Ace-High Poker Dice

Five dice, three rolls.
You may re-roll any number of dice. Move keepers to the bottom; you can move them back up.
Use the numbers to make standard poker hands (except for flushes because there are no suits).
Ones are high, like aces, except in a straight (see below).
No, you don’t need special dice.

First, click play the house to let the house play.
Then click roll the dice and try to beat it.
First to win 21 hands wins the match.
To play by yourself, click start over if necessary, then just roll the dice.

Hands in order of rank:

five of a kind		“five aces”
four of a kind		“four threes”
full house		“twos over sixes”
straight		“straight, five high”
three of a kind		“three fours”
two pair		“aces and fives”
one pair		“pair of twos”
high card		“bust”

The rest of the dice (“kickers”) are used to break ties.

five high
six high
ace high

relative odds
five of a kind:	6
four of a kind:	150
full house:	300
straight:	360
three of a kind:	1200
two pair:	1800
one pair:	3600
bust:	360

after three rolls
five of a kind:	254
four of a kind:	1156
full house:	2522
straight:	378
three of a kind:	1283
two pair:	1850
one pair:	332
bust:	1

after three rolls, house strategy
five of a kind:	326
four of a kind:	1550
full house:	1737
straight:	377
three of a kind:	1792
two pair:	1522
one pair:	471
bust:	1

Straights are a special case. Using novelty dice with 9-10-J-Q-K-A card ranks printed on them, only two kinds of straight are possible, king or ace high; there is no ace-low straight. The equivalent with regular dice is to allow only straights with five or six high. Under these conditions, a straight is actually less likely than a full house and should beat it. But allowing ones to be either high or low like aces, a straight can have five, six, or ace high. Now a straight is more likely than a full house, just like using cards (so why not, you ask?). Some people dodge the issue and count straights as busts. Take your pick:

allow ace-high straight; full house beats a straight (just like cards)
full house beats a straight (card odds)
straight beats a full house (dice odds)
straight is a bust

The basic strategy is to keep duplicates (pairs, triples, etc.) or a straight, and re-roll the rest. It is never an advantage to keep four dice and go for a straight (but you are welcome to, says the house).

• The player has an inherent advantage of about 8.4% over the house due to being able to re-roll unwinnable or lost hands (such as two pair vs. four of a kind) and stopping with a winning hand (no re-rolling kickers).

• An advantageous house strategy is to re-roll the lower of two pair, or the pair of a full house, after the first roll only. The player, of course, may imitate this strategy.

• A further advantage is for the house to keep the dice concealed, only revealing them when saving dice between rolls. The house will always end up with at least one hole die, greatly reducing the player’s inherent advantage.

• (A more advantageous player strategy takes the house’s hand into consideration, and can increase the player’s advantage by at least 1 - 2%.)

The odds of ending up with each hand are given to the right. Note that using dice, busts are inherently as likely as a straight.

All odds were determined by simulations of 100,000,000 hands, allowing ace-high straight. The other straight rules vary the odds by up to about 0.5%.

If it was good enough for Edward G. Robinson, it’s good enough for me.
“It’s a dollar if you lose, and if you win, you get $2 worth of merchandise.”

house:	0
you:	0