I'm putting Ganch to the test. I don't think he can get this.

[raiders72002]

What are the odds of running up a balance of $70,000 in black jack when the max bet is $1000?

[HedgeHog]

Did you mean $100 per hand? Nevermind, I just read $1000 per hand is apparently allowed at BOL.

[robzilla]

JJ said No puzzzzles!

[raiders72002]

JJ said No puzzzzles!

[Patrick McIrish]

If Ganch doesn't answer I'll take a stab.

[MrX]

Can you deposit $69,000?

[Justin7]

What are the rules? And shuffle points?

[raiders72002]

I don't play online blackjack so I'm just throwing something out here. Feel free to give me suggestions to revise.

Jokerfly says he only made $3000 in deposits but let's increase that 10x and go with a starting bankroll of $30,000.

Single deck, shuffle after each hand. Is that the way it's done online?

[Dark Horse]

Depends on how many hands you play. If you give a casino 3 million in action, that is 3000 hands for 1000. Right?

So you would have to go about 1535-1465, give or take, to be up 70 hands, if all hands were played for 1000.

A little management would improve whatever odds are involved in that.

[louisvillekid]

i've never played BJ online for real money, but i assume most places use a program of anywhere from 6-8 deck shoe, unless stated otherwise.

[Ganchrow]

Microgaming Vegas Strip Blackjack is one of the most commonly played versions of BJ played online and has some of the best odds.

The rules are 4 Decks, split up to 3 hands, S17, no surrender, double any two cards, double after split ok, one card only on split aces, dealer peeks for BJ and reshuffle after every hand.

When played with perfect composition dependent basic strategy has a payout likelihood matrix of:

<style> .ganch { font-size: 11px; font-family: Verdana, Arial, Helvetica, sans-serif; }</style> <table border=0 cellpadding=2 cellspacing=1> <tr> <td align=left class=ganch> Result </td> <td align=leftclass=ganch> Probability
</td> </tr> <tr> <td align=left class=ganch> -6 </td> <td align=right class=ganch> 0.0004790%
</td> </tr> <tr> <td align=left class=ganch> -5 </td> <td align=right class=ganch> 0.0051775%
</td> </tr> <tr> <td align=left class=ganch> -4 </td> <td align=right class=ganch> 0.0421265%
</td> </tr> <tr> <td align=left class=ganch> -3 </td> <td align=right class=ganch> 0.2009820%
</td> </tr> <tr> <td align=left class=ganch> -2 </td> <td align=right class=ganch> 4.1727300%
</td> </tr> <tr> <td align=left class=ganch> -1 </td> <td align=right class=ganch> 43.4707615%
</td> </tr> <tr> <td align=left class=ganch> &nbsp;0 </td> <td align=right class=ganch> 8.6984795%
</td> </tr> <tr> <td align=left class=ganch> +1 </td> <td align=right class=ganch> 32.6935805%
</td> </tr> <tr> <td align=left class=ganch> +1.5 </td> <td align=right class=ganch> 4.5429575%
</td> </tr> <tr> <td align=left class=ganch> +2 </td> <td align=right class=ganch> 5.8557220%
</td> </tr> <tr> <td align=left class=ganch> +3 </td> <td align=right class=ganch> 0.2372925%
</td> </tr> <tr> <td align=left class=ganch> +4 </td> <td align=right class=ganch> 0.0685955%
</td> </tr> <tr> <td align=left class=ganch> +5 </td> <td align=right class=ganch> 0.0098010%
</td> </tr> <tr> <td align=left class=ganch> +6 </td> <td align=right class=ganch> 0.0013150%
</td> </tr> </table>
This corresponds to an average of -0.3538197% units per hand with a standard deviation of 115.175354%.

The following stats are the results of a 6,160,000 trial (and counting) Monte Carlo simulation with the player continuing until up $70,000 or -$5,000.
<table border=0 cellpadding=2 cellspacing=1> <tr> <td align=left class=ganch> </td> <td align=left class=ganch>
</td> </tr> <tr> <td align=left class=ganch> N </td> <td align=right class=ganch> 6,160,000
</td> </tr> <tr> <td align=left class=ganch> Expectation </td> <td align=right class=ganch> -$891.67
</td> </tr> <tr> <td align=left class=ganch> Std. Dev. </td> <td align=right class=ganch> $17,309.87
</td> </tr> <tr> <td align=left class=ganch> Loss Average </td> <td align=right class=ganch> -$5,106.06
</td> </tr> <tr> <td align=left class=ganch> Win Average </td> <td align=right class=ganch> $70,182.14
</td> </tr> <tr> <td align=left class=ganch> Win % </td> <td align=right class=ganch> 5.598%
</td> </tr> <tr> <td align=left class=ganch> Win % Std. Err. </td> <td align=right class=ganch> 0.009%
</td> </tr> </table>

The rules have assumed that the player will never bet more than his remaining bankroll on a single bet but would add additional money to complete a double or split necessary. Furthermore, the player will never bet more than the additional amount he'd need to win to reach his upper target.

Example A: Player has $500 of his bankroll remaining, he would then bet only $500 on the following and. Were he to need to split twice, and double once, he'd add another $1,500 more to his stake.

Example B: Player's bankroll stands at $69,500. He'd only bet $500 on the next hand,

In case anyone's interested, my simulation program uses the Mersenne Twister pseudorandom number generator seeded with 624 32-bit (true) randomly generated numbers from random.org.

[Dark Horse]

How long did that take you?

Don't say five minutes.

[Ganchrow]

How long did that take you?

Don't say five minutes.

I wrote a composition dependent blackjack perfect strategy calculator a couple years ago and have written countless Monte Carlo simulators over the years.

[Dark Horse]

Count of Monte Carlo...

Is it possible to have a standard Monte Carlo simulator where a person can enter data for a variety of systems, or does each simulator have to be written from scratch? Would be great as betting tool.

[jjgold]

Ganch is a dick but the guy is brilliant, why would any book take this guys action? I never saw a math guy so good.

[raiders72002]

Can anyone throw out a question for Ganch that takes him longer than 10 minutes to do?

[raiders72002]

Poster machiavelli over at MW use to be the best math guy on the forums.

He crushed WSEX on interactives and they tried to get him to work there.

I've had email correspondence with him to try to get him to post some plays.

He quit gambling and posting on the forums to pursue other activities.

Mach was brilliant but Ganch is the King.

[jjgold]

Ganch will piss all over that guy Machiavelli

They are not in the same league

[operaman]

Lets make it hard for the ganchanator.

Assuming the same rules.

but allowing for two hands to be played at the same time and single deck.
Max bet 1000 min bet 1 for each hand( so from 2 - 2000 initialy bet per deal), what would the greatest player advantage be per deal?

This is a kind of unfair question, but if you want to give it a whirl go ahead.

[Ganchrow]

Lets make it hard for the ganchanator.

Assuming the same rules.

but allowing for two hands to be played at the same time.
Max bet 1000 min bet 1 for each hand( so from 2 - 2000 wagered per hand), what would the greatest player advantage be per deal?

This is a kind of unfair question, but if you want to give it a whirl go ahead.

The original question was how likely it would be for the player to end up winning 70 units before losing 5 units, playing ** Vegas Strip, redealing after every hand. Under those same rules, I'm not sure I understand what you mean by "what would the greatest player advantage be per deal?"

(If you're wondering whether the player's probability of "winning" the game would increase were he to play multiple hands against the dealer, the answer would be yes).

[operaman]

Sorry for being unclear.

Same game rules(** vegas strip) except only one deck. Playing two hands at once. min bet 1 max bet 1000

What percent advantage does the player have?
Or what is the EV of the game when playing two hands at once?

[imgv94]

Ganch is just the fvckin man. Simple as that, he is the man.

[cloudagh]

The following stats are the results of a 6,160,000 trial (and counting) Monte Carlo simulation with the player continuing until up $70,000 or -$5,000.

Ganch, great work here. Do you have stats on how many hands played on average for the bust and win outcomes? Also the max and min number of hands to bust or win would be interesting.

[Ganchrow]

Sorry for being unclear.

Same game rules(** vegas strip) except only one deck. Playing two hands at once. min bet 1 max bet 1000

What percent advantage does the player have?
Or what is the EV of the game when playing two hands at once?

1-deck ** Vegas Strip (w/2 splits max) would have a player advantage of of 0.1811%.

Playing two hands simultaneously will change those odds very slightly due to modifications to composition dependent strategy from the effects of card removal. Running a simulation of the degree to which this would occur (or writing a program to calculate it exactly) is probably not worth the time given the huge number of trials necessary to detect so small a difference.

(After 200,000,000 two-handed trials I'm coming up with a player edge of 0.1867%
with a standard error of 0.0135%, telling us nothing of statistical importance.)

[Ganchrow]

Ganch, great work here. Do you have stats on how many hands played on average for the bust and win outcomes?

Sorry, I did not save that information. What I can tell you from the data is that each trial lasted about 252.01 deals on average.

Also the max and min number of hands to bust or win would be interesting.

The theoretical min number of hands to bust would obviously be 1 (occurring with probability of ~ 0.0004790% + 0.0051775% = 0.0056565%), while the theoretical min number of hands to win would be 12 (occurring with probability ~ 1.26497&times;10^-46%, assuming my combinatorics are correct). The theoretical max number of hands would of course be infinite.

[operaman]

1-deck ** Vegas Strip (w/2 splits max) would have a player advantage of of 0.1811%.

Playing two hands simultaneously will change those odds very slightly due to modifications to composition dependent strategy from the effects of card removal. Running a simulation of the degree to which this would occur (or writing a program to calculate it exactly) is probably not worth the time given the huge number of trials necessary to detect so small a difference.

(After 59,240,000 (and counting) two-handed trials I'm coming up with a player edge of 0.1847% with a standard error of 0.0249% which tells us nothing of statistical importance.))

Does making a bet with the first hand of 1 and the second hand of 1000 with the intention of busting/spliting with the first hand when profitable to do so to change things?

For simplicity you could assign a smaller first bet amount so
the lost ev for improper strat wouldn't need to be figured.
maybe 0-1000

How about three handed with a 1-1-1000 wagering setup?

[Ganchrow]

Does making a bet with the first hand of 1 and the second hand of 1000 with the intention of busting/spliting with the first hand when profitable to do so to change things?

For simplicity you could assign a smaller first bet amount so
the lost ev for improper strat wouldn't need to be figured.
maybe 0-1000

How about three handed with a 1-1-1000 wagering setup?

The only value a player gains by drawing out extra cards with early min bets hands would be the very minimal modification to composition dependent strategy it would allow for the max bet hand.

[operaman]

The only value a player gains by drawing out extra cards with early min bets hands would be the very minimal modification to composition dependent strategy it would allow for the max bet hand.

Obviously, the whole point of the question was concerning composition modification to the last hands strategy.

Would it really be minimal modification?

Taken to an extreme a 6 handed one deck game would yeild a HUGE composition strat advantage. (1-1-1-1-1-1000)

In a nutshell I am interested in the ev curve as known cards are removed from the deck.

[Ganchrow]

Obviously, the whole point of the question was concerning composition modification to the last hands strategy.

Would it really be minimal modification?

Taken to an extreme a 6 handed one deck game would yeild a HUGE composition strat advantage. (1-1-1-1-1-1000)

In a nutshell I am interested in the ev curve as known cards are removed from the deck.

The difficulty here is that this would be a rather slow simulation the way my comp-dependent engine is currently programmed.

Intellectual curiosity aside, is there an actual practical application to this?

[operaman]

There is a real world problem I am trying to figure out that is related.

I understand that obtaining a comprehensive answer would be quite tedious. That is the reason I was wanting others to do the work for me. lol

<----EVIILLLL

Thanks for the help that was offered.

[Ganchrow]

There is a real world problem I am trying to figure out that is related.

I understand that obtaining a comprehensive answer would be quite tedious. That is the reason I was wanting others to do the work for me. lol

<----EVIILLLL

Thanks for the help that was offered.

PM me the info if you want to keep it private.