Derivations For Starting Hands With One Pair
Starting hands with one pair (XXYZ) can improve to three of a kind, a full house or four of a kind when either an X card is on the board or when two or three of the remaining Y or Z cards (YY or YYY) is on the board. They also improve to a full house if three or more of another rank is on the board (rrr or rrrr), although any other hand holding a pair also makes a full house with this board. These hands make two pair if another pair (rr) appears on the board. The following tables show all the ways for XXYZ 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 | XX*** | 15,180 | 0.0088652 | 111.8 : 1 | |
YYY** | 1,980 | 0.0011563 | 863.8 : 1 | ||
XXYYY | −2 | −0.0000012 | −856,153 : 1 | ||
Total (see #1 below) | 17,158 | 0.0100204 | 98.8 : 1 | ||
Full house | XYYZZ | 18 | 0.0000105 | 95,127.0 : 1 | |
XYYZr | 1,440 | 0.0008410 | 1,188.1 : 1 | ||
XYY?? | 9,360 | 0.0054663 | 181.9 : 1 | ||
XYZrr | 1,080 | 0.0006307 | 1,584.5 : 1 | ||
XYrrs | 25,920 | 0.0151375 | 65.1 : 1 | ||
Xrrss | 3,240 | 0.0018922 | 527.5 : 1 | ||
Xrrst | 69,120 | 0.0403667 | 23.8 : 1 | ||
YYZZr | 360 | 0.0002102 | 4,755.4 : 1 | ||
YYZ?? | 14,040 | 0.0081995 | 121.0 : 1 | ||
rrr** | 37,840 | 0.0220989 | 44.3 : 1 | ||
rrrXX | −40 | −0.0000234 | −42,808.6 : 1 | ||
rrrr* | 440 | 0.0002570 | 3,890.6 : 1 | ||
Total (see #2 below) | 162,818 | 0.0950871 | 9.5 : 1 | ||
Three of a kind | XYZrs | 12,960 | 0.0075687 | 131.1 : 1 | |
XYrst | 92,160 | 0.0538222 | 17.6 : 1 | ||
Xrstu | 107,520 | 0.0627926 | 14.9 : 1 | ||
YYrrs | 12,960 | 0.0075687 | 131.1 : 1 | ||
YYrst | 46,080 | 0.0269111 | 36.2 : 1 | ||
Total | 271,680 | 0.1586634 | 5.3 : 1 | ||
Two pair | YZrrs | 19,440 | 0.0113531 | 87.1 : 1 | |
YZrst | 69,120 | 0.0403667 | 23.8 : 1 | ||
Yrrss | 9,720 | 0.0056766 | 175.2 : 1 | ||
Yrrst | 207,360 | 0.1211000 | 7.3 : 1 | ||
rrsst | 51,840 | 0.0302750 | 32.0 : 1 | ||
rrstu | 322,560 | 0.1883778 | 4.3 : 1 | ||
Total | 680,040 | 0.3971491 | 1.5 : 1 | ||
One pair | Yrstu | 322,560 | 0.1883778 | 4.3 : 1 | |
rstuv | 258,048 | 0.1507022 | 5.6 : 1 | ||
Total | 580,608 | 0.3390800 | 1.9 : 1 |
Read more about this topic: Probability Derivations For Making Rank-based Hands In Omaha Hold 'em
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