Classic and Last Hood Standing

Both modes use the same table, the same gun and the same fair spin. They differ in how long the game runs and who gets paid.

#Side by side

k is the number of players dealt in. The rake arithmetic is on the Rake page.

#Classic

One round. The cylinder has k live chambers for k players. The gun starts at a random seat and passes clockwise until the bang. The shot player forfeits their buy-in. Every survivor gets their own buy-in back plus an equal share of that forfeited buy-in minus the rake. Any leftover from the division, called dust, goes to the rake.

If everyone clicks once per turn, every seat has the same 1 in k chance of being the one shot.

#Last Hood Standing

Rounds repeat. After each bang the shot hood is out. The cylinder is reloaded with one live chamber for each player still alive, the gun goes to a freshly drawn random seat, and play continues. The game ends when one hood is left.

The winner takes everyone else's buy-ins, W = (k - 1) x S, minus the rake, on top of getting their own buy-in back. Everyone else loses their buy-in. If everyone clicks once per turn, every player has the same 1 in k chance of being the last hood standing.

Every round draws its own start seat and bullet from the same committed seeds, with the labels rhr/start/<round> and rhr/bullet/<round>.

#One real game, both ways

This is the sample game from The provably fair spin, played out. Four players sit at seats 0, 2, 3 and 5: Ada, Bo, Cy and Dee. The tier is Ruble, with a 1.00 USDG buy-in and a 5% rake. The commit they all saw begins 0a49d7e2.

How they play: everyone clicks once and passes, except Bo, who takes one dare whenever the extra click would be at 1 in 3 or better. The values below come from the seeds, so you can reproduce every line with the script on the fairness page.

round  alive      start seat                                    bullet chamber
0      0,2,3,5    9736575802941359749 mod 4 = 1 -> seat 2       3106201186547696671 mod 4 = 3
1      0,2,3      2116355319820926433 mod 3 = 1 -> seat 2       5002787690207603443 mod 3 = 1
2      0,2        15113494395687190491 mod 2 = 1 -> seat 2      2109071997588524699 mod 2 = 1

#Round 0: four chambers, Bo starts, the bullet is in chamber 3

Dee is shot. Cy survived a click at 1-in-2 odds, which is what the Ice Veins achievement asks for.

Look at what Bo's dare did. It used chamber 1, so Cy and Dee each reached the bullet one chamber sooner. Had nobody dared, the same chamber 3 would have been pulled by Ada, not Dee. The dare paid Bo nothing. It raised Bo's own chance of being shot in this round from 1 in 4 to 2 in 4, and it moved the bang from Ada to Dee. This is why dares are never free.

#If this were Classic, the game ends here

The rake is 5% of 1.00, which is 0.05. The three survivors split the other 0.95, which is 0.316666 each with 0.000002 left over, and the leftover joins the rake. Check: 3 x 0.316666 + 0.050002 = 1.00, exactly what Dee lost.

#If this is Last Hood Standing, the game goes on

Dee is out. Three hoods are alive, so the next cylinder has three live chambers.

Round 1. Bo starts again, and the bullet is in chamber 1.

Bo does not dare this time: after the first click only two chambers are left, which is worse than the 1-in-3 Bo asked for. Cy is out.

Round 2. A duel between Ada and Bo, two chambers.

Ada is out. Bo is the last hood standing.

The winnings pool is 3 x 1.00 = 3.00. The rake is 5% of that, 0.15, so Bo nets 3.00 - 0.15 = 2.85. Check: 2.85 - 3.00 + 0.15 = 0. Nothing in Bo's 2.85 came from the dare. It is the pot minus the rake.

#Verify this game yourself

The stand-alone verifier takes a game record: the same JSON the server gives players after a game. Here is the record for the game above. Paste it in, and the verifier re-derives the commit, the mix and every round, replays the clicks and passes in order, and compares the result with the settlement in the record.

{
  "version": 1,
  "gameNo": "48213",
  "mode": "LAST_HOOD",
  "stake": "1000000",
  "rakeBps": 500,
  "maxPullsPerTurn": 3,
  "commit": "0a49d7e28602f9bb6694706ea461385fe0be12f75d4b4b915b6cf1496b9832e3",
  "serverSeed": "d7e47f6f05c1cebdeb619e39bbab6e106f93bbb87d0dcca7353cff2f9fb0e317",
  "seats": [
    { "seat": 0, "playerId": "ada", "clientSeed": "6743704c1f2aa8a19e02f7a4ee0e99ab" },
    { "seat": 2, "playerId": "bo", "clientSeed": "cdadbc5070a582539a18e9cafc21ed22" },
    { "seat": 3, "playerId": "cy", "clientSeed": "a9f2640aa370453b4d27717bf6ce5d35" },
    { "seat": 5, "playerId": "dee", "clientSeed": "2f197ec9aefbfe8693896c9a28ca3cb7" }
  ],
  "actions": [
    { "seat": 2, "action": "PULL", "auto": false },
    { "seat": 2, "action": "PULL", "auto": false },
    { "seat": 2, "action": "PASS", "auto": false },
    { "seat": 3, "action": "PULL", "auto": false },
    { "seat": 3, "action": "PASS", "auto": false },
    { "seat": 5, "action": "PULL", "auto": false },
    { "seat": 2, "action": "PULL", "auto": false },
    { "seat": 2, "action": "PASS", "auto": false },
    { "seat": 3, "action": "PULL", "auto": false },
    { "seat": 2, "action": "PULL", "auto": false },
    { "seat": 2, "action": "PASS", "auto": false },
    { "seat": 0, "action": "PULL", "auto": false }
  ],
  "settlement": {
    "mode": "LAST_HOOD",
    "stake": "1000000",
    "rakeBps": 500,
    "k": 4,
    "rake": "150000",
    "nets": [
      { "seat": 0, "net": "-1000000" },
      { "seat": 2, "net": "2850000" },
      { "seat": 3, "net": "-1000000" },
      { "seat": 5, "net": "-1000000" }
    ],
    "winnerSeats": [2],
    "loserSeats": [5, 3, 0]
  }
}

Read the record against the walkthrough. The actions are the 12 decisions in order. Bo clicks twice and passes, Cy clicks and passes, and Dee clicks and is shot. Bo clicks and passes, and Cy clicks and is shot. Bo clicks and passes, and Ada clicks and is shot. The settlement is the Last Hood Standing table you just read, in millionths of a USDG: 1000000 is 1.00 USDG, so Bo's 2850000 is +2.85.

Change a single digit of a seed, a seat, an action or the settlement and the verifier rejects the record. In the app, your game history also keeps the commit your browser saw before the game and checks against that, so a record is never trusted on the strength of its own commit.

#Which mode should you play

Classic is quicker and the swings are smaller: most of the time you win a modest share, and now and then you lose one buy-in. Last Hood Standing is longer and more dramatic: most of the time you lose one buy-in, and now and then you take the whole pot. It also costs more per game, because the rake is taken on the whole winnings pool. At six players on a 5% tier, the average cost is 0.83% of your buy-in in Classic and 4.17% in Last Hood Standing. See Rake.

The spin is equally fair in both. Neither mode changes your odds of being shot when everyone clicks once.