Probability Derivations For Making Rank-based Hands in Omaha Hold 'em - Derivations For Starting Hands With Two Pair

Derivations For Starting Hands With Two Pair

Starting hands with two pair (XXYY) can improve to three of a kind, a full house or four of a kind when one or more of the four remaining X or Y cards appears (X, XX or XY). They also improve to a full house if three or more of another rank appears on the board (rrr or rrrr), although any other hand holding a pair also makes at least a full house with this board. If another pair appears the hand makes two pair, although any other hand holding a pair also makes at least two pair. The following tables show all the ways for XXYY to make four of a kind, a full house, three of a kind, two pair or one pair on the flop, turn and river.

Derivations for rank type XXYY (two pair) on the flop
Hand to make Board Derivation Combos Probability Odds
Four of a kind XX* 92 0.0053191 187.0 : 1
Full house Xrr 264 0.0152636 64.5 : 1
rrr 44 0.0025439 392.1 : 1
Total 308 0.0178076 55.2 : 1
Three of a kind XY? 176 0.0101758 97.3 : 1
Xrs 3,520 0.2035153 3.9 : 1
Total 3,696 0.2136910 3.7 : 1
Two pair rrs 2,640 0.1526364 5.6 : 1
One pair rst 10,560 0.6105458 0.6 : 1
Derivations for rank type XXYY (two pair) on the turn
Hand to make Board Derivation Combos Probability Odds
Four of a kind XXYY 1 0.0000051 194,579.0 : 1
XXYr 176 0.0009045 1,104.6 : 1
XX?? 1,892 0.0097235 101.8 : 1
Total 2,069 0.0106332 93.0 : 1
Full house XYrr 264 0.0013568 736.0 : 1
Xrrr 176 0.0009045 1,104.6 : 1
Xrrs 10,560 0.0542707 17.4 : 1
rrrr 11 0.0000565 17,688.1 : 1
rrrs 1,760 0.0090451 109.6 : 1
Total 12,771 0.0656337 14.2 : 1
Three of a kind XYrs 3,520 0.0180902 54.3 : 1
Xrst 42,240 0.2170829 3.6 : 1
Total 45,760 0.2351732 3.3 : 1
Two pair rrss 1,980 0.0101758 97.3 : 1
rrst 47,520 0.2442183 3.1 : 1
Total 49,500 0.2543941 2.9 : 1
One pair rstu 84,480 0.4341659 1.3 : 1
Derivations for rank type XXYY (two pair) on the river
Hand to make Board Derivation Combos Probability Odds
Four of a kind XXYY* 44 0.0000257 38,917.0 : 1
XXY?? 3,784 0.0022099 451.5 : 1
XX??? 26,488 0.0154692 63.6 : 1
Total 30,316 0.0177048 55.5 : 1
Full house XYrrr 176 0.0001028 9,728.0 : 1
XYrrs 10,560 0.0061671 161.2 : 1
Xrrrs 7,040 0.0041114 242.2 : 1
Xrrss 7,922 0.0046253 215.2 : 1
Xrrst 190,080 0.1110083 8.0 : 1
rrr?? 34,320 0.0200432 48.9 : 1
rrrr* 484 0.0002827 3,536.8 : 1
Total 250,580 0.1463408 5.8 : 1
Three of a kind XYrst 42,240 0.0246685 39.5 : 1
Xrstu 337,920 0.1973481 4.1 : 1
Total 380,160 0.2220167 3.5 : 1
Two pair rrsst 71,280 0.0416281 23.0 : 1
rrstu 506,880 0.2960222 2.4 : 1
Total 578,160 0.3376503 2.0 : 1
One pair rstuv 473,088 0.2762874 2.6 : 1

Read more about this topic:  Probability Derivations For Making Rank-based Hands In Omaha Hold 'em

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