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Powerball Powerplay - Is it worth wagering it?
Powerball Powerplay - Is it worth paying the extra $1 (meaning, does it improve the expected value of the return per $ bet)? Short answer - not really. Long answer: It depends on (a) the Expected Value of the Jackpot, and (b) whether you consider improvement of a negative Expected Value of the return (less negative return per $ bet, or in other words, smaller loss) worth it. You can read about how Powerplay works at the Powerball website. Basically, you pay an extra dollar per bet
Jul 8, 2022, 5:35 pm - Orange71 - Mathematics Forum

Craps Pass Line With Odds Bet - Casino Advantage
The equivalent % House advantage per unit bet for Don't Pass with Odds is (45/11)[1/(2n+3)]. n is the Odds multiplier (1x, 2x, 5x, 10x, etc.) Here is the summary:
Sep 8, 2022, 3:31 pm - Orange71 - Mathematics Forum

Powerball Powerplay - Is it worth wagering it?
Depends on how many tickets you're buying but because the minimum multiplier is 2, IMO the extra buck is worth it. Most of like to dream but realistically we should expect to win a smaller secondary prize and Power Play upgrades smaller wins.
Jul 26, 2022, 12:19 am - Stack47 - Mathematics Forum

Powerball Powerplay - Is it worth wagering it?
One correction: with Powerplay the prize for the match all 5 main balls without Powerball tier is $2M, regardless of the Powerplay Multiplier, whereas without Powerplay it would only $1M. I had accounted for this in my calculations.
Jul 8, 2022, 10:37 pm - Orange71 - Mathematics Forum

Craps Pass Line With Odds Bet - Casino Advantage
Yes, the odds bet, sometimes called free odds , is universally paid according to the true probabilities, without house advantage. However, before making this bet, you must make the Pass Line bet first, and that has a 1.414% house advantage. The casinos vary in how much you can bet on the odds as a multiplier of the original Pass Line bet. For example, a casino that offers 10x Odds on a $10 Pass Line bet will let you bet up to $100 on the odds bet. As an example of how odds or free odds func
Sep 6, 2022, 8:14 pm - Orange71 - Mathematics Forum

Craps Pass Line Simulation
Here's a slightly more complex Python program variation with Pass Line Odds bets possible if a point is hit in the initial roll. A Pass Line Odds bet is a secondary bet that offers a true odds return (i.e. no casino advantage), but it is only possible if a point occurs. This stipulation is a reason the casinos offer it. It is not possible to achieve an overall player advantage due to the initial-roll house edge. However, the greater the odds bet, the smaller the house edge is. I had a separate p
Aug 1, 2023, 12:04 pm - Orange71 - Mathematics Forum

Egypt Nos
Mathematics in ancient Egypt Table of Contents The introduction of writing in Egypt in the predynastic period ( c. 3000 BCE) brought with it the formation of a special class of literate professionals, the scribes . By virtue of their writing skills, the scribes took on all the duties of a civil service: record keeping, tax accounting, the management of public works (building projects and the like), even the prosecution of war through overseeing military supplies and payrolls. Young men enrol
Apr 15, 2024, 7:26 pm - eddessaknight - Mathematics Forum

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