I was doing some google research and wanted to know the odds of hitting a high hand to see how much a $500 high hand every 10 minutes would add to my hourly and see if it was worth driving extra time to go play there.

I couldn't really find any useful information on google.

The high hand has to be at least AAA22 or better to qualify and than has to hold.

There are about 20 tables playing in this room.

The promotion is only good on Texas hold'em on the 1/3 and 2/5 tables.

There was a similar thread in the Probability Forum a few months ago which I will link below.

https://forumserver.twoplustwo.com/2...-odds-1719817/

There are at least four variables to consider here. A couple of them you can try to calculate exactly, but a couple of them you can only estimate.

1. The odds of making a qualifying high hand.
2. The odds of having it hold up.
3. The number of hands that are dealt per table in the relevant time frame.
4. The number of seated players during that time.

A couple of years ago, I made AAAAQ with 15 minutes to go on the time period for a $500 bonus on a busy Saturday. I was nervous during those 15 minutes because I had no idea how likely that hand was to hold up. It did hold up, but when I got home I looked up the odds of making a straight flush, multiplied those odds by my estimate of the number of seated players at 25 qualifying tables, and multiplied those odds by my estimate of the number of hands that could be dealt in 15 minutes (maybe 8 or 9). It turned out that the odds of someone making a straight flush to beat me were about 50-50 in those circumstances (I ignored the odds of someone making exactly AAAAK for the sake of simplicity).

The problem with the probability charts in the thread whosnext linked to is that they assume every player stays in until the river every hand, and they don't include high hands in which only one hole card plays, which your room may allow.

So I would approach your problem this way: 20 tables x 9 players x 8.5 hands dealt in 15 minutes = 1,530 unique poker hands dealt in this room every 15 minutes. What are the chances that someone will make AAA22 or better once in 1,530 poker hands? Maybe 80%? That's a ballpark guesstimate based on what I've observed in a busy room that has high-hand bonuses every 30 minutes, in which only one hole card must play.

You can use probability charts to try to calculate that more precisely if you want. But your calculations are always going to include estimates of the number of players (since there are often lobbyers and open seats), the frequency of hands dealt (since this will depend a lot on both the dealer and the action at a given table), and the frequency of qualifying hands being played to the river.

So the value of this promotion per hour is 80% (my ballpark guesstimate) x 4 (1 every 15 minutes) x $500 divided by 180 (total number of seated players) = $8.89/hour. That's the EV of this promotion to you.

i think that another interesting question is: because high hands are so rare, should we play without considering them and put them in the 'rouge wave' category?

of coarse on straight flush boards we have to consider them especially when one card can make the SF, but im more referring to boards where we have boats and our opponent is repping quads (quads are a high hand right?). this happens a lot more in omaha

The room I play in you have to use both hole cards. There has to be a way to calculate the odds.

Also it would be nice to know if you wanted to sell or buy a high hand for a smaller pay out.

It's somewhat complicated if you have to use 2 hole cards because you have to go through each potential case.

4 of a kind for example you'd have to include (AK)AAAXX but exclude (AX)AAAKX where they parens are your hole cards. It's certainly not impossible just lots of edge cases. Though they probably don't effect the probability to a significant degree. I might try something later because I find practicing this combinatoric questions fun.

Deriving the prob of making an exact hand is often the "easy" part.

Of course, for a high hand jackpot that exact hand must win the pot (nobody else has a higher hand). Taking that factor into account is often the "hard" part.

Agree which is why I think this is more interesting than the normal how often do I make this hand questions.

The 2 hole cards seems to add some odd edge cases as well making it more difficult. For example if you make a fullhouse with A2 but the board pairs. Your winning hand is the fullhouse with the pair on board which won't qualify.

I also assume there is no tie like if you and the same player make the same high hand the first player that made the hand is the player that has claim to the jackpot unless it is unseated by a better hand.