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How Powerball jackpot odds compare to other Lottery games?

The Powerball jackpot for Wednesday's drawing is now $1.5 billion and counting. Powerball has only had one jackpot winner since the odds of winning the largest prize decreased to 1 in 292,201,338 in October 2015. To my surprise, Wolfram Alpha knows the odds of winning other lottery games, and more importantly, it has an answer to How do I win the lottery?

Data about other lotteries from WolframAlpha can be easily accessed using the Wolfram Language. Here I sorted them from lower to bigger odds of winning the lottery:

data = {First[#], Last[#], 
     Quiet[WolframAlpha[ Last[#] <> " Lotteries", {{"LotteryGamesInCountry", 1}, "ComputableData"}]]} & /@ EntityValue[CountryData[All], {"Flag", "Name"}];
lottos = SortBy[
  Flatten[Thread[List[#[[1]], #[[2]], Part[Drop[#[[3]], 1], All, 1], 1/ToExpression@Last@StringSplit[#] & /@ Part[Drop[#[[3]], 1], All, 2]]] & /@ 
    Select[data, ! MissingQ[Last[#]] &], 1], Last]

Country Lotteries

Ok, but how does it really compare with Powerball?

ListLogPlot[{Map[Tooltip[Last[#], Column[#]] &, lottos], 
  Tooltip[ConstantArray[1/292201338, Length[lottos]], Column[{CountryData["US", "Flag"], "Powerball", 1/292201338}]]}, 
 Joined -> {False, True}, 
 Ticks -> {MapIndexed[{First@#2, Rotate[Part[#1, 3] <> " (" <> Part[#1, 2] <> ")", 80 Degree], 0.01} &, SortBy[lottos, Last]], Automatic}, 
 Filling -> {1 -> Axis}, ImageSize -> 800]

World Lotteries

And how does Powerball compare with other Lotteries within the US?

data = DeleteMissing[Quiet[WolframAlpha[# <> " Lotteries", {{"LotteryGamesInState", 1}, "ComputableData"}]] & /@ 
Complement[CountryData[Entity["Country", "UnitedStates"],  "Regions"], {"Alabama", "Alaska", "Hawaii", "Mississippi", "Nevada", "Utah", "Wyoming"}]];
lottosUS = SortBy[Union[Flatten[Thread[List[Part[Drop[#, 1], All, 1],  1/ToExpression@Last@StringSplit[#] & /@ 
Part[Drop[#, 1], All, 2]]] & /@ data, 1]], Last];
ListLogPlot[Map[Tooltip[Last[#], Column[#]] &,  Prepend[lottosUS, {"Powerball (October 2015)", 1/292201338}]], 
Ticks -> {MapIndexed[{First@#2, Rotate[First[#1], 85 Degree],  0.01} &, Prepend[lottosUS, {"Powerball (October 2015)", 1/292201338}]], 
Automatic}, Filling -> Axis, ImageSize -> 800]

enter image description here

Certainly, the new Powerball odds of winning the lottery are the lowest in the US!

POSTED BY: Bernat Espigulé
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