I wrote, "You do about 1% better by holding trip A's vs Aces full. Since dealt Aces full occurs about once in 9,000 hands, the overall net gain from playing that hand correctly is 0.0001%. That's a $1 saving for every $1 million in bets."
Specifically, a 5-unit bet has an EV of 50.574 if you hold the trips, compared to 50.000 if you hold the FH. The difference is indeed "about 1%" of the EV, BUT it's 11.5% of the initial bet. (Thanks go to my old friend "Shoe" for pointing this out.) This makes the cost about 10 times greater than I had calculated, but luckily, 10 times almost nothing is still almost nothing. In this case, the savings for every $1,000,000 in bets is actually $12.70.
There is a similar but even smaller correction to be made for the AAXX vs AA decision. The result is that you actually save 95 cents per $100,000 bets, not 50 cents as I'd written.
--Dunbar
---In vpFREE@yahoogroups.com, <h_dunbar@...> wrote :
Lone Locust is correct, but both decisions are pretty close, and making the wrong choice is almost costless.
You do about 1% better by holding trip A's vs Aces full. Since dealt Aces full occurs about once in 9,000 hands, the overall net gain from playing that hand correctly is 0.0001%. That's a $1 saving for every $1 million in bets. I'm sure that if you have any bankroll considerations at all at the level you're playing, you're better off keeping the full house. (I just wanted to get that in before NOTI said it! ;>)
Holding AA over AAxx nets you a tiny 0.15% gain. You have a 0.37% chance of being dealt AAXX, so the total gain is 0.15%*0.37% = 0.00054%. (For every $100,000 in action, you save about 50 cents by making the right decision.)
Harry also suggested following "A over 2 hi (exc suited JQ)." That's gotta be an "oops", right? Harry, maybe you were thinking DDB, but even then it would be something like "A over unsuited 2 hi (exc JQ)."
--Dunbar
---In vpFREE@yahoogroups.com, <zorak@...> wrote :
On Wed, 18 Jul 2019,
harry.porter@... [vpFREE] wrote:
> Hope you at least add:
> Pair AA over 2 pr, AAA over FH, A over 2 hi (exc suited JQ).
It's admittedly been quite a long time since I played 10/7 but
I don't remember breaking AAxx to hold just AA. 9/7 maybe?
AAA > AAAxx, yes.