Online Blackjack - a 'Fair' game?

[vgyhnji]

I have previously posted elsewhere basic figures (from my own gameplay) to illustrate if I believe a particular software to be playing a ‘fair’ game of Blackjack.

I use the word ‘fair’ because I have merely sought to show that the results obtained from the gaming session in question are in line with the basic results expected ie: 47.49% wins to 52.51% losses (ignoring pushes) in an 8 deck game, dealer stands on all 17.

I guess one would expect, over the fullness of time, a personal average to move, and stay closer to, these figures.

‘Fair’ however may not mean that other areas of the game operate within accepted statistics and with this in mind and the frequently appearing subject of wins vesus stakes I would like to present my latest set of statistics.

These are the sum of consecutive sessions played recently with just one casino operating with CryptoLogic (WagerLogic) software.

Total hands played with a result (ie:excl pushes) = 22158
Won = 10548 = 47.60%
Lost = 11610 = 52.40%
Doubles and splits total = 2530
(excl splits where one hand wins the other loses – considered as a push)
Doubles won = 1470 = 58.10%

All in all a ‘fair’ set of results

Now the subject of staking. Frequently posts include ‘why do I always seem to hit losers when I increase my stake from X to Y and so on’ etc etc and the assumptions always seem to be made (with little or no statistical evidence) that the software has some switch mechanism or other to recognise stakes.

All my casino play is at either minimum stakes or 50x minimum, in this case all play for the results above was either at £1 or £50 (no other stakes).

These then are the resulting stats for minimum, maximum staked hands, BJ occurrences and doubles/splits as follows:

Hands played at min stakes = 12876 (58.11% of hands played)
Of the 12876 hands played at min stakes those won were 6087 = 47.27%

Hands played at max stakes = 9282 (41.89% of hands played)
Of the 9282 hands played at max stakes those won were 4461 = 48.06%

‘Fair’, in fact a higher percentage of hands played at maximum stakes were won.

Total winning Blackjacks = 1144 (above expectation)
Winning Blackjacks occurring at min stakes = 645 = 56.38%
(58.11% of all hands played were at minimum stakes)

Winning Blackjacks occurring at max stakes = 499 = 43.62%
(41.89% of all hands played were at maximum stakes)

= given the split of min/max stake hands played was 58.11% to 41.89% the distribution of Blackjacks, if anything, could be seen as weighted in favour of maximum stake hands.

Total doubles and splits at min stakes = 1462 (57.79% of all doubles/splits)
Of the 1462 doubles/splits played at min stakes those won were 825 = 56.43%
(Lost = 637)

Total doubles and splits at max stakes = 1068 (42.21% of all doubles/splits)
Of the 1068 doubles/splits played at max stakes those won were 645 = 60.39%
(Lost = 423)

The distribution of doubles/splits to min and max staked hands, 57.79%/42.21% is very close to the distribution of hands played at min and max stakes, 58.11%/41.89% = ‘fair’.

The larger percentage of doubles won at max stakes compared to those at min, if anything, suggests a weighting in favour of maximum stake hands.

I won’t go in to why the Max/Min stakes, BJ and DD/SS distribution ‘seems’ weighted in favour of the player – but clearly there is NO evidence to suggest any advantage to the casino.

[Vesuvio]

It's good to see someone actually taking the time to come up with statistics for play at on-line casinos.

Is there any way you could re-use your data to check if the software behaves 'streakily'? For instance, could you build two sets of data - one for hands after the last 3 won, the other for hands after the last 3 lost - and then compare the two sets of data and see if they show similar results?

It's probably too time consuming, I know, but I'd be very curious to see the result! (though I might need psychological counselling if it turns out Cryptologic deals a normal game of BJ after all )

[scrollock]

Originally Posted by Vesuvio

It's good to see someone actually taking the time to come up with statistics for play at on-line casinos.

Is there any way you could re-use your data to check if the software behaves 'streakily'? For instance, could you build two sets of data - one for hands after the last 3 won, the other for hands after the last 3 lost - and then compare the two sets of data and see if they show similar results?

It's probably too time consuming, I know, but I'd be very curious to see the result! (though I might need psychological counselling if it turns out Cryptologic deals a normal game of BJ after all )

vesuvio, the poster is probably a cryptologic employee

[vgyhnji]

Vesuvio

From the example given below,

Hands Result
1 0
2 1
3 1
4 1
5 1
6 0
7 1
8 0
9 0
10 0
11 1
12 0
13 0
14 1
15 1
16 0
17 1
18 1
19 0
20 0
21 0
22 0
23 1
24 1
25 0
26 0
27 0
28 0
29 0
30 1

Is this how you want to analyse the results?

1 - Establish how many times three wins in a row occur – in this case twice (2,3,4 & 3,4,5), likewise three losers in a row - this time six (8,9,10 – 19,20,21 – 20,21,22 – 25,26,27 – 26,27,28 & 27,28,29).

2 -Establish the proportion of winners to losers following either three wins or three losers in a row – in this case winners/losers following winners = 1/1 = 50%/50% and winners/losers following losers = 3/3 = 50%/50%.

Won't take long on Excel and can do later if it is what you want.

[Vesuvio]

Originally Posted by vgyhnji

Is this how you want to analyse the results?

1 - Establish how many times three wins in a row occur – in this case twice (2,3,4 & 3,4,5), likewise three losers in a row - this time six (8,9,10 – 19,20,21 – 20,21,22 – 25,26,27 – 26,27,28 & 27,28,29).

2 -Establish the proportion of winners to losers following either three wins or three losers in a row – in this case winners/losers following winners = 1/1 = 50%/50% and winners/losers following losers = 3/3 = 50%/50%.

Won't take long on Excel and can do later if it is what you want.

vgyhnji, that's almost what I wanted, except that in your example you should only use hand 5 (after 3 wins) and not hand 6 (after 4 wins). Likewise hand 22 should be counted as being after 3 losses, but not hand 23 (after 4).

I realise I was a bit ambiguous on that. 3 wins/losses is just an arbitrary figure - it could be 2 or 4 or 5, but it should be a reasonable way of looking at what happens in what the player might perceive as a 'streak'.

"Establishing the proportion of winners to losers" should give a good indication if the hands after 3 wins are similar to the hands after 3 losses. You could also make other tests if it looked as though there were any significant differences between the two sets of data (double downs won, player dealt 20, dealer busts etc.).

[GrandMaster]

Originally Posted by scrollock

vesuvio, the poster is probably a cryptologic employee

This statement is based on what???

[vgyhnji]

Vesuvio

The stats you wanted are as follows:

'Initial' run of three consecutive wins = 1278 occurrences
Win immediately after = 585 = 45.77%

'Initial' run of three consecutive losses = 1501 occurrences
Loss immediately after = 768 = 51.17%

1. - Losing 'streaks' of three occur more frequently than winning ones.

2. - Losing 'streaks' of three are more likely to turn into losing 'streaks' of four (and probably more) than winning ones.

However, given that we must expect a net loss of games played over a long period of play (in my example a total of 1062 during 22158 decided) this 'scenario' has to happen - does it not?

[bpb]

Originally Posted by vgyhnji

Vesuvio

The stats you wanted are as follows:

'Initial' run of three consecutive wins = 1278 occurrences
Win immediately after = 585 = 45.77%

'Initial' run of three consecutive losses = 1501 occurrences
Loss immediately after = 768 = 51.17%

1. - Losing 'streaks' of three occur more frequently than winning ones.

2. - Losing 'streaks' of three are more likely to turn into losing 'streaks' of four (and probably more) than winning ones.

However, given that we must expect a net loss of games played over a long period of play (in my example a total of 1062 during 22158 decided) this 'scenario' has to happen - does it not?

Yes, given that the probability of winning any given blackjack hand is around 43%, then losing streaks of 3 should happen more frequently than winnings streaks of 3. (The 3:2 payout on BJ and doubling/splitting are what bring the house edge in BJ down to less than 1%)

[Vesuvio]

Originally Posted by vgyhnji

Vesuvio

The stats you wanted are as follows:

'Initial' run of three consecutive wins = 1278 occurrences
Win immediately after = 585 = 45.77%

'Initial' run of three consecutive losses = 1501 occurrences
Loss immediately after = 768 = 51.17%

1. - Losing 'streaks' of three occur more frequently than winning ones.

2. - Losing 'streaks' of three are more likely to turn into losing 'streaks' of four (and probably more) than winning ones.

However, given that we must expect a net loss of games played over a long period of play (in my example a total of 1062 during 22158 decided) this 'scenario' has to happen - does it not?

Thanks! I agree your conclusions are just what would be expected.

What I was interested in was seeing if after three consecutive wins the percentage of wins would be higher than expected (the probabilities are skewed during a "streak") & after three losses it would be lower. From your figures it looks as though if anything the opposite's the case, though it's probably not a statistically significant variation from the expected result.

I'd still be curious to see a thorough analysis of their multi-hand BJ (the game I mainly play there). I doubt I'll ever believe it's a fair game, but I'm happy to admit it might just be paranoia brought on by over-exposure to on-line casinos! (am I the only one who feels sorry for the hand furthest to the right that seems to go bust far more than the others? )

[Gluten]

Nice job on these results. What would you say is your own error percentage - as we all make errors...?

These are my own results from intercasino.


Total Hands....: 517
Single Wins.....: 178
Single Pushes..: 37
Single Losses...: 221
Double Wins.....: 19
Double Push.....: 3
Double Losses..: 19
Player BJ.........:18
Dealer BJ..........22

Longest losing streak: 12
Longest winning streak: 5

Won 46.34% of doubles
Lost 46.34% of doubles

Win/lose % (not counting doubling)
Win: 34%
Lose: 43%
Push: 7%

I have made *atleast* 4 errors during these sessions - these are the ones I am aware of.

As can be seen - these figures are not as generous as the first posters's....Especially not the doubles which are quite frankly terrible!