Derivations For Starting Hands With No Pair
Starting hands with no pair (XYZR) can improve when two or three of the remaining X, Y, Z or R cards (XX or XXX) appears on the board. These hands can make two pair or a full house when two of more ranks from the hand appear (XY or XXY). They also can make three of a kind or a pair if two or three other ranks (ss or sss) appear, although these boards are likely to improve other hands at least as much. The following tables show all the ways for XYZR to make four of a kind, a full house, three of a kind, two pair, one pair or no pair (high card) on the flop, turn and river.
|
||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
|
Hand to make | Board | Derivation | Combos | Probability | Odds |
---|---|---|---|---|---|
Four of a kind | XXX** | 3,960 | 0.0023127 | 431.4 : 1 | |
Full house | XXYYZ | 324 | 0.0001892 | 5,283.9 : 1 | |
XXYYs | 1,944 | 0.0011353 | 879.8 : 1 | ||
XXYZR | 324 | 0.0001892 | 5,283.9 : 1 | ||
XXYZs | 11,664 | 0.0068119 | 145.8 : 1 | ||
XXY?? | 68,040 | 0.0397359 | 24.2 : 1 | ||
Total | 82,296 | 0.0480616 | 19.8 : 1 | ||
Three of a kind | XX??? | 85,680 | 0.0500378 | 19.0 : 1 | |
XYsss | 1,944 | 0.0011353 | 879.8 : 1 | ||
Xssst | 13,824 | 0.0080733 | 122.9 : 1 | ||
ssss* | 396 | 0.0002313 | 4,323.0 : 1 | ||
sss?? | 17,856 | 0.0104281 | 94.9 : 1 | ||
Total | 119,700 | 0.0699058 | 13.3 : 1 | ||
Two pair | XYZRs | 2,916 | 0.0017030 | 586.2 : 1 | |
XYZ?? | 68,040 | 0.0397359 | 24.2 : 1 | ||
XYsst | 93,312 | 0.0544950 | 17.4 : 1 | ||
XYstu | 290,304 | 0.1695400 | 4.9 : 1 | ||
Total | 454,572 | 0.2654739 | 2.8 : 1 | ||
One pair | Xsstt | 15,552 | 0.0090825 | 109.1 : 1 | |
Xsstu | 290,304 | 0.1695400 | 4.9 : 1 | ||
Xstuv | 387,072 | 0.2260533 | 3.4 : 1 | ||
ssttu | 36,288 | 0.0211925 | 46.2 : 1 | ||
sstuv | 193,536 | 0.1130267 | 7.8 : 1 | ||
Total | 922,752 | 0.5388950 | 0.9 : 1 | ||
No pair | stuvw | 129,024 | 0.0753511 | 12.3 : 1 |
Read more about this topic: Probability Derivations For Making Rank-based Hands In Omaha Hold 'em
Famous quotes containing the words starting, hands and/or pair:
“He was at a starting point which makes many a mans career a fine subject for betting, if there were any gentlemen given to that amusement who could appreciate the complicated probabilities of an arduous purpose, with all the possible thwartings and furtherings of circumstance, all the niceties of inward balance, by which a man swings and makes his point or else is carried headlong.”
—George Eliot [Mary Ann (or Marian)
“Since theres no help, come let us kiss and part;
Nay, I have done, you get no more of me,
And I am glad, yea, glad with all my heart
That thus so cleanly I myself can free;
Shake hands for ever, cancel all our vows,
And when we meet at any time again,
Be it not seen in either of our brows
That we one jot of former love retain.”
—Michael Drayton (15631631)
“I well recall my horror when I heard for the first time, of a journalist who had laid in a pair of what were then called bicycle pants and taken to golf; it was as if I had encountered a studhorse with his hair done up in frizzes, and pink bowknots peeking out of them. It seemed, in some vague way, ignominious, and even a bit indelicate.”
—H.L. (Henry Lewis)