Hello! Decision ??? At my casino,if your table...

[SittingBull]

and seat is selected U win 50.00. /forums/images/icons/laugh.gif
However,U are giving the opportunity to win an ADDITIONAL 100.00 as follows: /forums/images/icons/laugh.gif
3 five-card hands are dealt faced down.
If U choose the WINNING hand U win the ADDITIONAL 100.00.
If U do not select the winning hand,then U lose 25.00 of your ORIGINAL 50.00 . /forums/images/icons/mad.gif

Should U "Play the game" for another 100.00 OR just take the sure win of 50.00?? /forums/images/icons/confused.gif Assume ALL ties are in your favor.
My reasoning is as follows:(neglecting all ties)
The probability of picking the winning hand is 1/3 and of picking a loser is 2/3.
So your EV =(1/3)(100)-(2/3)(25)=+16.66... /forums/images/icons/shocked.gif
However,if U do not play, then
EV=(3/3)(50)-(0/3)(50)=+50.00... /forums/images/icons/laugh.gif
So it seems as if NOT playing is MORE profitable --although BOTH situations would be profitable.
Hmmm
Happy Pokering, /forums/images/icons/laugh.gif
SittingBull

[DPCondit]

Neglecting ties, you should go for it.

Assuming 1/3rd of the time you have the winner, that is worth 100 + 50 = 150.00.

2/3rds of the time you only get 25.00.

So, 150 + 25 + 25 = 200 over three tries.

200/3 = 66.67 which is 16.67 more than 50.00.

Don

[SittingBull]

[BruceZ]

However,if U do not play, then
EV=(3/3)(50)-(0/3)(50)=+50.00...

That's incorrect, if you do not play your EV is 0. 1(0) = 0. Just like the EV of a fold is always 0.

Of course you should play. You're getting 4-1 on a 2-1 shot. Your ev is 1/3(100) - 2/3(25) = 16.67.

[Cyrus]

"At my casino, if your table and seat is selected U win 50.00."

That is money you won and put in your pocket. It's your money now! That bet is over and done with. Congratulations on being a lucky person.

"U are giving the opportunity to win an ADDITIONAL 100.00 as follows:"

Okay. New bet.

"3 five-card hands are dealt faced down.
If U choose the WINNING hand U win the ADDITIONAL 100.00.
If U do not select the winning hand,then U lose 25.00 of your ORIGINAL 50.00 ."

You could have won previously 10 cents or $1 million. You'd still be asked to wager $50 in the new bet. This is a new bet! Forget about the "previous $100". That new bet is optional, right? Therefore you evaluate it on its own.

"Should U Play the game for another 100.00 OR just take the sure win of 50.00?? Assume ALL ties are in your favor."

Go for it. Disregarding the small (but beneficial anyway) probability of 2 hands tied, you have

[(1/3)(+$100)] + [2/3)(-$25)] = $33.33 - $16.67 = positive EV, as was already pointed out in this thread

_________________________________________

Because I'm sure you still feel you're gambling away the "casino's money", money you barely had a chance to warm your pocket with, just assume that the $100 you won is all that's happened. Then you go home. And come back the next evening at the card room. And there's a friend of yours at the bar who offers the same bet (one out of 3 poker hands wins $100, etc).

You'd take him up on that, right? Sure, you would! (We are assuming that you're friend is not a cheat!) And the $25 you will be betting against him with, you don't know or even care if they came from your salary, or last night's ATM withdrawal ,or that lucky $100 seat draw! It's a whole new day and a whole new bet.

Just realize now that having the two bets happening one right after the other changes nothing from the underlying math.

One more thing : All the above is easy to say when we are talking about sums that are generally accepted as being small. But if that was $25,000 versus winning $100,000 and all your fortune in life is less than twenty grand, then, what would you do??

Well, EV or no EV, you would be absolutely correct to think hard before accepting to bet those $25,000! (I wouldn't.)

[Cyrus]

Read

<ul type="square">..You could have won previously 10 cents or $1 million. You'd still be asked to wager $25 in the new bet. ...

Because I'm sure you still feel you're gambling away the "casino's money", money you barely had a chance to warm your pocket with, just assume that the $50 you won is all that's happened.[/list]

[SittingBull]

know Y I flunked out of Graduate School when I failed "The Theory of Probability" course. /forums/images/icons/frown.gif
Happy Pokering, /forums/images/icons/laugh.gif
SittingBull

[SittingBull]

your teaching skill. Your teaching post is excellent. /forums/images/icons/laugh.gif
The "big bet" part was thought provoking! /forums/images/icons/confused.gif
Since U would NOT bet your last 25K,I believe U would NOT play in a 30/60 poker game with a bankroll of 5K since U are a favorite to bust out EVEN if U are one of two or three top favorites in this game.
U implied that the short-term fluctuation of games of chance--even if U are a long-term favorite--can easily wipe U out(gambler's ruin). /forums/images/icons/mad.gif
Thanks again for your excellent clarification. /forums/images/icons/laugh.gif
Happy pokering, /forums/images/icons/laugh.gif
SittingBull

[Cyrus]

"The "big bet" part was thought provoking! Since U would NOT bet your last 25K,I believe U would NOT play in a 30/60 poker game with a bankroll of 5K since U are a favorite to bust out EVEN if U are one of two or three top favorites in this game. U implied that the short-term fluctuation of games of chance--even if U are a long-term favorite--can easily wipe U out(gambler's ruin)."

Thanks for the kind words, too kind.

I added the bit about that "big bet" not to mention "gambler's ruin" but because I felt it should be pointed out that EV isn't always everything! Of course, there are gamblers or advantage players who will tell you that if their EV is positive they will bet in a flash their all.

Even though I wouldn't, that doesn't make those gamblers' action wrong. For them, the thrill of risking so much is obviously a much greater kick than my relative need for greater certainty in the pocket. This is a very valuable concept, called by persons well versed in probability such as BruceZ, utility. It denotes essentially personal preference. Gambler prefers thrill, I prefer paycheck. To each his own.

Suppose you and I have to drive from A to B. I want to save on gas money so I choose to go the shortest route which, however, I know is a route stuck with traffic. But I don't mind waiting a bit, with the car motor running idly, as long as I'm saving money. You on the other hand want to get there fast, so you take the route that'll take you to the destination quicker, although it'll cost you some extra gas money because it's a detour, although a very deserted detour, plus you'll be speeding.

You prefer to save time, I prefer to save money; same "game", different utilities.

In the case of that game with the $25,000 bet, the EV is exactly the same whether Bill Gates is wagering the money or I am wagering the money. Only thing is, Bill Gates' utility and mine are probably way too different! (Run a search on the web for more on that intriguing topic.)

[BruceZ]

I believe U would NOT play in a 30/60 poker game with a bankroll of 5K since U are a favorite to bust out EVEN if U are one of two or three top favorites in this game.

Here are some risk of ruins for a 30-60 game with a 5K bankroll.

<pre><font class="small">code:</font><hr>
$/hr sigma BB risk of ruin

30 8 27.2%
30 10 43.5%
30 12 56.1%
40 8 17.6%
40 10 32.9%
40 12 46.2%
50 8 11.4%
50 10 24.9%
50 12 38.1%
60 8 7.4%
60 10 18.9%
60 12 31.4%

</pre><hr>
r = exp(-2uB/sigma^2)

r = risk of ruin
u = hourly rate
sigma = hourly standard deviation

The only one of these cases where you are a favorite to go bust is when you make $30/hr with a standard deviation of 12 BB. This could be the case for many good players, but some can do better than this. Still, the risk of ruin is quite high even for the best players. Note that doubling the bankroll to 10K has the effect of squaring the risk of ruin, hence making it dramatically smaller since it is a number less than 1. In general, increasing the bankroll by a factor of n raises the risk of ruin to the nth power even for non-integer n.

[SittingBull]

what bankroll must he have if he wants his ruin risk to be less than 10%? Assume a SD of 20BB's per hr.
Happy pokering,
/forums/images/icons/laugh.gif SittingBull

[BruceZ]

Just invert above formula. B is bankroll:

B = -(sigma^2/2u)ln(r)

For r = 10% = 0.1 and SD = 20*60 = $1200:

win rate = $10/hr, B = $165,786
win rate = $20/hr, B = $82,893
win rate = $30/hr, B = $55,262
win rate = $40/hr, B = $41,447
win rate = $50/hr, B = $33,157
win rate = $60/hr, B = $27,631

These bankrolls are very large (450-2700+ BB) because the standard deviation is so large.

[SittingBull]

larger bankroll to win a smaller hourly rate than he would need to win a larger hourly rate. What am i missing?? /forums/images/icons/confused.gif
Hmmm
Just wondering,
SittingBull

[BruceZ]

For a given standard deviation, the less you win, the larger bankroll you need, since your winnings are too small to overcome the swings caused by your standard deviation. We are assuming a constant standard deviation independent of winnings. Often, winning less will decrease your standard deviation, and winning more will increase it, so you need to know both to make this calculation. Bankroll and risk of ruin depend more on standard deviation than win rate since they depend on the square of the standard deviation or the variance.

20 bb/hr might be a standard deviation for a shorthanded game, or a very volatile game. People play these games because they can win more money. If you win twice as much money, but at the same time you also double your standard deviation, then you will need twice the bankroll to play this game for the same risk of ruin. You would have to win 4 times as much money in order to have the same risk of ruin with the same bankroll.

[BruceZ]

If your win rate were only $10/hr in a 30-60 game, you would be much better off playing in a 10-20 game if you could win that same $10/hr, because then your standard deviation would be 1/3 as much, and you would only need 1/9 as much bankroll for the same risk of ruin.

[SittingBull]

game is -10BB's to +10BB's.
Is this information sufficient to estimate my SD? Or would U need more information?
Just wondering, /forums/images/icons/shocked.gif
SittingBull

[BruceZ]

If your average swing per hour is +/- 10 bb, then your standard deviation should be approximately 12.5 bb. That is, 10 bb is .8*sigma. Note that this is different from saying half of your results lie within +/- 10 bb, and half lie outside. That would mean 10 bb was .67*sigma, and sigma would be approximately 14.9 bb. Your results should lie within +/- 1 sigma 68% of the time. All of these methods will tend to overestimate sigma a little since your actual hourly results are not exactly normally distributed. To get your true standard deviation you would average the square of your hourly swings to get the variance, then take the square root. See Mason's essay on computing your standard deviation in the essay section for variable length sessions.

The .8*sigma comes from:

[2/(sqrt(2pi)*sigma)]*integral[0 to infinity]x*exp[-x^2/(2*sigma^2)]
= 2*sigma/sqrt(2pi) = .8*sigma.

[SittingBull]

[rigoletto]

Make them a proposal: Youhave to choose a winner among 4 hands. After you choose they remove one of the loosing hands and you get to choose again! This way you get 2:1 instead of 3:1 /forums/images/icons/wink.gif