that angels have wings? No votes (0%) I think Hanukkah should last only seven days. No votes (0%)

3 members have voted

Wizard
• Posts: 26842
Joined: Oct 14, 2009
December 22nd, 2023 at 3:33:22 PM permalink
Suppose you put no value on your time and can sit on a video poker machine until it hits a royal.

Let's assume there is an 8/5 Bonus Poker game with a 0.5% meter rise. What is the least jackpot (for a royal) you should play at?

It is easy to say the game is immediately positive with a jackpot of 1135.56 units. However, I argue it's still a positive play under that under the conditions stated above. Why? Because you'll be increasing the jackpot as you play and will eventually recoup that money when the royal hits.

Here are some figures which may help in your calculations.

Return from all fixed pays = 0.971776
Probability of jackpot = 1 in 40,233.

My figure is 934.39 units, but I welcome challenges to it.

I'm sure somebody would otherwise chime in that the strategy changes as the jackpot grows to increase the probability, but let's not muddy the waters with that.

The question for the poll is what is your favorite of the December holidays?
Last edited by: Wizard on Dec 23, 2023
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
ThatDonGuy
• Posts: 6546
Joined: Jun 22, 2011
December 22nd, 2023 at 7:24:20 PM permalink
The way I see it, the expected number of plays is 40,233, and you are expected to lose 0.028224 per play, but you will gain back 0.005 per play when you hit the jackpot, so the expected loss per play is now 0.23224, which means it becomes an AP if the jackpoot > 40,233 x 0.023224 = about 934.37.

However, this assumes the jackpot pays off in full on a 1-unit bet.

Also, this takes future bets into account when calculating the HE. Isn't this the "flaw" we point out in the "a 7-step martingale at double-zero roulette only really has a HE of 0.34% because you are actually betting 127 against the casino's 1?
Wizard
• Posts: 26842
Joined: Oct 14, 2009
December 22nd, 2023 at 7:41:27 PM permalink
Quote: ThatDonGuy

The way I see it, the expected number of plays is 40,233, and you are expected to lose 0.028224 per play, but you will gain back 0.005 per play when you hit the jackpot, so the expected loss per play is now 0.23224, which means it becomes an AP if the jackpoot > 40,233 x 0.023224 = about 934.37.

Glad to hear we get the same number.

Quote:

However, this assumes the jackpot pays off in full on a 1-unit bet.

Also, this takes future bets into account when calculating the HE. Isn't this the "flaw" we point out in the "a 7-step martingale at double-zero roulette only really has a HE of 0.34% because you are actually betting 127 against the casino's 1?

I'm not sure I see your points here.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
ChumpChange
• Posts: 5019
Joined: Jun 15, 2018
December 22nd, 2023 at 8:29:59 PM permalink
So one unit at a quarter VP machine is \$1.25 if playing 5 coins for the progressive JP.
934.37 units X \$1.25 = \$1,167.99
1135.56 units X \$1.25 = \$1,419.25

I personally would play the machine up to a JP of \$1,199 so there's no tax. How much tax is there on the \$1,419.25 hand pay? I don't know. The rules have changed since decades ago. But if I play 12,000 hands and lose about 10 cents a hand, I'll be in the losing column even if the Royal Flush appears after that, unless there's two of them.
Last edited by: ChumpChange on Dec 22, 2023
Mental
• Posts: 1508
Joined: Dec 10, 2018
December 23rd, 2023 at 5:04:11 AM permalink
What are the chances that a player values their time at precisely zero? I submit that this is infinitely unlikely versus any other number in the set of real numbers.

Yes, you count the full meter contribution if you have infinite time. Don't we all? The problem becomes more interesting in the presence of competition.
Gambling is a math contest where the score is tracked in dollars. Try not to get a negative score.
DogHand
• Posts: 1721
Joined: Sep 24, 2011
December 23rd, 2023 at 5:24:08 AM permalink
Quote: Wizard

<snip>p.s. That should be "aire" not "air."

Wiz,

No... "air" as a verb means to express one's opinion, so you used the correct homophone.

Dog Hand
ThatDonGuy
• Posts: 6546
Joined: Jun 22, 2011
December 23rd, 2023 at 6:51:52 AM permalink
Quote: Wizard

Quote: ThatDonGuy

However, this assumes the jackpot pays off in full on a 1-unit bet.

Also, this takes future bets into account when calculating the HE. Isn't this the "flaw" we point out in the "a 7-step martingale at double-zero roulette only really has a HE of 0.34% because you are actually betting 127 against the casino's 1?

I'm not sure I see your points here.

The first one refers to the fact that you usually have to bet 5 units in order to win the maximum/progressive on a Royal in VP.

The second refers to the on-and-off-going discussion the forum seems to have about how, if you treat, say, a 7-step Martingale as a single bet that pays 1-127. That reasoning applies only if you are committed to making the full set of 7 bets every time. Similarly, the VP progressive becomes an AP at 934.4 is true only if you are committed to playing until you get a Royal.
Wizard
• Posts: 26842
Joined: Oct 14, 2009
December 23rd, 2023 at 7:47:52 AM permalink
Quote: DogHand

No... "air" as a verb means to express one's opinion, so you used the correct homophone.

Thank you!
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
100xOdds
• Posts: 4442
Joined: Feb 5, 2012
December 23rd, 2023 at 8:00:43 AM permalink
Quote: ThatDonGuy

The second refers to the on-and-off-going discussion the forum seems to have about how, if you treat, say, a 7-step Martingale as a single bet that pays 1-127.

That reasoning applies only if you are committed to making the full set of 7 bets every time. Similarly, the VP progressive becomes an AP at 934.4 is true only if you are committed to playing until you get a Royal.

7-step Martingale?
In all the years of gambling, i've never heard of this Martingale strategy but google says it's been around this forum since 2012:
https://wizardofvegas.com/forum/gambling/betting-systems/11144-how-did-my-baccarat-system-survive-100-shoes/

Questions:
- Why stop at 7?
- If you don't hit on the 7th try, you eat the loss and start the count over again?
- how do you get a he=.34% if you win? 1/127 = .79%

I can see this in european Roulette (black/red) or ez-Bacc.
Can this system be used in games where there's player decisions?
ie: Blackjack or ultimate texas holdem? (I have lost 7 in a row a few times in a day in both these games)

edit:
Veronica rhymes with hanakah.
Merry xmas to all the followers of the Flying Spaghetti monster. Hail noodleheads
Last edited by: 100xOdds on Dec 23, 2023
Craps is paradise (Pair of dice). Lets hear it for the SpeedCount Mathletes :)
Dieter
• Posts: 5794
Joined: Jul 23, 2014
December 23rd, 2023 at 8:19:27 AM permalink
Quote: 100xOdds

Questions:
- Why stop at 7?