Merry Christmas ... and a quiz

[slapdash]

I'm off on Sunday for two weeks holiday. Have a happy Christmas and a great New Year,
everybody.

Thought I'd leave you with a festive poker quiz to think about while you're cooking
the turkey. I don't necessarily know the answers to all of these.



(1) Playing a 10-player $10/$20 No Limit Holdem cash table on Boxing Day, everybody
starts with $1000. On the first hand, you are dealt pocket aces under the gun, and
being under the misapprehension that "St. Stephen's Day" refers to St. Stephen of
Hungary, you go all in.

However, Santa Claus brought you a Wand of Calling for Christmas, with which you can
make each other player call or fold as you wish. Unfortunately, Santa didn't bring
you the magic spectacles that you really wanted, with which you could have seen what
everybody's cards were.

Assuming you want to maximize your expected winnings on the hand, who do you force to
call, and who do you force to fold?



(2) Snowpoker.com have a special royal flush jackpot for Christmas. For the first royal
flush, everybody at the table wins a year's supply of reindeer food.

At each of two tables, one Texas Holdem and one seven card Stud, 7 players sit down and
proceed to call/check every hand down in the hope of winning the jackpot. Assuming they
play the same number of hands per hour, which table is more likely to win the jackpot?



(3) Same as (2), but the rules say you have to use both of your pocket cards (in Holdem)
or both of your first two downcards (in Stud) to make the royal flush. Which table is more
likely to win the jackpot?



(4) There is a lesser jackpot for the first straight flush: same rules as in (3). Which
table is more likely to win it?



(5) You're playing a heads up seven card stud cash game against Santa Claus. He's completely
hammered you (Ho, ho, ho! ). You're down to your last dollar, and the antes put you all
in. You decide that, win or lose, this is your last hand. Santa deals, and being a generous
and jolly guy, before he deals his own up-card, he lets you look at your first three cards
and choose whether to play this hand as straight stud, razz, or stud hi/lo (eight or better).

Assuming you want to maximize your expected winnings, are there any cards you could have
that would make you choose hi/lo?



(6) I get back on 1 January and won't play any focus games before then.

Will I still be in the top 100 when I get back?

[GotaFancy?(BPP)]

(1) All of them call
(2) Chances are the same
(3) Chances are the same
(4) They are the same (am I missing something? )
(5) No
(6) I wont answer, because I know exactlt how many points you'll be on.....

[slapdash]

Originally Posted by GotaFancy?

(4) am I missing something?

Wasn't intending to answer any questions before I left, apart from clarifying
the questions if necessary, but ... yes!

Admittedly, the chances of the two tables in (2), (3) and (4) are very close,
but not identical.

[ubermonkey1]

right here are my answers.

1 anybody with a ace or pocket pair call ,all the rest fold
2 holdem table should be a slightly better bet for the royal flush
3 odds go back to even
4 same as above
5 yes aa2 suited not the best for razz with 2 aces and id rate it slightly better than playing it in stud high
6 yes ,i reckon you must have a couple of hundred at least in the last few weeks so you would be top 100 easy

dunno if i got any right ,probably not

[slapdash]

Originally Posted by ubermonkey1

right here are my answers.

1 anybody with a ace or pocket pair call ,all the rest fold

I'm afraid you have to decide without knowing what they have.

[slapdash]

I'm back! Answers (where I know them) for the quiz ...

Originally Posted by slapdash(BBP)

(1) Playing a 10-player $10/$20 No Limit Holdem cash table on Boxing Day, everybody
starts with $1000. On the first hand, you are dealt pocket aces under the gun, and
being under the misapprehension that "St. Stephen's Day" refers to St. Stephen of
Hungary, you go all in.

However, Santa Claus brought you a Wand of Calling for Christmas, with which you can
make each other player call or fold as you wish. Unfortunately, Santa didn't bring
you the magic spectacles that you really wanted, with which you could have seen what
everybody's cards were.

Assuming you want to maximize your expected winnings on the hand, who do you force to
call, and who do you force to fold?

Of course, you're less likely to win if there are more players in the pot, but
you'll win more when you do win, and this more than makes up for the
smaller chance of winning ... until you get to 10 players:

8 players: 38.7% chance of winning, so expected return of $8000 * 0.387 = $3096 (ignoring blinds).

9 players: 34.7% chance of winning, so expected return of $9000 * 0.347 = $3123.

10 players: 31.1% chance of winning, so expected return of $10000 * 0.311 = $3110.

So you should force all but one of the players to call, and that one might as
well be the big blind, to make the pot slightly bigger.

(2) Snowpoker.com have a special royal flush jackpot for Christmas. For the first royal
flush, everybody at the table wins a year's supply of reindeer food.

At each of two tables, one Texas Holdem and one seven card Stud, 7 players sit down and
proceed to call/check every hand down in the hope of winning the jackpot. Assuming they
play the same number of hands per hour, which table is more likely to win the jackpot?



(3) Same as (2), but the rules say you have to use both of your pocket cards (in Holdem)
or both of your first two downcards (in Stud) to make the royal flush. Which table is more
likely to win the jackpot?



(4) There is a lesser jackpot for the first straight flush: same rules as in (3). Which
table is more likely to win it?

In all of these, the chance of any particular player getting a royal/straight
flush doesn't depend on which game it is: it's just the chance of making the
hand from seven random cards (using two specified cards from the seven
in problems (3) and (4)).

The chance that somebody at the table will get a royal/straight flush is
about seven times as high, but not exactly, as this counts more than once
the occasions when more than one player gets one. So the question is
really about which table is more likely to get more than one qualifying hand
on the same deal.

(2) If a particular player makes a royal flush in holdem, there's a 1 in 21
chance that he does it using the 5 community cards, so that all seven
players make a royal flush. This is far higher than the chance that a second
player makes a royal flush in stud. So the stud table is more likely to get a
royal flush first.

(3) With these rules, it's not possible to have two qualifying hands on the
same deal in holdem, but it is in stud, so the holdem table is more likely to
get a royal flush first.

(4) This turns out to be very close, but the holdem table is slightly more
likely.

If you want actual figures for the chance of a qualifying hand:

(2) Holdem: 217 times per million.
Stud: 226 times per million.

(3) Holdem: 107735 times per billion.
Stud: 107729 times per billion.

(4) Holdem: 1076737 times per billion.
Stud: 1076697 times per billion.

(5) You're playing a heads up seven card stud cash game against Santa Claus. He's completely
hammered you (Ho, ho, ho! ). You're down to your last dollar, and the antes put you all
in. You decide that, win or lose, this is your last hand. Santa deals, and being a generous
and jolly guy, before he deals his own up-card, he lets you look at your first three cards
and choose whether to play this hand as straight stud, razz, or stud hi/lo (eight or better).

Assuming you want to maximize your expected winnings, are there any cards you could have
that would make you choose hi/lo?

Don't know, but if there are such cards, then:

Comparing straight stud with hi/lo, there's no difference if there's no qualifying
low hand, and if there is one, then there's no difference to the high half of
the pot, so you just need that if there's a qualifying low hand then the
chance of winning low should be greater than the chance of winning
high.

Comparing razz with hi/lo, if there is a qualifying low hand then there's no
difference to the low half of the pot, but for the other half of the pot,
you're just comparing the chance of winning high with the chance of
winning low, exactly as in the comparison of straight stud and hi/lo, so you
need to do worse at hi/lo here. But if there's no qualifying low hand, the
whole pot goes to the best high hand in hi/lo and to the best low hand in
razz, so you need that if there's no qualifying low hand then the chance
of winning low should be less than the chance of winning high.

Maybe something like K32 would work?

(6) I get back on 1 January and won't play any focus games before then.

Will I still be in the top 100 when I get back?

No. 105th.

[GotaFancy?(BPP)]

Welcome back mate

My head hurts!!!!