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The Dennis

Maximum Lives in SMB2

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This was a fun bit of math/theory that I worked through on another forum. Figured it may be relevant to your interests.

Super Mario Brothers 2 had an interesting extra lives system. There were a few one-ups scattered throughout the levels, that you could only collect once per game. The MAIN way for getting extra lives was in the shadow world system. There were hidden potions that made a door to take you to the shadow world for a few seconds; you could put them near leaves, and the leaves in the shadow world, when pulled up, yielded coins that could be used in a slot machine at the end of each level. One coin = one slot pull, and you could get a 1-up (match 3 in a row or get a cherry in the first slot), a 2-up (get 2 cherries in the first 2 slots), or a 5-up (get 3 cherries in a row). As it turns out, the game itself limits your lives at 255, where gaining any more lives doesn't affect the counter. But the question was asked: if there was no limit to the amount of coins or lives you could collect, how many lives could you get in a playthrough? The answer was a bit larger than expected.

Some information to help understand the computations:

-The shadow world is shaped exactly the same as the regular world, except flipped horizontally. The screen is fixed where you enter the shadow world, and doesn't scroll.

-You get two visits to the shadow world per level, with a short time limit each time. After the second visit, the leaves in the shadow world no longer give coins.

-If you manage to suicide while in the shadow world, it doesn't count as one of the two visits. No enemies in the shadow world, so you have to find a hole.

-Each coin has a potential for 5 lives (matching 3 cherries at the end of the level).

Alright, here comes the new games theory. (Click each level number for a map!)

1-1 start: 3 lives, Play as Toad

-Grab 1-up: 4 lives

-Grab first potion, run to section A

-(3x)Drop potion at top of section A, grab 4 coins, suicide: 1 life, 12 coins

-Grab first potion, run to section B

-High-jump off hopping enemy at peak of its jump

-Drop potion, grab 8 coins: 1 life, 20 coins

-Go in door to left of section B and come back out

-Grab first potion, run to section B

-High-jump off hopping enemy at peak of its jump

-Drop potion, grab 8 coins: 1 life, 28 coins

Complete level: 141 lives (1 base, + 28 coins x 5up)

1-2 start: 141 lives, Play as Toad

-Grab 1-up: 142 lives

-Run to section A

-(141x) Grab potion left of section A, drop directly above exit door, grab s7 coins, suicide: 1 life, 980 coins

NOTE: If the potion is dropped any further to the right, you can't suicide.

-Grab potion left of section A, drop between leaves, grab 9 coins: 1 life, 989 coins

-Go in exit door and come back out

-Grab potion left of section A, drop between leaves, grab 9 coins: 1 life, 998 coins

Complete level: 4,991 lives (1 base, + 998 coins x 5up)

1-3 start: 4,991 lives, Play as Toad

-Grab first potion, run to section A

-(4,990x)Drop potion next to leaves, grab 5 coins, suicide: 1 life, 24,950 coins

-Grab first potion, run to section A, drop potion next to leaves, grab 5 coins: 1 life, 24,955 coins

-Run to entrance door to right of section A and come back out

-Grab section potion, run to section A, drop potion next to leaves, grab 5 coins: 1 life, 24,960 coins

Complete level: 124,801 lives (1 base, + 24,960 coins x 5up)

2-1 start: 124,801 lives, Play as Toad

-Grab potion, drop next to leaves, grab 3 coins: 124,801 lives, 3 coins

-Go down pipe and come back up

-Grab potion, drop next to leaves, grab 3 coins: 124,801 lives, 6 coins

Complete level: 124,831 lives (124,801 base, + 6 coins x 5up)

2-2 start: 124,831 lives, Play as Toad

-Grab 1-up: 124,832 lives

-Head left of 1-up to section A

-(124,831x) Grab and drop potion, grab four coins, suicide: 1 life, 499,324 coins

-Head to section A, grab and drop potion, grab four coins: 1 life, 499,328 coins

-Leave through door and come back in

-Head to section A, grab and drop potion, grab four coins: 1 life, 499,332 coins

Complete level: 2,496,661 lives (1 base, + 499,332 coins x 5up)

2-3 start: 2,496,661 lives, Play as Toad

-Go to section A, grab potion

-(2,496,660x) Drop potion two steps left of leftmost leaf, grab 3 coins, climb to bottom of ladder and fall off left to suicide: 1 life, 7,489,980 coins

NOTE: it is impossible to collect the 4th coin in this section. If potion is dropped any further right, you can't climb down the ladder.

-Go to section B

-Grab and drop potion, grab 8 coins: 1 life, 7,489,988 coins

-Go out exit door and come back in

-Grab and drop potion, grab 8 coins: 1 life, 7,489,996 coins

Complete level: 37,449,981 lives (1 base, + 7,489,996 coins x 5up)

3-1 start: 37,449,981 lives, Play as Toad

-Grab first potion, go to section A

-(37,449,980x) Drop potion 3 steps left of the leaf next to the top of the ladder, grab 3 coins, suicide: 1 life, 112,349,940 coins

NOTE: almost impossible to do. Dropping potion any further to the right and you can't suicide. Success requires sliding off left side of ladder to freefall, getting bottom-left coin immediately (it can be finicky), and walljumping back up the ladder precisely.

-Go to section B

-Grab potion, drop one step to the left, grab 12 coins: 1 life, 112,349,952 coins

NOTE: even with Toad, it is impossible to grab more than 12 coins within the time limit.

-Exit the left door and go back in

-Grab potion, drop one step to the left, grab 12 coins: 1 life, 112,349,964 coins

Complete level: 561,749,821 lives (1 base, + 112,349,964 coins x 5up)

3-2 start: 561,749,821 lives, Play as Toad

-Go to section A, Grab and drop potion, grab 4 coins: 561,749,821 lives, 4 coins

-Die to enemies: 561,749,820 lives, 4 coins

-Go to section A, Grab and drop potion, grab 4 coins: 561,749,820 lives, 8 coins

Complete level: 561,749,860 lives (561,749,820 base + 8 coins x 5up)

NOTE: while it looks like you may be able to get the second potion to a cliff, you can't climb or drop down the ladder, so you are blocked in.

3-3 start: 561,749,860 lives, Play as Toad

-Go to section A, Grab and drop potion, grab 3 coins: 561,749,860 lives, 3 coins

-Go through left door and come back out

-Go to section A, Grab and drop potion, grab 3 coins: 561,749,860 lives, 6 coins

Complete level: 561,749,890 lives (561,749,860 base + 6 coins x 5up)

4-1 start: 561,749,890 lives, Play as Toad

-Go to section B, grab potion

-Go to section A

-(561,749,889x) Drop to left of leaves, grab 6 coins, suicide: 1 life, 3,370,499,334 coins

NOTE: tough, but possible

-Go to section B, grab potion

-Go to section A

-Drop to left of leaves, grab 6 coins: 1 life, 3,370,499,340 coins

-Grab and drop other potion, grab 5 coins: 1 life, 3,370,499,345 coins

Complete level: 16,852,496,726 lives (1 base, + 3,370,499,345 coins x 5up)

4-2 start: 16,852,496,726 lives, Play as Toad

-Go to section A, grab potion

-Go to section B

-(16,852,496,725x) Drop potion on middle platform on the rightmost leaf, grab 7 coins, suicide: 1 life, 117,967,477,075 coins

NOTE: tough, but possible

-Go to section A, grab potion

-Go to section B

-Drop potion on middle platform, grab 7 coins: 1 life, 117,967,477,082 coins

-Go left to door next to section A, enter and come back

-Go to section A, grab potion

-Go to section B

-Drop potion on middle platform, grab 7 coins: 1 life, 117,967,477,089 coins

Complete level: 589,837,385,446 lives (1 base, + 117,967,477,089 coins x 5up)

4-3 start: 589,837,385,446 lives, Play as Toad

-Grab potion, ride egg to section A

-(589,837,385,445x) Drop potion on topleft ledge, grab 6 coins, suicide: 1 life, 3,539,024,312,670 coins

-Grab and drop potion, grab 2 coins: 1 life, 3,539,024,312,672 coins

-Go in door and back out

-Grab potion, ride egg to section A, drop and grab 6 coins: 1 life, 3,539,024,312,678 coins

Complete level: 17,695,121,563,391 lives (1 base, + 3,539,024,312,678 coins x 5up)

5-1 start: 17,695,121,563,391 lives, Play as Toad

-Go to section B, grab 1-up, grab potion: 17,695,121,563,392 lives

-Go to section A

NOTE: yes, it's possible.

-(17,695,121,563,391x) Drop potion, grab 7 coins, suicide: 1 life, 123,865,850,943,737 coins

-Go to section B, grab potion, go to section A

-Drop potion, grab 7 coins: 1 life, 123,865,850,943,744 coins

-Go through door to left and come back in

-Go to section B, grab potion, go to section A

-Drop potion, grab 7 coins: 1 life, 123,865,850,943,751 coins

Complete level: 619,329,254,718,756 lives (1 base, + 123,865,850,943,751 coins x 5up)

5-2 start: 619,329,254,718,756 lives, Play as Luigi

-Go to section A

-(619,329,254,718,755x) Grab potion, drop on top of pipe, grab 4 coins, suicide: 1 life, 2,477,317,018,875,020 coins

-Go to section A, grab potion

-Go to section B, drop potion, grab 5 coins: 1 life, 2,477,317,018,875,025 coins

-Go to section A, grab potion

-Go to section B, drop potion, grab 5 coins: 1 life, 2,477,317,018,875,030 coins

Complete level: 12,386,585,094,375,151 lives (1 base, + 2,477,317,018,875,030 coins x 5up)

5-3 start: 12,386,585,094,375,151 lives, Play as Luigi

-Go to section B, grab potion

-High-jump to section A

-(12,386,585,094,375,150x) Drop potion on pipe, grab 3 coins, suicide: 1 life, 37,159,755,283,125,450 coins

-Go to section B, grab potion

-Go to section C, drop potion, grab 5 coins: 1 life, 37,159,755,283,125,455 coins

-Go to section A, go down ladder and back up

-Go to section B, grab potion

-Go to section C, drop potion, grab 5 coins: 1 life, 37,159,755,283,125,460 coins

Complete level: 185,798,776,415,627,301 lives (1 base, + 37,159,755,283,125,460 coins x 5up)

6-1 start: 185,798,776,415,627,301 lives, Play as Toad

-Grab potion, go to section A

-Drop potion, grab 4 coins: 185,798,776,415,627,301 lives, 4 coins

-Grab potion, go to section A

-Drop potion, grab 4 coins: 185,798,776,415,627,301 lives, 8 coins

-Grab 1-up: 185,798,776,415,627,302 lives, 8 coins

Complete level: 185,798,776,415,627,342 lives (185,798,776,415,627,302 base, + 8 coins x 5up)

6-2 start: 185,798,776,415,627,342 lives

-Grab potion

-(185,798,776,415,627,341x) Drop potion, grab 1 coin, suicide: 1 life, 185,798,776,415,627,341 coins

-Grab and drop potion, grab 1 coin: 1 life, 185,798,776,415,627,342 coins

-Go back to beginning door, go in and come back out

-Grab and drop potion, grab 1 coin: 1 life, 185,798,776,415,627,343 coins

Complete level: 928,993,882,078,136,716 lives (1 base, + 195,798,776,415,627,343 coins x 5up)

6-3 start: 928,993,882,078,136,716 lives, Play as Toad

-Go to section A

-Bomb-clear a path from the top so that there is a path between the two leaves and the six leaves

-(928,993,882,078,136,715x) Grab potion, drop at bottom between leaves, grab 8 coins (and mushroom first time), suicide: 1 life, 7,431,951,056,625,093,720 coins

-Bomb-clear a path from the top so that there is a path between the two leaves and the six leaves

-Grab potion, drop one step left from the lone, topmost leaf, grab 9 coins: 1 life, 7,431,951,056,625,093,729 coins

NOTE: There is barely enough time to get all 9 coins, with only a few frames to spare. If you didn't grab the mushroom, it gets in the way of the 9th coin.

-Go to the vine on the right, climb up and back down

-Bomb-clear a path from the top so that there is a path between the two leaves and the six leaves

-Grab potion, drop one step left from the lone, topmost leaf, grab 9 coins: 1 life, 7,431,951,056,625,093,738 coins

Complete level: 37,159,755,283,125,468,691 lives (1 base, + 7,431,951,056,625,093,738 coins x 5up)

7-1 start: 37,159,755,283,125,468,691 lives, Play as Toad

-Go to section A

-(37,159,755,283,125,468,690x) Grab potion, drop in middle of leaves, grab 3 coins, suicide: 1 life, 111,479,265,849,376,406,073 coins

-Go to section B

-Grab and drop potion, grab 6 coins: 1 life, 111,479,265,849,376,406,079 coins

-Go out the door and back in

-Grab and drop potion, grab 6 coins: 1 life, 111,479,265,849,376,406,085 coins

Complete level: 557,396,329,246,882,030,426 lives (1 base, + 111,479,265,849,376,406,085 coins x 5up)

7-2: No extra lives, no bonus round at end of level

Total possible lives: 557,396,329,246,882,030,426

Put in perspective, if you got to 7-2 with this many lives, and then lost a life every second since the Big Bang, as of today you would be just shy of 1/1,000th the way to

a game over.

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I know the numbers are big but it was just a little bit of basic calculator work and some critical thinking, it wasn't a month-long project or anything :)

But no, no summer classes. Done with college.

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Pffft, we all know the limit to 1-ups in any old video game game is 256 lives. It's just a fact :tomatoface:.

Hilarious read, though... Do you have any idea how long it would take to achieve that theoretical number of lives? Especially since you actually need to die the number of lives from the previous stage in order to collect the number of lives possible for the next?

Mind boggling stuff.

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But is it possible, in theory or in practice, to attain 255 lives by the end of the game?

(I think the answer is yes.)

... did you even read the first post? I think we can all agree with absolute certainty that it's THEORETICALLY possible to achieve at least 255 lives before the end of the game. Actually, it's closer to something over 500 quindrillion lives before the end.

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Pffft, we all know the limit to 1-ups in any old video game game is 256 lives. It's just a fact :tomatoface:.

...

Do you have any idea how long it would take to achieve that theoretical number of lives?

Yeah, I did mention the 255/256 thing early on there before the math assault commenced!

Uh, I have no idea how long it would take. I could calculate it, but it would all rest on estimates of time spent doing things (say, average one minute per death/run through level, four seconds per slot machine roll, etc). Maybe I'll get back to you on that.

But is it possible, in theory or in practice, to attain 255 lives by the end of the game?

(I think the answer is yes.)

It absolutely is! You can actually cheese the slot machine by timing it correctly, although it takes some practice. The game only has two 'digits' to display the number of lives you have as well, but it doesn't use hex digits to display your lives. So it counts 00-99, then it goes A0-A9, B0-B9, etc. The 'number' it maxxes out on is P4, or 255.

smb2.png

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... did you even read the first post? I think we can all agree with absolute certainty that it's THEORETICALLY possible to achieve at least 255 lives before the end of the game. Actually, it's closer to something over 500 quindrillion lives before the end.

Yes, I did. But since there is an actual max...well, if i just thought about it, you should be able to do it according to the first post, reaching your target a lot quicker (by the end of 1-2)

I am really more concerned with the practical aspect of it. It's been a long time since I've played SMB2..and I may have another reason to give it a go. Maybe even with a more conservative hope for the 2ups if they're easier, can I reach 256?

Meh. Still doesn't entice me to play it again.

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Yeah, as previously noted, due to architectural purposes, you'd end up hitting 255 lives. Then you better hope the 'lives' value doesn't wrap around to 0, or worse, a signed value (-256).

Pretty hilariously awesome job, there.

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If it didn't actually cap at 255, I would love to see someone with an emulator attempt to hit this absolute maximum number of lives. How bored one would have to be to do that, I don't know, but it would still be awesome.

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Gario also did ask how long it would take.. if you went through doing each of those steps one time as quickly as possible, you'd be able to figure it out exactly.

But just looking at the number... even if it's one second per attempt (and it's certainly more than that) that's still a very long time: 557,396,329,246,882,030,426 seconds x 1 min/60 sec x 1 hour/60 min x 1 day/24 hours = 6,451,346,403,320,393.8706 days.... x 1 year/365.25 days = 17,662,823,828,392.591 years.

By perspective, the Earth formed 4.6 billion years ago and the first bacteria appeared on earth approximately 3.5 bya... so if you believe in evolution, and if you believe that our species will survive long enough, you should also believe that if you can actually trick your children and your children's children etc. into finishing up this task for you once you die, the characters in the game will inevitably bear no resemblance to humans..if we're even still humans.

kind of like toad, really.

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Alright folks we all know that is a lot of hours.

Now.

Lets assume that every human being was capable of playing SMB2 since the day of their birth. Lets also now assume that a limitless amount of people could work towards getting the maximum number of lives in SMB2 simultaneously, and that each human being since the dawn of time did in fact contribute 18 hours of every day to the accomplishment of this feat.

In one mighty cumulative effort, How long would it take for humanity to reach this goal? Would it have happened before our lifetime? After? perhaps one of us would log that final 1up!

Get crackin!

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Yeah, as previously noted, due to architectural purposes, you'd end up hitting 255 lives. Then you better hope the 'lives' value doesn't wrap around to 0, or worse, a signed value (-256).

2s complement of an 8-bit value would overflow to -128 after 127, not -256.

Let it be known that Kenogu Labz (Nathan Armstrong) is a dumb.

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The game doesn't wrap the lives around. I remember hearing that SMB1 does that but haven't checked... I have, however, checked SMB2, and it just stays at 255 until you lose a life. Extra lives do nothing.

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How many people are on the Earth, 6.5 billion, atm? Assuming no growth rate...

17,662,823,828,392,591 years / 6,500,000,000 people = 2717357.52 years to complete the project per person involved.

I was listening to this while reading the thread. It puts it into a whole new perspective. It makes me wonder, though - what IS the bare minimum of time spent to do something like this? The little musical ditties every time you get a few lives takes longer than a second, for example, and Toad picking up the vegetables continues to count for time (he takes about 1/2 a second... but that adds up when dealing with these houses.

Oh yeah, listen to this while listening to this stuff - it's freakin' awesome, lol.

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2s complement of an 8-bit value would overflow to -128 after 127, not -256.

Let it be known that Kenogu Labz (Nathan Armstrong) is a dumb.

But, since it was previously stated that the maximum was 255, it could be assumed that (for whatever reason) the value used could be a signed 9-bit integer. No, that makes no architectural sense. Yes, it was only made to be humorous. Slack it off, eh?

Also, I'd be in for concurrent gameplay to get all those lives. Time paradox ftw, though, since everyone would have to be playing all sections of the game simultaneously. Talk about a concurrency nightmare..

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