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Nutz

Introduction

Nutz is a dice game that has been known to be played at the Crown casino in Melbourne. It is like Yahtzee in that five dice are used, with matching dice held and singletons re-rolled, up to three rolls, as long as there is at least a pair. The re-rolling strategy is fixed so there is no element of skill, other than bet selection. There are seven bets available on the winning hand.

Rules

  1. The game uses five six-sided dice.
  2. The available bets are as follows. Pays are on a "to one" basis.
    • Nutz (five of a kind) — Pays 100 if achieved on the first roll, 25 if on the second or third roll.
    • Pair — Pays 25
    • Straight or No Hand — Pays 9
    • Quads — Pays 5
    • Trips — Pays 5
    • Two Pair — Pays 3
    • Full House — Pays 2
  3. After the first roll, any pair, two pair, trips, or four of a kind will be set aside and the rest of the dice re-rolled. In the event of any hand that makes use of all five dice, including a "No Hand", then that shall be the final outcome with no further rolling.
  4. After the second roll, any dice that match those set aside after the first roll shall also be set aside. As after the first roll, if a five-dice combination is achieved at this point, then play will stop. Otherwise there will be a third roll.
  5. After the third roll, any dice that match those set aside after the first and second rolls shall also be set aside.
  6. The dealer will pay winning bets according to the final combination of the five dice.

Following are examples of the various hands:

  • Nutz — 5-5-5-5-5.
  • Pair — 2-3-5-5-6
  • Straight — 2-3-4-5-6
  • No Hand — 1-3-4-5-6
  • Quads — 2-5-5-5-5
  • Trips — 2-3-3-3-6
  • Two Pair — 1-1-3-5-5
  • Full House — 2-2-6-6-6

Analysis

Following is my analysis of the Nutz bet. The lower right cell shows a house edge of 10.63%.

Nutz Analysis

Rolls Needed Pays Combinations Probability Return
1 100 362,797,056 0.000772 0.077160
2 or 3 25 14,752,627,200 0.031376 0.784405
Loss -1 455,069,560,320 0.967852 -0.967852
Total   470,184,984,576 1.000000 -0.106286

All other bets are simple win or lose bets and covered in the following table. Combinations are out of a possible 615 = 470,184,984,576.

All Other Bets

Bet Pays Combinations Probability Return
Pair 25 16,796,160,000 0.035722 -0.071216
Straight or No Hand 9 43,535,646,720 0.092593 -0.074074
Quads 5 67,884,480,000 0.144378 -0.133731
Trips 5 72,783,360,000 0.154797 -0.071216
Two Pair 3 105,479,884,800 0.224337 -0.102652
Full House 2 148,590,028,800 0.316025 -0.051926

Strategy

The lowest house edge is on the full house at 5.19%. If you must play, I would recommend betting on that only.

External Links

  • Rack card
  • Discussion about Nutz in my forum at Wizard of Vegas.

Written by: Michael Shackleford