Math Problems and Texas Hold'em Bonus

On the Wizard's Texas Hold'em Bonus page, he states:

Quote:

A brute force approach was used to cycle through all possible cominations of cards. In total 7,089,794,712,000 hands were played out, requiring 72 days of computer time to loop through them all.

I created a SQL based version of this Texas Hold'em Bonus game and stumbled upon something that may help the Wizard calculate these odds much more quickly in the future.

There may be seven billion different individual combinations of two hands that can be dealt in Texas Hold'em Bonus but in hand evaluation, suits do not count. When you condense all of the possible hand strengths down, they come out to a very manageable number, less than 5000. Once you know how many combinations can occur in each hand strength ( for example, there are only 10 different possible Straights but 1277 different combinations of Flushes ) you can weight the results and do the math from the condensed table.

Meanwhile, I wanted to post my Texas Hold'em Bonus strategy that is easy to remember and gets the house edge down to about 3.6%. This is obviously far from the ideal of 2.037% but it's easy.

Fold on unsuited 2-3, 2-4, 2-5, 2-6, 2-7
Everything else, bet the flop.

On the Turn:
When holding a pocket pair, bet only if there is at least one community card lower than your pair, don't bet a pair of Twos, always bet a pair of Aces.
Bet if you have 10-A, J-A, Q-A or K-A.
On Non-Pairs, bet the outside straight or four card flush if your low card is 5 or better (even if only one hole card is contributing to the effort).
If your hole card(s) improve the flop by a factor of one hand strength, nothing becomes a pair, pair becomes two pair or thee of a kind (including pocket Twos!!), etc.. then bet. If your hole cards do not improve the flop, then do not bet.

On the River:
When holding a pocket pair, bet only if there is at least one community card lower than your pair, again, don't bet a pair of Twos, always bet pocket rockets.
If your hole card(s) improve the community cards by a factor of one hand strength then bet. If your hole cards do not improve the flop, then do not bet.

Of course the above doesn't cover every situation where you would want to make a bet, for example, if you're holding K-Q and the flop is three Aces, I'd go ahead and bet. So improvements can be made on the fly but I thought the above would be a handy rule-of-thumb approach. Also, remember to leave the table when you're winning because in the long run, you will lose.

I have a small revision, I ran a few more simulations and it looks like four card flushes are good to bet on the turn bet but if you tighten up the outside straight, it works a little better as well so I'll revise the advice to the following:

On the Turn:
When holding a pocket pair, bet only if there is at least one community card lower than your pair, don't bet a pair of Twos, always bet a pair of Aces.
Bet if you have 10-A, J-A, Q-A or K-A.
Bet the outside straight if your low card is 7 or better or if you hold an Ace.
Bet all four card flushes.
If your hole card(s) improve the flop by a factor of one hand strength, nothing becomes a pair, pair becomes two pair or thee of a kind (including pocket Twos!!), etc.. then bet. If your hole cards do not improve the flop, then do not bet.

Quote: s2dbaker

There may be seven billion different individual combinations of two hands that can be dealt in Texas Hold'em Bonus but in hand evaluation, suits do not count.

why?

As much as I appreciate you taking your time and knowledge to do such research, 3.6% is really not good enough for a 2.0% HE game

Well, that's my opinion since I'm AP. There are probably people who don't care about HE anyway xD

How did you even find this ancient thread?? it doesn't even appear under OP's "threads started by" list.

I'm pretty sure you can get some reduction by only caring about suited/non-suited (rather than specific suits) on the initial 2 cards, but beyond that, I think suits do matter. I tried to figure out how to get additional savings from the board's suitedness, but couldn't figure anything out.

edit: Oops. I looked from the end of the list, not realizing they were sorted by most recent post.

it's not ancient, it's the 3rd on the list for poker. poker subforum is just kinda dead

Quote: Neutrino

it's not ancient, it's the 3rd on the list for poker. poker subforum is just kinda dead

August 18th, 2010 at 6:18:41 AM

Quote: socks

August 18th, 2010 at 6:18:41 AM

I be damned. did not see that, ask the guy who bumped it

Quote: Neutrino

I be damned. did not see that, ask the guy who bumped it

duh, I searched for the topic. I thought the game would be offered at Wheeling [they mention it on their site, but evidently it is available only occasionally ].