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Search: Posts Made By: BillC
Forum: Probability 05-01-2007, 02:29 PM
Replies: 1
Views: 136
Posted By BillC
Re: five card poker with 6th common card

How about with 3 common cards? 5?
Forum: Probability 04-25-2007, 05:10 PM
Replies: 1
Views: 136
Posted By BillC
five card poker with 6th common card

Suppose you deal out five card hands and then deal out a sixth common card. The best 5 card poker hand wins. What is the proability of a tie ?

Is there software out there to simulate this?
Forum: Probability 03-09-2007, 12:33 PM
Replies: 4
Views: 118
Posted By BillC
Re: EV and Variance

It would be surprising if the distribution for 10 hours is far form normal, but I am just not sure 10 hours suffices. I know that there have been studies about this on this site. I just remember...
Forum: Probability 03-08-2007, 08:40 PM
Replies: 4
Views: 118
Posted By BillC
Re: EV and Variance

I'm not so sure that you can invoke the Central Limit Theorem here. Short-term results can be much more extreme than predicted by the usual random walk model.
Forum: Poker Theory 03-08-2007, 08:21 PM
Replies: 3
Views: 117
Posted By BillC
Re: Sit and go and the Kelly criteria

But that 20-30 buy-in rule is based on the Kelly criterion.
Whether you like it or not, your choice of stakes is based on some estimate of your win rate or SD (unless you are overbankrolled or...
Forum: Poker Theory 03-07-2007, 10:43 AM
Replies: 4
Views: 99
Posted By BillC
Re: Security equivalent?

Its called Certainty Equivalent and it can be computed using your utility function often via quadratic approximation. Search

Kelly CE
Risk Adjustment for poker players
bjmath.com
Forum: Poker Theory 03-07-2007, 12:51 AM
Replies: 3
Views: 117
Posted By BillC
Re: Sit and go and the Kelly criteria

Figure your win rate r and variance v for large sample. Your bankroll should be v/r for full Kelly. So lets say you make 10$ per tourney with a standard deviation of 100$, your optimal bank will be...
Forum: Probability 12-04-2006, 03:02 PM
Replies: 10
Views: 1,001
Posted By BillC
Re: RoR in X amount of hands. Derivation?

I've been looking for a derivation for the trip ROR formula. Can anyone point me in the right direction?
/images/graemlins/confused.gif
Forum: Small Stakes 11-21-2006, 09:03 PM
Replies: 2
Views: 58
Posted By BillC
JJ on the button

1-2 NL, Hero (weak very tight) is on button with 180. UTG has about 300.
UTG calls, fold to cutoff who makes it 10.
Hero makes it 30.
UTG makes it 60.
All fold to button who calls.
Flop AQx rb...
Forum: Medium Stakes 11-08-2006, 12:07 PM
Replies: 1
Views: 66
Posted By BillC
2-5 Nit hand

2-5 full aggessive B&M game (100-300 buyin).
I'm in MP with about 500. I've been very nitty tight and starting to have the sense of being pushed around. I get ATo and bring it in making it 20 to...
Forum: Probability 10-19-2006, 03:22 AM
Replies: 10
Views: 1,001
Posted By BillC
Re: RoR in X amount of hands.

Does Schlesinger's trip ROR formula have a derivation in print. If so, I'd like to see it.
Forum: Poker Theory 10-14-2006, 06:40 PM
Replies: 8
Views: 116
Posted By BillC
Re: Kelly Criterion / Bankroll Management

The c=6 is the "optimal f" suggested by R. Vince (amazon him and see our paper on bjmath.com).
As in poker, a lot of the time investors don't know their edge and variance with much accuracy, so...
Forum: Probability 10-13-2006, 04:16 PM
Replies: 14
Views: 4,585
Posted By BillC
Re: bankroll concepts - risk of ruin

If you are engaged in an activity that say gives you a certain win rate r and variance v per unit of time (or e.g. 100 hands), betting k times Kelly translates into having a bankroll of v/(kr). The...
Forum: Two Plus Two Internet Magazine 10-12-2006, 03:49 PM
Replies: 8
Views: 246
Posted By BillC
Re: Bankroll article

In our paper on bjmath.com, there is a formula for the expected exit times for fractional Kelly betting. It is the "obvious" function of the win rate r.
Forum: Probability 10-12-2006, 03:33 PM
Replies: 14
Views: 4,585
Posted By BillC
Re: bankroll concepts - risk of ruin

1. You must take into account future bankroll supplements when discussing risk of ruin. If you do not, any discussion seems absurd. If you have an alternate bankroll model you will just have to end...
Forum: Probability 10-11-2006, 03:32 PM
Replies: 14
Views: 4,585
Posted By BillC
Re: bankroll concepts - risk of ruin

I am making some assumptions to invoke Kelly of course. Some fool might want to bet his whole BR on a coin flip, but Kelly is optimal in well-known senses, which one can read about.

Bankrolls...
Forum: Probability 10-11-2006, 10:50 AM
Replies: 14
Views: 4,585
Posted By BillC
Re: bankroll concepts - risk of ruin

Your risk of ruin is approximated by a function of your bankroll, expectation and variance. Therefore as you bank changes, so does your risk of ruin. There is no "once and for all" number.

If...
Forum: Poker Theory 05-18-2006, 01:07 AM
Replies: 13
Views: 348
Posted By BillC
Re: kelly criterion

Here is a text of the article. A new article that gives precise calculation and analysis of precise excess pot odds required is in the works. Comments welcome.

BillC

What Poker Players Can...
Forum: Poker Theory 03-19-2006, 05:26 PM
Replies: 13
Views: 348
Posted By BillC
Re: kelly criterion

The concept is a more precise version of the advice that one should forgo marginal +EV, high SD situatons. So for example if you have a longshot draw, you need slightly higher pot odds than dictated...
Forum: Probability 03-05-2006, 11:47 PM
Replies: 4
Views: 112
Posted By BillC
Re: Has anyone come up with a ROR formula that includes...

Actually, the t-distibution is for the case where the standard deviation is unknown.
Forum: Probability 02-16-2006, 04:20 PM
Replies: 4
Views: 116
Posted By BillC
Re: Advanced Probability (math or stat majors probably only need apply

I agree with the others that you should be more clear (I would take points off for sloppiness). I presume 0<c<1.

It is unethical to get 2+2'ers to do your HW for you...Otoh, you can't believe...
Forum: Probability 02-07-2006, 09:11 PM
Replies: 6
Views: 529
Posted By BillC
Re: Bankroll Management in Limit Poker and Fractional Brownian Motion

As a practical matter, why don't you just increase your variance to account for higher swings? This is the main remedy or easy out to the applying diffusion models.

After all, it is idle...
Forum: Poker Theory 02-07-2006, 07:30 PM
Replies: 8
Views: 362
Posted By BillC
Re: NL vs. Limit variance

You need to clarify whether you mean standard deviation or variance (the square of SD, measured in doolars squared).

You also need to give an idea of sample size.
Forum: Internet Gambling 12-07-2004, 05:43 PM
Replies: 60
Views: 2,284
Posted By BillC
Re: \"How many hands do I need to play...\" definitive answer

To get within 10% of actual win rate you need a sample of about 40,000 hours. To get an estimate to within 20%, you need only 10,000 hours. I am assuming that SD/EV=10 here. If you want to figure...
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