No Limit Hold'em: Theory and practice

[mdb]

page 33 says that JJ is a 4.5:1 dog vs. AA preflop. Does someone know how to calculate those odds?

[belloc]

[ QUOTE ]
page 33 says that JJ is a 4.5:1 dog vs. AA preflop. Does someone know how to calculate those odds?

[/ QUOTE ]

Well, you need to figure out how the JJ hand can beat AA. It can win with a Jack on board (AND no Ace), or with any straight to the J, Q, or K (except 9TJQK), or with a four-flush that doesn't include one of the Ace suits.

If you include all those straights and flushes, it becomes a more than trivial probability problem, so the practical way is to run out a simulation a few million times and let it tell you how often the JJ wins.

Depending on suits, it generally comes out to between 79 and 81 percent, or about 4 to 4.5 to 1.

[SplawnDarts]

Lots of random boards.

If you want an at-the-table estimate, you can use the 2% rule. JJ has 2 outs 5 time so 2 * 5 * 2% = 20% chance of winning, which is a 4:1 dog. Not exact, but close enough. The extra .5 in the real number is AA's redraw to better trips.

[PantsOnFire]

[ QUOTE ]
Lots of random boards.

If you want an at-the-table estimate, you can use the 2% rule. JJ has 2 outs 5 time so 2 * 5 * 2% = 20% chance of winning, which is a 4:1 dog. Not exact, but close enough. The extra .5 in the real number is AA's redraw to better trips.

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JJ also has more ways to make a straight although that percentage is probably not very high. As well, the suits count for something for four flush boards.

I like your math approach though because it is easy to do and you don't really need to be that accurate in most circumstances.

[belloc]

[ QUOTE ]
[ QUOTE ]
Lots of random boards.

If you want an at-the-table estimate, you can use the 2% rule. JJ has 2 outs 5 time so 2 * 5 * 2% = 20% chance of winning, which is a 4:1 dog. Not exact, but close enough. The extra .5 in the real number is AA's redraw to better trips.

[/ QUOTE ]
JJ also has more ways to make a straight although that percentage is probably not very high. As well, the suits count for something for four flush boards.

I like your math approach though because it is easy to do and you don't really need to be that accurate in most circumstances.

[/ QUOTE ]

The "2% rule" is helpful when counting outs for draws after the flop, but you really need to have at your fingertips all the qualitatively different preflop hand matchups (esp. for tournament play).

Examples:

Overpair vs. Underpair: 4.5 to 1 (~82%)
Underpair vs. Overcards: 6 to 5 (~55%)
Pair vs. One overcard: 7 to 3 (~70%)
Overpair vs. Two undercards: 6.5 to 1 (~87%)
Overcards vs. Live undercards: 3 to 2 (~60%)
One overcard vs. Live cards: 3 to 2 (~60%)

There are several other permutations, but generally, you'll want to have these down cold for decisions before the flop. Some things (like suitedness & connectedness) affect these percentages a bit, but these are in the ballpark.

IIRC, the Miller/Sklansky NLHETAP book has all of these given somewhere near the back. I'm sure Harrington does too.