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.
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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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